Contact instabilities of anisotropic and inhomogeneous soft elastic films

Science.gov (United States)

Tomar, Gaurav; Sharma, Ashutosh

2012-02-01

Anisotropy plays important roles in various biological phenomena such as adhesion of geckos and grasshoppers enabled by the attachment pods having hierarchical structures like thin longitudinal setae connected with threads mimicked by anisotropic films. We study the contact instability of a transversely isotropic thin elastic film when it comes in contact proximity of another surface. In the present study we investigate the contact stability of a thin incompressible transversely isotropic film by performing linear stability analysis. Based on the linear stability analysis, we show that an approaching contactor renders the film unstable. The critical wavelength of the instability is a function of the total film thickness and the ratio of the Young's modulus in the longitudinal direction and the shear modulus in the plane containing the longitudinal axis. We also analyze the stability of a thin gradient film that is elastically inhomogeneous across its thickness. Compared to a homogeneous elastic film, it becomes unstable with a longer wavelength when the film becomes softer in going from the surface to the substrate.

A finite strain Eulerian formulation for compressible and nearly incompressible hyperelasticity using high-order B-spline finite elements

KAUST Repository

Duddu, Ravindra

2011-10-05

We present a numerical formulation aimed at modeling the nonlinear response of elastic materials using large deformation continuum mechanics in three dimensions. This finite element formulation is based on the Eulerian description of motion and the transport of the deformation gradient. When modeling a nearly incompressible solid, the transport of the deformation gradient is decomposed into its isochoric part and the Jacobian determinant as independent fields. A homogeneous isotropic hyperelastic solid is assumed and B-splines-based finite elements are used for the spatial discretization. A variational multiscale residual-based approach is employed to stabilize the transport equations. The performance of the scheme is explored for both compressible and nearly incompressible applications. The numerical results are in good agreement with theory illustrating the viability of the computational scheme. © 2011 John Wiley & Sons, Ltd.

Sound transmission through lined, composite panel structures: Transversely isotropic poro-elastic model

Science.gov (United States)

Kim, Jeong-Woo

A joint experimental and analytical investigation of the sound transmission loss (STL) and two-dimensional free wave propagation in composite sandwich panels is presented here. An existing panel, a Nomex honeycomb sandwich panel, was studied in detail. For the purpose of understanding the typical behavior of sandwich panels, a composite structure comprising two aluminum sheets with a relatively soft, poro-elastic foam core was also constructed and studied. The cores of both panels were modeled using an anisotropic (transversely isotropic) poro-elastic material theory. Several estimation methods were used to obtain the material properties of the honeycomb core and the skin plates to be used in the numerical calculations. Appropriate values selected from among the estimates were used in the STL and free wave propagation models. The prediction model was then verified in two ways: first, the calculated wave speeds and STL of a single poro-elastic layer were numerically verified by comparison with the predictions of a previously developed isotropic model. Secondly, to physically validate the transversely isotropic model, the measured STL and the phase speeds of the sandwich panels were compared with their predicted values. To analyze the actual treatment of a fuselage structure, multi-layered configurations, including a honeycomb panel and several layers such as air gaps, acoustic blankets and membrane partitions, were formulated. Then, to find the optimal solution for improving the sound barrier performance of an actual fuselage system, air layer depth and glass fiber lining effects were investigated by using these multi-layer models. By using the free wave propagation model, the first anti-symmetric and symmetric modes of the sandwich panels were characterized to allow the identification of the coincidence frequencies of the sandwich panel. The behavior of the STL could then be clearly explained by comparison with the free wave propagation solutions. By performing a

Comparison between isotropic linear-elastic law and isotropic hyperelastic law in the finite element modeling of the brachial plexus.

Science.gov (United States)

Perruisseau-Carrier, A; Bahlouli, N; Bierry, G; Vernet, P; Facca, S; Liverneaux, P

2017-12-01

Augmented reality could help the identification of nerve structures in brachial plexus surgery. The goal of this study was to determine which law of mechanical behavior was more adapted by comparing the results of Hooke's isotropic linear elastic law to those of Ogden's isotropic hyperelastic law, applied to a biomechanical model of the brachial plexus. A model of finite elements was created using the ABAQUS ® from a 3D model of the brachial plexus acquired by segmentation and meshing of MRI images at 0°, 45° and 135° of shoulder abduction of a healthy subject. The offset between the reconstructed model and the deformed model was evaluated quantitatively by the Hausdorff distance and qualitatively by the identification of 3 anatomical landmarks. In every case the Hausdorff distance was shorter with Ogden's law compared to Hooke's law. On a qualitative aspect, the model deformed by Ogden's law followed the concavity of the reconstructed model whereas the model deformed by Hooke's law remained convex. In conclusion, the results of this study demonstrate that the behavior of Ogden's isotropic hyperelastic mechanical model was more adapted to the modeling of the deformations of the brachial plexus. Copyright © 2017 Elsevier Masson SAS. All rights reserved.

Constitutive relations in multidimensional isotropic elasticity and their restrictions to subspaces of lower dimensions

Science.gov (United States)

Georgievskii, D. V.

2017-07-01

The mechanical meaning and the relationships among material constants in an n-dimensional isotropic elastic medium are discussed. The restrictions of the constitutive relations (Hooke's law) to subspaces of lower dimension caused by the conditions that an m-dimensional strain state or an m-dimensional stress state (1 ≤ m < n) is realized in the medium. Both the terminology and the general idea of the mathematical construction are chosen by analogy with the case n = 3 and m = 2, which is well known in the classical plane problem of elasticity theory. The quintuples of elastic constants of the same medium that enter both the n-dimensional relations and the relations written out for any m-dimensional restriction are expressed in terms of one another. These expressions in terms of the known constants, for example, of a three-dimensional medium, i.e., the classical elastic constants, enable us to judge the material properties of this medium immersed in a space of larger dimension.

Symmetry-Free, p-Robust Equilibrated Error Indication for the hp-Version of the FEMin Nearly Incompressible Linear Elasticity

OpenAIRE

Dörsek, Philipp; Melenk, Jens M.

2017-01-01

We consider the extension of the p-robust equilibrated error estimator due to Braess, Pillwein and Schöberl to linear elasticity. We derive a formulation where the local mixed auxiliary problems do not require symmetry of the stresses. The resulting error estimator is p-robust, and the reliability estimate is also robust in the incompressible limit if quadratics are included in the approximation space. Extensions to other systems of linear second-order partial differential equations are discu...

Steady shear characteristic and behavior of magneto-thermo-elasticity of isotropic MR elastomers

International Nuclear Information System (INIS)

Gao, Wei; Wang, Xingzhe

2016-01-01

The magneto-thermo-elastic steady shear behaviors of isotropic smart composites of silicon rubber matrix randomly filled with ferromagnetic particles, commonly referred to as magnetorheological (MR) elastomers, are investigated experimentally and theoretically in the present study. The strip specimens of the MR elastomer composite with different ferromagnetic particle concentrations are fabricated and implemented for lap-shear tests under both magnetic and thermal fields. It is illustrated that the magneto-thermo-elastic shear modulus of the MR elastomer is markedly enhanced with the volume fraction of ferromagnetic particles and the applied external magnetic field, while the shear modulus is decreased with the environment temperature. To qualitatively elucidate the magneto-thermo-elastic shear performance of this kind of magnetic smart composites, a modified constitutive of hyperelasticity is suggested taking into account the influence of magnetic field and temperature on the magnetic potential energy and strain energy. The theoretical modeling predictions on the stress–strain behaviors for different applied magnetic fields and environment temperatures are compared to experimental observations to demonstrate a good agreement. (paper)

Compatible-strain mixed finite element methods for incompressible nonlinear elasticity

Science.gov (United States)

Faghih Shojaei, Mostafa; Yavari, Arash

2018-05-01

We introduce a new family of mixed finite elements for incompressible nonlinear elasticity - compatible-strain mixed finite element methods (CSFEMs). Based on a Hu-Washizu-type functional, we write a four-field mixed formulation with the displacement, the displacement gradient, the first Piola-Kirchhoff stress, and a pressure-like field as the four independent unknowns. Using the Hilbert complexes of nonlinear elasticity, which describe the kinematics and the kinetics of motion, we identify the solution spaces of the independent unknown fields. In particular, we define the displacement in H1, the displacement gradient in H (curl), the stress in H (div), and the pressure field in L2. The test spaces of the mixed formulations are chosen to be the same as the corresponding solution spaces. Next, in a conforming setting, we approximate the solution and the test spaces with some piecewise polynomial subspaces of them. Among these approximation spaces are the tensorial analogues of the Nédélec and Raviart-Thomas finite element spaces of vector fields. This approach results in compatible-strain mixed finite element methods that satisfy both the Hadamard compatibility condition and the continuity of traction at the discrete level independently of the refinement level of the mesh. By considering several numerical examples, we demonstrate that CSFEMs have a good performance for bending problems and for bodies with complex geometries. CSFEMs are capable of capturing very large strains and accurately approximating stress and pressure fields. Using CSFEMs, we do not observe any numerical artifacts, e.g., checkerboarding of pressure, hourglass instability, or locking in our numerical examples. Moreover, CSFEMs provide an efficient framework for modeling heterogeneous solids.

A first-principles study of cementite (Fe{sub 3}C) and its alloyed counterparts: Elastic constants, elastic anisotropies, and isotropic elastic moduli

Energy Technology Data Exchange (ETDEWEB)

Ghosh, G., E-mail: g-ghosh@northwestern.edu [Department of Materials Science and Engineering, Robert R. McCormick School of Engineering and Applied Science, Northwestern University, 2220 Campus Drive, Evanston, IL 60208-3108 (United States)

2015-08-15

A comprehensive computational study of elastic properties of cementite (Fe{sub 3}C) and its alloyed counterparts (M{sub 3}C (M = Al, Co, Cr, Cu, Fe, Hf, Mn, Mo, Nb, Ni, Si, Ta, Ti, V, W, Zr, Cr{sub 2}FeC and CrFe{sub 2}C) having the crystal structure of Fe{sub 3}C is carried out employing electronic density-functional theory (DFT), all-electron PAW pseudopotentials and the generalized gradient approximation for the exchange-correlation energy (GGA). Specifically, as a part of our systematic study of cohesive properties of solids and in the spirit of materials genome, following properties are calculated: (i) single-crystal elastic constants, C{sub ij}, of above M{sub 3}Cs; (ii) anisotropies of bulk, Young’s and shear moduli, and Poisson’s ratio based on calculated C{sub ij}s, demonstrating their extreme anisotropies; (iii) isotropic (polycrystalline) elastic moduli (bulk, shear, Young’s moduli and Poisson’s ratio) of M{sub 3}Cs by homogenization of calculated C{sub ij}s; and (iv) acoustic Debye temperature, θ{sub D}, of M{sub 3}Cs based on calculated C{sub ij}s. We provide a critical appraisal of available data of polycrystalline elastic properties of alloyed cementite. Calculated single crystal properties may be incorporated in anisotropic constitutive models to develop and test microstructure-processing-property-performance links in multi-phase materials where cementite is a constituent phase.

Finite amplitude, horizontal motion of a load symmetrically supported between isotropic hyperelastic springs.

Science.gov (United States)

Beatty, Millard F; Young, Todd R

2012-03-01

The undamped, finite amplitude horizontal motion of a load supported symmetrically between identical incompressible, isotropic hyperelastic springs, each subjected to an initial finite uniaxial static stretch, is formulated in general terms. The small amplitude motion of the load about the deformed static state is discussed; and the periodicity of the arbitrary finite amplitude motion is established for all such elastic materials for which certain conditions on the engineering stress and the strain energy function hold. The exact solution for the finite vibration of the load is then derived for the classical neo-Hookean model. The vibrational period is obtained in terms of the complete Heuman lambda-function whose properties are well-known. Dependence of the period and hence the frequency on the physical parameters of the system is investigated and the results are displayed graphically.

Phased array compaction cell for measurement of the transversely isotropic elastic properties of compacting sediments

Energy Technology Data Exchange (ETDEWEB)

Nihei, K.T.; Nakagawa, S.; Reverdy, F.; Meyer, L.R.; Duranti, L.; Ball, G.

2010-12-15

Sediments undergoing compaction typically exhibit transversely isotropic (TI) elastic properties. We present a new experimental apparatus, the phased array compaction cell, for measuring the TI elastic properties of clay-rich sediments during compaction. This apparatus uses matched sets of P- and S-wave ultrasonic transducers located along the sides of the sample and an ultrasonic P-wave phased array source, together with a miniature P-wave receiver on the top and bottom ends of the sample. The phased array measurements are used to form plane P-waves that provide estimates of the phase velocities over a range of angles. From these measurements, the five TI elastic constants can be recovered as the sediment is compacted, without the need for sample unloading, recoring, or reorienting. This paper provides descriptions of the apparatus, the data processing, and an application demonstrating recovery of the evolving TI properties of a compacting marine sediment sample.

Error estimation and adaptivity for incompressible hyperelasticity

KAUST Repository

Whiteley, J.P.; Tavener, S.J.

2014-01-01

SUMMARY: A Galerkin FEM is developed for nonlinear, incompressible (hyper) elasticity that takes account of nonlinearities in both the strain tensor and the relationship between the strain tensor and the stress tensor. By using suitably defined

An analytical solution for the elastic response to surface loads imposed on a layered, transversely isotropic and self-gravitating Earth

Science.gov (United States)

Pan, E.; Chen, J. Y.; Bevis, M.; Bordoni, A.; Barletta, V. R.; Molavi Tabrizi, A.

2015-12-01

We present an analytical solution for the elastic deformation of an elastic, transversely isotropic, layered and self-gravitating Earth by surface loads. We first introduce the vector spherical harmonics to express the physical quantities in the layered Earth. This reduces the governing equations to a linear system of equations for the expansion coefficients. We then solve for the expansion coefficients analytically under the assumption (i.e. approximation) that in the mantle, the density in each layer varies as 1/r (where r is the radial coordinate) while the gravity is constant and that in the core the gravity in each layer varies linearly in r with constant density. These approximations dramatically simplify the subsequent mathematical analysis and render closed-form expressions for the expansion coefficients. We implement our solution in a MATLAB code and perform a benchmark which shows both the correctness of our solution and the implementation. We also calculate the load Love numbers (LLNs) of the PREM Earth for different degrees of the Legendre function for both isotropic and transversely isotropic, layered mantles with different core models, demonstrating for the first time the effect of Earth anisotropy on the LLNs.

An analytical solution for the elastic response to surface loads imposed on a layered, transversely isotropic and self-gravitating Earth

OpenAIRE

Pan, E.; Chen, J.Y.; Bevis, M.; Bordoni, Andrea; Barletta, Valentina Roberta; Tabrizi, A. Molavi

2015-01-01

We present an analytical solution for the elastic deformation of an elastic, transversely isotropic, layered and self-gravitating Earth by surface loads. We first introduce the vector spherical harmonics to express the physical quantities in the layered Earth. This reduces the governing equations to a linear system of equations for the expansion coefficients. We then solve for the expansion coefficients analytically under the assumption (i.e. approximation) that in the mantle, the density in ...

A new technique for generating the isotropic and linearly anisotropic components of elastic and discrete inelastic transfer matrices

International Nuclear Information System (INIS)

Garcia, R.D.M.

1984-01-01

A new technique for generating the isotropic and linearly anisotropic componets of elastic and discrete inelastic transfer matrices is proposed. The technique allows certain angular integrals to be expressed in terms of functions that can be computed by recursion relations or series expansions alternatively to the use of numerical quadratures. (Author) [pt

In-Situ Characterization of Isotropic and Transversely Isotropic Elastic Properties Using Ultrasonic Wave Velocities

NARCIS (Netherlands)

Pant, S; Laliberte, J; Martinez, M.J.; Rocha, B.

2016-01-01

In this paper, a one-sided, in situ method based on the time of flight measurement of ultrasonic waves was described. The primary application of this technique was to non-destructively measure the stiffness properties of isotropic and transversely isotropic materials. The method consists of

Wave propagation in isotropic- or composite-material piping conveying swirling liquid

International Nuclear Information System (INIS)

Chen, T.L.C.; Bert, C.W.

1977-01-01

An analysis is presented for the propagation of free harmonic waves in a thin-walled, circular cylindrical shell of orthotropic or isotropic material conveying a swirling flow. The shell motion is modeled by using the dynamic orthotropic version of the Sanders improved first-approximation linear shell theory and the fluid forces are described by using inviscid incompressible flow theory. Frequency spectra are presented for pipes made of isotropic material and composite materials of current engineering interest. (Auth.)

Frictionless contact of a rigid punch indenting a transversely isotropic elastic layer

Directory of Open Access Journals (Sweden)

Rajesh Patra

2016-03-01

Full Text Available This article is concerned with the study of frictionless contact between a rigid punch and a transversely isotropic elastic layer. The rigid punch is assumed to be axially symmetric and is being pressed towards the layer by an applied concentrated load. The layer is resting on a rigid base and is assumed to be ufficiently thick in comparison with the amount of indentation by the rigid punch. The relationship between the applied load $P$ and the contact area is obtained by solving the mathematically formulated problem through use of Hankel transform of different order. Effect of indentation on the distribution of normal stress at the surface as well as the relationship between the applied load and the area of contact have been shown graphically.

Wave propagation in a transversely isotropic magneto-electro-elastic solid bar immersed in an inviscid fluid

Directory of Open Access Journals (Sweden)

R. Selvamani

2016-01-01

Full Text Available Wave propagation in a transversely isotropic magneto-electro-elastic solid bar immersed in an inviscid fluid is discussed within the frame work of linearized three dimensional theory of elasticity. Three displacement potential functions are introduced to uncouple the equations of motion, electric and magnetic induction. The frequency equations that include the interaction between the solid bar and fluid are obtained by the perfect slip boundary conditions using the Bessel functions. The numerical calculations are carried out for the non-dimensional frequency, phase velocity and attenuation coefficient by fixing wave number and are plotted as the dispersion curves. The results reveal that the proposed method is very effective and simple and can be applied to other bar of different cross section by using proper geometric relation.

Adaptation of generalized Hill inequalities to anisotropic elastic ...

African Journals Online (AJOL)

user

Thallium manganese chloride(TIMnCl 3 ). 101.4. 16.5. 32.2. 5.2 For Isotropic Media. For some materials, it is possible to make approaches from cubic symmetry to isotropic symmetry. With cubic symmetry, three independent elastic constants are needed. If the medium is elastically isotropic, the elastic properties are ...

Combining finite element and finite difference methods for isotropic elastic wave simulations in an energy-conserving manner

KAUST Repository

Gao, Longfei

2018-02-22

We consider numerical simulation of the isotropic elastic wave equations arising from seismic applications with non-trivial land topography. The more flexible finite element method is applied to the shallow region of the simulation domain to account for the topography, and combined with the more efficient finite difference method that is applied to the deep region of the simulation domain. We demonstrate that these two discretization methods, albeit starting from different formulations of the elastic wave equation, can be joined together smoothly via weakly imposed interface conditions. Discrete energy analysis is employed to derive the proper interface treatment, leading to an overall discretization that is energy-conserving. Numerical examples are presented to demonstrate the efficacy of the proposed interface treatment.

Combining finite element and finite difference methods for isotropic elastic wave simulations in an energy-conserving manner

KAUST Repository

Gao, Longfei; Keyes, David E.

2018-01-01

We consider numerical simulation of the isotropic elastic wave equations arising from seismic applications with non-trivial land topography. The more flexible finite element method is applied to the shallow region of the simulation domain to account for the topography, and combined with the more efficient finite difference method that is applied to the deep region of the simulation domain. We demonstrate that these two discretization methods, albeit starting from different formulations of the elastic wave equation, can be joined together smoothly via weakly imposed interface conditions. Discrete energy analysis is employed to derive the proper interface treatment, leading to an overall discretization that is energy-conserving. Numerical examples are presented to demonstrate the efficacy of the proposed interface treatment.

Comparative analysis of different variants of the Uzawa algorithm in problems of the theory of elasticity for incompressible materials

Directory of Open Access Journals (Sweden)

Nikita E. Styopin

2016-09-01

Full Text Available Different variants of the Uzawa algorithm are compared with one another. The comparison is performed for the case in which this algorithm is applied to large-scale systems of linear algebraic equations. These systems arise in the finite-element solution of the problems of elasticity theory for incompressible materials. A modification of the Uzawa algorithm is proposed. Computational experiments show that this modification improves the convergence of the Uzawa algorithm for the problems of solid mechanics. The results of computational experiments show that each variant of the Uzawa algorithm considered has its advantages and disadvantages and may be convenient in one case or another.

Structural, elastic and electronic Properties of isotropic cubic crystals of carbon and silicon nanotubes : Density functional based tight binding calculations.

Directory of Open Access Journals (Sweden)

Alexander L. Ivanovskii

2008-01-01

Full Text Available Atomic models of cubic crystals (CC of carbon and graphene-like Si nanotubes are offered and their structural, cohesive, elastic and electronic properties are predicted by means of the DFTB method. Our main findings are that the isotropic crystals of carbon nanotubes adopt a very high elastic modulus B and low compressibility β, namely B = 650 GPa, β = 0.0015 1/GPa. In addition, these crystals preserve the initial conductivity type of their “building blocks”, i.e. isolated carbon and Si nanotubes. This feature may be important for design of materials with the selected conductivity type.

Smoothed particle hydrodynamics modelling in continuum mechanics: fluid-structure interaction

Directory of Open Access Journals (Sweden)

Groenenboom P. H. L.

2009-06-01

Full Text Available Within this study, the implementation of the smoothed particle hydrodynamics (SPH method solving the complex problem of interaction between a quasi-incompressible fluid involving a free surface and an elastic structure is outlined. A brief description of the SPH model for both the quasi-incompressible fluid and the isotropic elastic solid is presented. The interaction between the fluid and the elastic structure is realised through the contact algorithm. The results of numerical computations are confronted with the experimental as well as computational data published in the literature.

Full elastic tensor of a crystal of the superhard compound ReB{sub 2}

Energy Technology Data Exchange (ETDEWEB)

Levine, J.B. [Department of Chemistry and Biochemistry and California NanoSystems Institute, University of California, Los Angeles, CA 90095-1569 (United States); Betts, J.B. [National High Magnetic Field Laboratory, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States); Garrett, J.D. [Brockhouse Institute for Materials Research, McMaster University, Hamilton, Ontario, L8S 4M1 (Canada); Guo, S.Q. [Composites Group, National Institute for Materials Science, Tsukuba 3050047 (Japan); Eng, J.T. [Department of Chemistry and Biochemistry and California NanoSystems Institute, University of California, Los Angeles, CA 90095-1569 (United States); Migliori, A., E-mail: migliori@cybermesa.com [National High Magnetic Field Laboratory, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States); Kaner, R.B., E-mail: kaner@chem.ucla.edu [Department of Chemistry and Biochemistry and California NanoSystems Institute, University of California, Los Angeles, CA 90095-1569 (United States)] [Department of Materials Science and Engineering, University of California, Los Angeles, CA 90095-1595 (United States)

2010-03-15

The search for superhard materials, driven by their widespread use in industrial applications, highlights one of the most difficult problems in the field of materials science: the accurate characterization of a material's intrinsic physical properties. This paper reports on the full elastic tensor of two polycrystalline isotropic specimens and one specimen of ReB{sub 2} consisting of highly oriented grains. The high-monocrystal bulk modulus value extracted from the grain-oriented specimen, measured by resonant ultrasound spectroscopy, validates the ultra-incompressibility of ReB{sub 2}. An observed hardness of 40 GPa and a Debye temperature of 731 K were calculated for the ReB{sub 2} crystal, confirming its superhard and super-stiff properties. All the measured moduli of the ReB{sub 2} grain-oriented crystal exceed the comparable ones for the polycrystal by amounts that cannot be explained by averaging over direction, which may reveal why recent measurements reported on ReB{sub 2} containing excess boron yield values that are not as hard or incompressible as the crystal.

Simulating propagation of decomposed elastic waves using low-rank approximate mixed-domain integral operators for heterogeneous transversely isotropic media

KAUST Repository

Cheng, Jiubing

2014-08-05

In elastic imaging, the extrapolated vector fields are decomposed into pure wave modes, such that the imaging condition produces interpretable images, which characterize reflectivity of different reflection types. Conventionally, wavefield decomposition in anisotropic media is costly as the operators involved is dependent on the velocity, and thus not stationary. In this abstract, we propose an efficient approach to directly extrapolate the decomposed elastic waves using lowrank approximate mixed space/wavenumber domain integral operators for heterogeneous transverse isotropic (TI) media. The low-rank approximation is, thus, applied to the pseudospectral extrapolation and decomposition at the same time. The pseudo-spectral implementation also allows for relatively large time steps in which the low-rank approximation is applied. Synthetic examples show that it can yield dispersionfree extrapolation of the decomposed quasi-P (qP) and quasi- SV (qSV) modes, which can be used for imaging, as well as the total elastic wavefields.

Contact mechanics and friction for transversely isotropic viscoelastic materials

NARCIS (Netherlands)

Mokhtari, Milad; Schipper, Dirk J.; Vleugels, N.; Noordermeer, Jacobus W.M.; Yoshimoto, S.; Hashimoto, H.

2015-01-01

Transversely isotropic materials are an unique group of materials whose properties are the same along two of the principal axes of a Cartesian coordinate system. Various natural and artificial materials behave effectively as transversely isotropic elastic solids. Several materials can be classified

Crack Tip Creep Deformation Behavior in Transversely Isotropic Materials

International Nuclear Information System (INIS)

Ma, Young Wha; Yoon, Kee Bong

2009-01-01

Theoretical mechanics analysis and finite element simulation were performed to investigate creep deformation behavior at the crack tip of transversely isotropic materials under small scale creep (SCC) conditions. Mechanical behavior of material was assumed as an elastic-2 nd creep, which elastic modulus ( E ), Poisson's ratio (v ) and creep stress exponent ( n ) were isotropic and creep coefficient was only transversely isotropic. Based on the mechanics analysis for material behavior, a constitutive equation for transversely isotropic creep behavior was formulated and an equivalent creep coefficient was proposed under plain strain conditions. Creep deformation behavior at the crack tip was investigated through the finite element analysis. The results of the finite element analysis showed that creep deformation in transversely isotropic materials is dominant at the rear of the crack-tip. This result was more obvious when a load was applied to principal axis of anisotropy. Based on the results of the mechanics analysis and the finite element simulation, a corrected estimation scheme of the creep zone size was proposed in order to evaluate the creep deformation behavior at the crack tip of transversely isotropic creeping materials

High-pressure crystal structure of elastically isotropic CaTiO3 perovskite under hydrostatic and non-hydrostatic conditions.

Science.gov (United States)

Zhao, Jing; Ross, Nancy L; Wang, Di; Angel, Ross J

2011-11-16

The structural evolution of orthorhombic CaTiO3 perovskite has been studied using high-pressure single-crystal x-ray diffraction under hydrostatic conditions up to 8.1 GPa and under a non-hydrostatic stress field formed in a diamond anvil cell (DAC) up to 4.7 GPa. Under hydrostatic conditions, the TiO6 octahedra become more tilted and distorted with increasing pressure, similar to other 2:4 perovskites. Under non-hydrostatic conditions, the experiments do not show any apparent difference in the internal structural variation from hydrostatic conditions and no additional tilts and distortions in the TiO6 octahedra are observed, even though the lattice itself becomes distorted due to the non-hydrostatic stress. The similarity between the hydrostatic and non-hydrostatic cases can be ascribed to the fact that CaTiO3 perovskite is nearly elastically isotropic and, as a consequence, its deviatoric unit-cell volume strain produced by the non-hydrostatic stress is very small; in other words, the additional octahedral tilts relevant to the extra unit-cell volume associated with the deviatoric unit-cell volume strain may be totally neglected. This study further addresses the role that three factors--the elastic properties, the crystal orientation and the pressure medium--have on the structural evolution of an orthorhombic perovskite loaded in a DAC under non-hydrostatic conditions. The influence of these factors can be clearly visualized by plotting the three-dimensional distribution of the deviatoric unit-cell volume strain in relation to the cylindrical axis of the DAC and indicates that, if the elasticity of a perovskite is nearly isotropic as it is for CaTiO3, the other two factors become relatively insignificant.

High-pressure crystal structure of elastically isotropic CaTiO3 perovskite under hydrostatic and non-hydrostatic conditions

International Nuclear Information System (INIS)

Zhao Jing; Ross, Nancy L; Wang, Di; Angel, Ross J

2011-01-01

The structural evolution of orthorhombic CaTiO 3 perovskite has been studied using high-pressure single-crystal x-ray diffraction under hydrostatic conditions up to 8.1 GPa and under a non-hydrostatic stress field formed in a diamond anvil cell (DAC) up to 4.7 GPa. Under hydrostatic conditions, the TiO 6 octahedra become more tilted and distorted with increasing pressure, similar to other 2:4 perovskites. Under non-hydrostatic conditions, the experiments do not show any apparent difference in the internal structural variation from hydrostatic conditions and no additional tilts and distortions in the TiO 6 octahedra are observed, even though the lattice itself becomes distorted due to the non-hydrostatic stress. The similarity between the hydrostatic and non-hydrostatic cases can be ascribed to the fact that CaTiO 3 perovskite is nearly elastically isotropic and, as a consequence, its deviatoric unit-cell volume strain produced by the non-hydrostatic stress is very small; in other words, the additional octahedral tilts relevant to the extra unit-cell volume associated with the deviatoric unit-cell volume strain may be totally neglected. This study further addresses the role that three factors-the elastic properties, the crystal orientation and the pressure medium-have on the structural evolution of an orthorhombic perovskite loaded in a DAC under non-hydrostatic conditions. The influence of these factors can be clearly visualized by plotting the three-dimensional distribution of the deviatoric unit-cell volume strain in relation to the cylindrical axis of the DAC and indicates that, if the elasticity of a perovskite is nearly isotropic as it is for CaTiO 3 , the other two factors become relatively insignificant. (paper)

Vibration analysis of elastic tanks partially filled with incompressible liquids in presence of a gravity field; Analyse vibratoire de reservoirs elastiques partiellement remplis de liquides incompressibles en presence d'un champ de gravite

Energy Technology Data Exchange (ETDEWEB)

Schotte, J.S. [Office National d' Etudes et de Recherches Aerospatiales (ONERA), 92 - Chatillon (France); Ohayon, R. [Conservatoire National des Arts et Metiers (CNAM), Structural Dynamics and Coupled Systems Dept., 75 - Paris (France)

2001-07-01

In order to control the trajectory of liquid propelled launch vehicles, optimum command systems need a realistic model for fluid-structure interactions in tanks partially filled with propellant under apparent gravity. Up to now, the interactions between an elastic tank of arbitrary shape and an internal incompressible homogeneous inviscid liquid with a free surface have been computed with the standard added mass method by omitting the gravity effects. The originality of the present work is to analyze the contributions of all terms depending on this constant acceleration and to show that the gravity effects can be considered as pre-stresses in structure and liquid. (authors)

Review of the modified finite particle method and application to incompressible solids

Directory of Open Access Journals (Sweden)

D Asprone

2016-10-01

Full Text Available This paper focuses on the application of the Modified Finite Particle Method (MFPM on incompressibile elasticity problems. MFPM belongs to the class of meshless methods, nowadays widely investigated due to their characteristics of being totally free of any kind of grid or mesh. This characteristic makes meshless methods potentially useful for the study of large deformations problems and fluid dynamics. In particular, the aim of the work is to compare the results obtained with a simple displacement-based formulation, in the limit of incompressibility, and some formulations proposed in the literature for full incompressibility, where the typical divergence-free constraint is replaced by a different equation, the so-called Pressure Poisson Equation. The obtained results show that the MFPM achieves the expected second-order accuracy on formulation where the equations imposed as constraint satisfies also the original incompressibility equation. Other formulations, differently, do not satisfy the incompressibility constraint, and thus, they are not successfully applicable with the Modified Finite Particle Method.

Reconstruction of constitutive parameters in isotropic linear elasticity from noisy full-field measurements

International Nuclear Information System (INIS)

Bal, Guillaume; Bellis, Cédric; Imperiale, Sébastien; Monard, François

2014-01-01

Within the framework of linear elasticity we assume the availability of internal full-field measurements of the continuum deformations of a non-homogeneous isotropic solid. The aim is the quantitative reconstruction of the associated moduli. A simple gradient system for the sought constitutive parameters is derived algebraically from the momentum equation, whose coefficients are expressed in terms of the measured displacement fields and their spatial derivatives. Direct integration of this system is discussed to finally demonstrate the inexpediency of such an approach when dealing with noisy data. Upon using polluted measurements, an alternative variational formulation is deployed to invert for the physical parameters. Analysis of this latter inversion procedure provides existence and uniqueness results while the reconstruction stability with respect to the measurements is investigated. As the inversion procedure requires differentiating the measurements twice, a numerical differentiation scheme based on an ad hoc regularization then allows an optimally stable reconstruction of the sought moduli. Numerical results are included to illustrate and assess the performance of the overall approach. (paper)

Determine variation of poisson ratios and thermal creep stresses and strain rates in an isotropic disc

Directory of Open Access Journals (Sweden)

Gupta Nishi

2016-01-01

Full Text Available Seth's transition theory is applied to the problem of thermal creep transition stresses and strain rates in a thin rotating disc with shaft having variable density by finite deformation. Neither the yield criterion nor the associated flow rule is assumed here. The results obtained here are applicable to compressible materials. If the additional condition of incompressibility is imposed, then the expression for stresses corresponds to those arising from Tresca yield condition. Thermal effect decreased value of radial stress at the internal surface of the rotating isotropic disc made of compressible material as well as incompressible material and this value of radial stress further much increases with the increase in angular speed. With the introduction of thermal effects, the maximum value of strain rates further increases at the internal surface for compressible materials as compare to incompressible material.

Elastic-plastic transition on rotating spherical shells in dependence of compressibility

Directory of Open Access Journals (Sweden)

Thakur Pankaj

2017-01-01

Full Text Available The purpose of this paper is to establish the mathematical model on the elastic-plastic transitions occurring in the rotating spherical shells based on compressibility of materials. The paper investigates the elastic-plastic stresses and angular speed required to start yielding in rotating shells for compressible and incompressible materials. The paper is based on the non-linear transition theory of elastic-plastic shells given by B.R. Seth. The elastic-plastic transition obtained is treated as an asymptotic phenomenon at critical points & the solution obtained at these points generates stresses. The solution obtained does not require the use of semi-empirical yield condition like Tresca or Von Mises or other certain laws. Results are obtained numerically and depicted graphically. It has been observed that Rotating shells made of the incompressible material are on the safer side of the design as compared to rotating shells made of compressible material. The effect of density variation has been discussed numerically on the stresses. With the effect of density variation parameter, rotating spherical shells start yielding at the internal surface with the lower values of the angular speed for incompressible/compressible materials.

Elastic properties of uniaxial-fiber reinforced composites - General features

Science.gov (United States)

Datta, Subhendu; Ledbetter, Hassel; Lei, Ming

The salient features of the elastic properties of uniaxial-fiber-reinforced composites are examined by considering the complete set of elastic constants of composites comprising isotropic uniaxial fibers in an isotropic matrix. Such materials exhibit transverse-isotropic symmetry and five independent elastic constants in Voigt notation: C(11), C(33), C(44), C(66), and C(13). These C(ij) constants are calculated over the entire fiber-volume-fraction range 0.0-1.0, using a scattered-plane-wave ensemple-average model. Some practical elastic constants such as the principal Young moduli and the principal Poisson ratios are considered, and the behavior of these constants is discussed. Also presented are the results for the four principal sound velocities used to study uniaxial-fiber-reinforced composites: v(11), v(33), v(12), and v(13).

Remarks on stability of magneto-elastic shocks

Directory of Open Access Journals (Sweden)

Włodzimierz Domański

2015-12-01

Full Text Available The problem of stability of plane shock waves for a model of perfect magnetoelasticityis investigated. Important mathematical properties, like loss of strict hyperbolicityand loss of genuine nonlinearity, and their consequences for the stability ofmagneto-elastic shocks are discussed. It is shown that some of these shocks do not satisfyclassical Lax stability conditions. Both compressible and incompressible models ofmagneto-elasticity are discussed.[b]Keywords[/b]: perfect magneto-elasticity, shock waves, stability conditions

Mathematical Modeling of Torsional Surface Wave Propagation in a Non-Homogeneous Transverse Isotropic Elastic Solid Semi-Infinite Medium Under a Layer

Science.gov (United States)

Sethi, M.; Sharma, A.; Vasishth, A.

2017-05-01

The present paper deals with the mathematical modeling of the propagation of torsional surface waves in a non-homogeneous transverse isotropic elastic half-space under a rigid layer. Both rigidities and density of the half-space are assumed to vary inversely linearly with depth. Separation of variable method has been used to get the analytical solutions for the dispersion equation of the torsional surface waves. Also, the effects of nonhomogeneities on the phase velocity of torsional surface waves have been shown graphically. Also, dispersion equations have been derived for some particular cases, which are in complete agreement with some classical results.

Effect of elastic anisotropy of crystal grain on stress intensity factor

Energy Technology Data Exchange (ETDEWEB)

Kamaya, Masayuki [Inst. of Nuclear Safety System Inc., Mihama, Fukui (Japan)

2002-09-01

The stress intensity factor (SIF) is used widely for evaluating integrity of cracked components. Usually, the SIF obtained under isotropic elastic conditions is used for the evaluations. Although, macroscopic elastic behaviors of polycrystal materials can be considered isotropic, each crystal has anisotropic elastic properties. This implies that if the crack size is small and the influence of anisotropic elastic properties on the stress around cracks is significant, the SIF evaluated under anisotropic elastic conditions may differ from the SIF obtained under isotropic elastic conditions. In the present study, the effect of anisotropic elasticity on the SIF was evaluated by using the finite element analysis (FEA). First, the SIF of semi-circular cracks located in a single crystal was evaluated. It was found that the SIF is affected crystal orientation. Secondly, FEA using a polycrystal model was performed. It was found that the change in the SIF was caused by crack tip crystal orientation as well as the deformation constraint from neighboring crystals. Finally, the statistical tendency of change in the SIF caused by the anisotropic elastic properties and the relationship with crack size were examined. The influence of the local SIF on crack growth behavior is also discussed. (author)

Effect of elastic anisotropy of crystal grain on stress intensity factor

International Nuclear Information System (INIS)

Kamaya, Masayuki

2002-01-01

The stress intensity factor (SIF) is used widely for evaluating integrity of cracked components. Usually, the SIF obtained under isotropic elastic conditions is used for the evaluations. Although, macroscopic elastic behaviors of polycrystal materials can be considered isotropic, each crystal has anisotropic elastic properties. This implies that if the crack size is small and the influence of anisotropic elastic properties on the stress around cracks is significant, the SIF evaluated under anisotropic elastic conditions may differ from the SIF obtained under isotropic elastic conditions. In the present study, the effect of anisotropic elasticity on the SIF was evaluated by using the finite element analysis (FEA). First, the SIF of semi-circular cracks located in a single crystal was evaluated. It was found that the SIF is affected crystal orientation. Secondly, FEA using a polycrystal model was performed. It was found that the change in the SIF was caused by crack tip crystal orientation as well as the deformation constraint from neighboring crystals. Finally, the statistical tendency of change in the SIF caused by the anisotropic elastic properties and the relationship with crack size were examined. The influence of the local SIF on crack growth behavior is also discussed. (author)

Precession of elastic waves in vibrating isotropic spheres and transversely isotropic cylinders subjected to inertial rotation

CSIR Research Space (South Africa)

Joubert, S

2006-05-01

Full Text Available and Manufacturing TRANSVERSELY ISOTROPIC CYLINDER - 1 φ φ r z a x y Ω P P O u v w z ( )1 1 1 2 1 1 rrr rz rr zr r zrz zz rz u r r z r v r r z r w r r z r ϕ ϕϕ ϕϕ ϕϕ ϕ ϕ σσ σ σ σ ρ ϕ σσ σ σ ρ ϕ σσ σ σ ρ ϕ... ∂ ∂ ∂ + + + − = ∂ ∂ ∂ ∂∂ ∂ + + + = ∂ ∂ ∂ ∂∂ ∂ + + + = ∂ ∂ ∂ && && && 6 CSIR Material Science and Manufacturing TRANSVERSELY ISOTROPIC CYLINDER - 2 ( )1 1 1 2 1 1 rrr rz rr zr r zrz zz rz u r r z r v r r z r w r r z r ϕ ϕϕ ϕϕ ϕϕ ϕ ϕ σσ σ σ σ ρ ϕ σσ σ σ ρ ϕ σσ σ σ ρ ϕ...

A program to calculate pulse transmission responses through transversely isotropic media

Science.gov (United States)

Li, Wei; Schmitt, Douglas R.; Zou, Changchun; Chen, Xiwei

2018-05-01

We provide a program (AOTI2D) to model responses of ultrasonic pulse transmission measurements through arbitrarily oriented transversely isotropic rocks. The program is built with the distributed point source method that treats the transducers as a series of point sources. The response of each point source is calculated according to the ray-tracing theory of elastic plane waves. The program could offer basic wave parameters including phase and group velocities, polarization, anisotropic reflection coefficients and directivity patterns, and model the wave fields, static wave beam, and the observed signals for pulse transmission measurements considering the material's elastic stiffnesses and orientations, sample dimensions, and the size and positions of the transmitters and the receivers. The program could be applied to exhibit the ultrasonic beam behaviors in anisotropic media, such as the skew and diffraction of ultrasonic beams, and analyze its effect on pulse transmission measurements. The program would be a useful tool to help design the experimental configuration and interpret the results of ultrasonic pulse transmission measurements through either isotropic or transversely isotropic rock samples.

Interparameter trade-off quantification and reduction in isotropic-elastic full-waveform inversion: synthetic experiments and Hussar land data set application

Science.gov (United States)

Pan, Wenyong; Geng, Yu; Innanen, Kristopher A.

2018-05-01

The problem of inverting for multiple physical parameters in the subsurface using seismic full-waveform inversion (FWI) is complicated by interparameter trade-off arising from inherent ambiguities between different physical parameters. Parameter resolution is often characterized using scattering radiation patterns, but these neglect some important aspects of interparameter trade-off. More general analysis and mitigation of interparameter trade-off in isotropic-elastic FWI is possible through judiciously chosen multiparameter Hessian matrix-vector products. We show that products of multiparameter Hessian off-diagonal blocks with model perturbation vectors, referred to as interparameter contamination kernels, are central to the approach. We apply the multiparameter Hessian to various vectors designed to provide information regarding the strengths and characteristics of interparameter contamination, both locally and within the whole volume. With numerical experiments, we observe that S-wave velocity perturbations introduce strong contaminations into density and phase-reversed contaminations into P-wave velocity, but themselves experience only limited contaminations from other parameters. Based on these findings, we introduce a novel strategy to mitigate the influence of interparameter trade-off with approximate contamination kernels. Furthermore, we recommend that the local spatial and interparameter trade-off of the inverted models be quantified using extended multiparameter point spread functions (EMPSFs) obtained with pre-conditioned conjugate-gradient algorithm. Compared to traditional point spread functions, the EMPSFs appear to provide more accurate measurements for resolution analysis, by de-blurring the estimations, scaling magnitudes and mitigating interparameter contamination. Approximate eigenvalue volumes constructed with stochastic probing approach are proposed to evaluate the resolution of the inverted models within the whole model. With a synthetic

A micromechanical approach for homogenization of elastic metamaterials with dynamic microstructure.

Science.gov (United States)

Muhlestein, Michael B; Haberman, Michael R

2016-08-01

An approximate homogenization technique is presented for generally anisotropic elastic metamaterials consisting of an elastic host material containing randomly distributed heterogeneities displaying frequency-dependent material properties. The dynamic response may arise from relaxation processes such as viscoelasticity or from dynamic microstructure. A Green's function approach is used to model elastic inhomogeneities embedded within a uniform elastic matrix as force sources that are excited by a time-varying, spatially uniform displacement field. Assuming dynamic subwavelength inhomogeneities only interact through their volume-averaged fields implies the macroscopic stress and momentum density fields are functions of both the microscopic strain and velocity fields, and may be related to the macroscopic strain and velocity fields through localization tensors. The macroscopic and microscopic fields are combined to yield a homogenization scheme that predicts the local effective stiffness, density and coupling tensors for an effective Willis-type constitutive equation. It is shown that when internal degrees of freedom of the inhomogeneities are present, Willis-type coupling becomes necessary on the macroscale. To demonstrate the utility of the homogenization technique, the effective properties of an isotropic elastic matrix material containing isotropic and anisotropic spherical inhomogeneities, isotropic spheroidal inhomogeneities and isotropic dynamic spherical inhomogeneities are presented and discussed.

Anisotropy function for proton-proton elastic scattering

International Nuclear Information System (INIS)

Saleem, Mohammad; Fazal-e-Aleem; Azhar, I.A.

1990-01-01

By using the generalized Chou-Yang model and the experimental data on pp elastic scattering at 53 GeV, the anisotropy function which reflects the non-isotropic nature of elastic scattering is computed for the reaction pp→pp. (author)

A simple mechanical model for the isotropic harmonic oscillator

International Nuclear Information System (INIS)

Nita, Gelu M

2010-01-01

A constrained elastic pendulum is proposed as a simple mechanical model for the isotropic harmonic oscillator. The conceptual and mathematical simplicity of this model recommends it as an effective pedagogical tool in teaching basic physics concepts at advanced high school and introductory undergraduate course levels.

Magma flow through elastic-walled dikes

NARCIS (Netherlands)

Bokhove, Onno; Woods, A.W.; de Boer, A

2005-01-01

A convection–diffusion model for the averaged flow of a viscous, incompressible magma through an elastic medium is considered. The magma flows through a dike from a magma reservoir to the Earth’s surface; only changes in dike width and velocity over large vertical length scales relative to the

Anisotropy function for proton-proton elastic scattering

Energy Technology Data Exchange (ETDEWEB)

Saleem, Mohammad; Fazal-e-Aleem; Azhar, I.A. (Punjab Univ., Lahore (Pakistan). Centre for High Energy Physics)

1990-07-01

By using the generalized Chou-Yang model and the experimental data on pp elastic scattering at 53 GeV, the anisotropy function which reflects the non-isotropic nature of elastic scattering is computed for the reaction pp{yields}pp. (author).

Static deformation due to a long buried dip-slip fault in an isotropic

Indian Academy of Sciences (India)

Closed-form analytical expressions for the displacements and the stresses at any point of a two-phase medium consisting of a homogeneous, isotropic, perfectly elastic half-space in welded contact with a homogeneous, orthotropic, perfectly elastic half-space due to a dip-slip fault of finite width located at an arbitrary ...

Higher gradient expansion for linear isotropic peridynamic materials

Czech Academy of Sciences Publication Activity Database

Šilhavý, Miroslav

2017-01-01

Roč. 22, č. 6 (2017), s. 1483-1493 ISSN 1081-2865 Institutional support: RVO:67985840 Keywords : peridynamics * higher-grade theories * non-local elastic-material model * representation theorems for isotropic functions Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 2.953, year: 2016 http:// journals .sagepub.com/doi/10.1177/1081286516637235

Higher gradient expansion for linear isotropic peridynamic materials

Czech Academy of Sciences Publication Activity Database

Šilhavý, Miroslav

2017-01-01

Roč. 22, č. 6 (2017), s. 1483-1493 ISSN 1081-2865 Institutional support: RVO:67985840 Keywords : peridynamics * higher-grade theories * non-local elastic-material model * representation theorems for isotropic functions Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 2.953, year: 2016 http://journals.sagepub.com/doi/10.1177/1081286516637235

Nematic elastomers: from a microscopic model to macroscopic elasticity theory.

Science.gov (United States)

Xing, Xiangjun; Pfahl, Stephan; Mukhopadhyay, Swagatam; Goldbart, Paul M; Zippelius, Annette

2008-05-01

A Landau theory is constructed for the gelation transition in cross-linked polymer systems possessing spontaneous nematic ordering, based on symmetry principles and the concept of an order parameter for the amorphous solid state. This theory is substantiated with help of a simple microscopic model of cross-linked dimers. Minimization of the Landau free energy in the presence of nematic order yields the neoclassical theory of the elasticity of nematic elastomers and, in the isotropic limit, the classical theory of isotropic elasticity. These phenomenological theories of elasticity are thereby derived from a microscopic model, and it is furthermore demonstrated that they are universal mean-field descriptions of the elasticity for all chemical gels and vulcanized media.

Anisotropy function for pion-proton elastic scattering

Energy Technology Data Exchange (ETDEWEB)

Saleem, Mohammad; Fazal-e-Aleem; Rashid, Haris

1988-09-01

By using the generalised Chou-Yang model and the experimental data on ..pi../sup -/p elastic scattering at 200 GeV/c, the anisotropy function which reflects the non-isotropic nature of elastic scattering is computed for the reaction ..pi../sup -/p -> ..pi../sup -/p.

Anisotropy function for pion-proton elastic scattering

International Nuclear Information System (INIS)

Saleem, Mohammad; Fazal-e-Aleem; Rashid, Haris

1988-01-01

By using the generalised Chou-Yang model and the experimental data on π - p elastic scattering at 200 GeV/c, the anisotropy function which reflects the non-isotropic nature of elastic scattering is computed for the reaction π - p → π - p. (author)

General thermo-elastic solution of radially heterogeneous, spherically isotropic rotating sphere

Energy Technology Data Exchange (ETDEWEB)

Bayat, Yahya; EkhteraeiToussi, THamid [Ferdowsi University of Mashhad, Mashhad (Iran, Islamic Republic of)

2015-06-15

A thick walled rotating spherical object made of transversely isotropic functionally graded materials (FGMs) with general types of thermo-mechanical boundary conditions is studied. The thermo-mechanical governing equations consisting of decoupled thermal and mechanical equations are represented. The centrifugal body forces of the rotation are considered in the modeling phase. The unsymmetrical thermo-mechanical boundary conditions and rotational body forces are expressed in terms of the Legendre series. The series method is also implemented in the solution of the resulting equations. The solutions are checked with the known literature and FEM based solutions of ABAQUS software. The effects of anisotropy and heterogeneity are studied through the case studies and the results are represented in different figures. The newly developed series form solution is applicable to the rotating FGM spherical transversely isotropic vessels having nonsymmetrical thermo-mechanical boundary condition.

Scalar evolution equations for shear waves in incompressible solids: a simple derivation of the Z, ZK, KZK and KP equations

KAUST Repository

Destrade, M.

2010-12-08

We study the propagation of two-dimensional finite-amplitude shear waves in a nonlinear pre-strained incompressible solid, and derive several asymptotic amplitude equations in a simple, consistent and rigorous manner. The scalar Zabolotskaya (Z) equation is shown to be the asymptotic limit of the equations of motion for all elastic generalized neo-Hookean solids (with strain energy depending only on the first principal invariant of Cauchy-Green strain). However, we show that the Z equation cannot be a scalar equation for the propagation of two-dimensional shear waves in general elastic materials (with strain energy depending on the first and second principal invariants of strain). Then, we introduce dispersive and dissipative terms to deduce the scalar Kadomtsev-Petviashvili (KP), Zabolotskaya-Khokhlov (ZK) and Khokhlov- Zabolotskaya-Kuznetsov (KZK) equations of incompressible solid mechanics. © 2010 The Royal Society.

Scalar evolution equations for shear waves in incompressible solids: a simple derivation of the Z, ZK, KZK and KP equations

KAUST Repository

Destrade, M.; Goriely, A.; Saccomandi, G.

2010-01-01

We study the propagation of two-dimensional finite-amplitude shear waves in a nonlinear pre-strained incompressible solid, and derive several asymptotic amplitude equations in a simple, consistent and rigorous manner. The scalar Zabolotskaya (Z) equation is shown to be the asymptotic limit of the equations of motion for all elastic generalized neo-Hookean solids (with strain energy depending only on the first principal invariant of Cauchy-Green strain). However, we show that the Z equation cannot be a scalar equation for the propagation of two-dimensional shear waves in general elastic materials (with strain energy depending on the first and second principal invariants of strain). Then, we introduce dispersive and dissipative terms to deduce the scalar Kadomtsev-Petviashvili (KP), Zabolotskaya-Khokhlov (ZK) and Khokhlov- Zabolotskaya-Kuznetsov (KZK) equations of incompressible solid mechanics. © 2010 The Royal Society.

Remarks on 'Poisson ratio beyond the limits of the elasticity theory'

International Nuclear Information System (INIS)

Wojciechowski, K.W.

2002-12-01

The non-chiral, elastically isotropic model exhibits Poison ratios in the range -1 ≤ σ ≤ 1 without any molecular rotation. The centres of discs-atoms are replaced in the vertices of a perfect triangle of the side length equal to σ. The positive sign of the Lame constant λ is not necessary for the stability of an isotropic system at any dimensionality. As the upper limit for the Poisson ratio in 2D isotropic systems is 1, crystalline or polycrystalline 2D systems can be obtained having the Poisson ratio exceeding 1/2. Both the traditional theory of elasticity and the Cosserat one exclude Poisson ratios exceeding 1/2 in 3D isotropic systems. Neighter anisotropy nor rotation are necessary to obtain extreme values of the Poisson ratio (author)

Indentation of elastically soft and plastically compressible solids

NARCIS (Netherlands)

Needleman, A.; Tvergaard, V.; Van der Giessen, E.

The effect of soft elasticity, i.e., a relatively small value of the ratio of Young's modulus to yield strength and plastic compressibility on the indentation of isotropically hardening elastic-viscoplastic solids is investigated. Calculations are carried out for indentation of a perfectly sticking

Elastic properties of icosahedral and decagonal quasicrystals

International Nuclear Information System (INIS)

Chernikov, Mikhail A

2005-01-01

Problems associated with determining the symmetry properties of the elastic constant tensor of icosahedral and decagonal quasicrystals are reviewed. Notions of elastic isotropy and anisotropy are considered, and their relation to the components of the elastic constant tensor is discussed. The question is addressed of how to determine experimentally whether a system under study is elastically isotropic. Experimental results produced by resonant ultrasound spectroscopy of icosahedral Al-Li-Cu and decagonal Al-Ni-Co single quasicrystals are discussed in detail. (methodological notes)

Viscous-elastic dynamics of power-law fluids within an elastic cylinder

Science.gov (United States)

Boyko, Evgeniy; Bercovici, Moran; Gat, Amir D.

2017-07-01

In a wide range of applications, microfluidic channels are implemented in soft substrates. In such configurations, where fluidic inertia and compressibility are negligible, the propagation of fluids in channels is governed by a balance between fluid viscosity and elasticity of the surrounding solid. The viscous-elastic interactions between elastic substrates and non-Newtonian fluids are particularly of interest due to the dependence of viscosity on the state of the system. In this work, we study the fluid-structure interaction dynamics between an incompressible non-Newtonian fluid and a slender linearly elastic cylinder under the creeping flow regime. Considering power-law fluids and applying the thin shell approximation for the elastic cylinder, we obtain a nonhomogeneous p-Laplacian equation governing the viscous-elastic dynamics. We present exact solutions for the pressure and deformation fields for various initial and boundary conditions for both shear-thinning and shear-thickening fluids. We show that in contrast to Stokes' problem where a compactly supported front is obtained for shear-thickening fluids, here the role of viscosity is inversed and such fronts are obtained for shear-thinning fluids. Furthermore, we demonstrate that for the case of a step in inlet pressure, the propagation rate of the front has a tn/n +1 dependence on time (t ), suggesting the ability to indirectly measure the power-law index (n ) of shear-thinning liquids through measurements of elastic deformation.

A hyper elasticity method for interactive virtual design of hearing aids

DEFF Research Database (Denmark)

Darkner, Sune; Erleben, Kenny

2011-01-01

We present a computational efficient method for isotropic hyper elasticity based on functional analysis. By selecting a class of shape functions, we arrive at a computational scheme which yields very sparse tensors. This enables fast computations of the hyper elastic energy potential and its...... derivatives. We achieve efficiency and performance through the use of shape functions that are linear in their parameters and through rotation into the eigenspace of the right Cauchy–Green strain tensor. This makes near real time evaluation of hyper elasticity of complex meshes on CPU relatively easy...... to implement. The approach does not rely on a specific shape function or material model but offers a general framework for isotropic hyper elasticity. The method is aimed at interactive and accurate non-linear hyper elastic modeling for a wide range of industrial virtual design applications, which we exemplify...

On the dual variable of the Cauchy stress tensor in isotropic finite hyperelasticity

Science.gov (United States)

Vallée, Claude; Fortuné, Danielle; Lerintiu, Camelia

2008-11-01

Elastic materials are governed by a constitutive law relating the second Piola-Kirchhoff stress tensor Σ and the right Cauchy-Green strain tensor C=FF. Isotropic elastic materials are the special cases for which the Cauchy stress tensor σ depends solely on the left Cauchy-Green strain tensor B=FF. In this Note we revisit the following property of isotropic hyperelastic materials: if the constitutive law relating Σ and C is derivable from a potential ϕ, then σ and lnB are related by a constitutive law derived from the compound potential ϕ○exp. We give a new and concise proof which is based on an explicit integral formula expressing the derivative of the exponential of a tensor. To cite this article: C. Vallée et al., C. R. Mecanique 336 (2008).

Examination of the PCICE method in the nearly incompressible, as well as strictly incompressible, limits

International Nuclear Information System (INIS)

Berry, Ray A.; Martineau, Richard C.

2007-01-01

The conservative-form, pressure-based PCICE numerical method (Martineau and Berry, 2004) (Berry, 2006), recently developed for computing transient fluid flows of all speeds from very low to very high (with strong shocks), is simplified and generalized. Though the method automatically treats a continuous transition of compressibility, three distinct, limiting compressibility regimes are formally defined for purposes of discussion and comparison with traditional methods - the strictly incompressible limit, the nearly incompressible limit, and the fully compressible limit. The PCICE method's behavior is examined in each limiting regime. In the strictly incompressible limit the PCICE algorithm reduces to the traditional MAC-type method with velocity divergence driving the pressure Poisson equation. In the nearly incompressible limit the PCICE algorithm is found to reduce to a generalization of traditional incompressible methods, i.e. to one in which not only the velocity divergence effect, but also the density gradient effect is included as a driving function in the pressure Poisson equation. This nearly incompressible regime has received little attention, and it appears that in the past, strictly incompressible methods may have been conveniently applied to flows in this regime at the expense of ignoring a potentially important coupling mechanism. This could be significant in many important flows; for example, in natural convection flows resulting from high heat flux. In the fully compressible limit or regime, the algorithm is found to reduce to an expression equivalent to density-based methods for high-speed flow. (author)

Elastic interaction between surface and spherical pore

International Nuclear Information System (INIS)

Ganeev, G.Z.; Kadyrzhanov, K.K.; Kislitsyn, S.B.; Turkebaev, T.Eh.

2000-01-01

The energy of elastic interaction of a gas-filled spherical cavity with a boundary of an elastic isotropic half-space is determined. The elastic field of a system of a spherical cavity - boundary is represented as an expansion in series of potential functions. The factors of expansions are determined by boundary conditions on a free surface of an elastic half-space and on a spherical surface of a cavity with pressure of gas P. Function of a Tresca-Miesesa on a surface of elastic surface is defined additionally with purpose creep condition determination caused by gas pressure in the cavity. (author)

Elastic and piezoelectric fields around a quantum wire of zincblende heterostructures with interface elasticity effect

Science.gov (United States)

Ye, Wei; Liu, Yifei

2018-04-01

This work formulates the solutions to the elastic and piezoelectric fields around a quantum wire (QWR) with interface elasticity effect. Closed-form solutions to the piezoelectric potential field of zincblende QWR/matrix heterostructures grown along [111] crystallographic orientation are found and numerical results of InAs/InP heterostructures are provided as an example. The piezoelectric potential in the matrix depends on the interface elasticity, the radius and stiffness of the QWR. Our results indicate that interface elasticity can significantly alter the elastic and piezoelectric fields near the interface. Additionally, when the elastic property of the QWR is considered to be anisotropic in contrary to the common isotropic assumption, piezoelectric potentials are found to be distinct near the interface, but the deviations are negligible at positions far away from the interface.

Torsional vibration of a pipe pile in transversely isotropic saturated soil

Science.gov (United States)

Zheng, Changjie; Hua, Jianmin; Ding, Xuanming

2016-09-01

This study considers the torsional vibration of a pipe pile in a transversely isotropic saturated soil layer. Based on Biot's poroelastic theory and the constitutive relations of the transversely isotropic medium, the dynamic governing equations of the outer and inner transversely isotropic saturated soil layers are derived. The Laplace transform is used to solve the governing equations of the outer and inner soil layers. The dynamic torsional response of the pipe pile in the frequency domain is derived utilizing 1D elastic theory and the continuous conditions at the interfaces between the pipe pile and the soils. The time domain solution is obtained by Fourier inverse transform. A parametric study is conducted to demonstrate the influence of the anisotropies of the outer and inner soil on the torsional dynamic response of the pipe pile.

Phase-field-crystal model for magnetocrystalline interactions in isotropic ferromagnetic solids

Science.gov (United States)

Faghihi, Niloufar; Provatas, Nikolas; Elder, K. R.; Grant, Martin; Karttunen, Mikko

2013-09-01

An isotropic magnetoelastic phase-field-crystal model to study the relation between morphological structure and magnetic properties of pure ferromagnetic solids is introduced. Analytic calculations in two dimensions were used to determine the phase diagram and obtain the relationship between elastic strains and magnetization. Time-dependent numerical simulations in two dimensions were used to demonstrate the effect of grain boundaries on the formation of magnetic domains. It was shown that the grain boundaries act as nucleating sites for domains of reverse magnetization. Finally, we derive a relation for coercivity versus grain misorientation in the isotropic limit.

Contact mechanics of articular cartilage layers asymptotic models

CERN Document Server

Argatov, Ivan

2015-01-01

This book presents a comprehensive and unifying approach to articular contact mechanics with an emphasis on frictionless contact interaction of thin cartilage layers. The first part of the book (Chapters 1–4) reviews the results of asymptotic analysis of the deformational behavior of thin elastic and viscoelastic layers. A comprehensive review of the literature is combined with the authors’ original contributions. The compressible and incompressible cases are treated separately with a focus on exact solutions for asymptotic models of frictionless contact for thin transversely isotropic layers bonded to rigid substrates shaped like elliptic paraboloids. The second part (Chapters 5, 6, and 7) deals with the non-axisymmetric contact of thin transversely isotropic biphasic layers and presents the asymptotic modelling methodology for tibio-femoral contact. The third part of the book consists of Chapter 8, which covers contact problems for thin bonded inhomogeneous transversely isotropic elastic layers, and Cha...

Simplified computational methods for elastic and elastic-plastic fracture problems

Science.gov (United States)

Atluri, Satya N.

1992-01-01

An overview is given of some of the recent (1984-1991) developments in computational/analytical methods in the mechanics of fractures. Topics covered include analytical solutions for elliptical or circular cracks embedded in isotropic or transversely isotropic solids, with crack faces being subjected to arbitrary tractions; finite element or boundary element alternating methods for two or three dimensional crack problems; a 'direct stiffness' method for stiffened panels with flexible fasteners and with multiple cracks; multiple site damage near a row of fastener holes; an analysis of cracks with bonded repair patches; methods for the generation of weight functions for two and three dimensional crack problems; and domain-integral methods for elastic-plastic or inelastic crack mechanics.

A thermodynamic framework for thermo-chemo-elastic interactions in chemically active materials

Science.gov (United States)

Zhang, XiaoLong; Zhong, Zheng

2017-08-01

In this paper, a general thermodynamic framework is developed to describe the thermo-chemo-mechanical interactions in elastic solids undergoing mechanical deformation, imbibition of diffusive chemical species, chemical reactions and heat exchanges. Fully coupled constitutive relations and evolving laws for irreversible fluxes are provided based on entropy imbalance and stoichiometry that governs reactions. The framework manifests itself with a special feature that the change of Helmholtz free energy is attributed to separate contributions of the diffusion-swelling process and chemical reaction-dilation process. Both the extent of reaction and the concentrations of diffusive species are taken as independent state variables, which describe the reaction-activated responses with underlying variation of microstructures and properties of a material in an explicit way. A specialized isothermal formulation for isotropic materials is proposed that can properly account for volumetric constraints from material incompressibility under chemo-mechanical loadings, in which inhomogeneous deformation is associated with reaction and diffusion under various kinetic time scales. This framework can be easily applied to model the transient volumetric swelling of a solid caused by imbibition of external chemical species and simultaneous chemical dilation arising from reactions between the diffusing species and the solid.

Analytic approximations for the elastic moduli of two-phase materials

DEFF Research Database (Denmark)

Zhang, Z. J.; Zhu, Y. K.; Zhang, P.

2017-01-01

Based on the models of series and parallel connections of the two phases in a composite, analytic approximations are derived for the elastic constants (Young's modulus, shear modulus, and Poisson's ratio) of elastically isotropic two-phase composites containing second phases of various volume...

Vibrational analysis of submerged cylindrical shells based on elastic foundations

International Nuclear Information System (INIS)

Shah, A.G.; Naeem, M.N.

2014-01-01

In this study a vibration analysis was performed of an isotropic cylindrical shell submerged in fluid, resting on Winkler and Pasternak elastic foundations for simply supported boundary condition. Love's thin shell theory was exploited for strain- and curvature- displacement relationship. Shell problem was solved by using wave propagation approach. Influence of fluid and Winkler as well as Pasternak elastic foundations were studied on the natural frequencies of submerged isotropic cylindrical shells. Results were validated by comparing with the existing results in literature. Vibration, Submerged cylindrical shell, Love's thin shell theory, Wave propagation method, Winkler and Pasternak foundations. (author)

Proposed higher order continuum-based models for an elastic ...

African Journals Online (AJOL)

Three new variants of continuum-based models for an elastic subgrade are proposed. The subgrade is idealized as a homogenous, isotropic elastic layer of thickness H overlying a firm stratum. All components of the stress tensor in the subgrade are taken into account. Reasonable assumptions are made regarding the ...

On the role of the transformation eigenstrain in the growth or shrinkage of spheroidal isotropic precipitations

International Nuclear Information System (INIS)

Fischer, F.D.; Boehm, H.J.

2005-01-01

The jumps of the strain and stress tensors on the surface of elastic homogeneous or inhomogeneous ellipsoidal inclusions embedded in an elastic matrix are obtained from results reported in the literature. They are used to derive closed-form expressions for the thermodynamic force in such matrix-inclusion systems that are subjected to a generally defined homogeneous transformation eigenstrain. A detailed study is presented for an isotropic spheroidal inclusion in an isotropic matrix in which the most important parameters are the inclusion's aspect ratio α and an eigenstrain triaxiality parameter d-bar. The fluctuations of the thermodynamic force are investigated for a set of specific transformation eigenstrain tensors and are presented for inclusion shapes ranging from disk-like to fiber-like spheroids

Fracton-Elasticity Duality

Science.gov (United States)

Pretko, Michael; Radzihovsky, Leo

2018-05-01

Motivated by recent studies of fractons, we demonstrate that elasticity theory of a two-dimensional quantum crystal is dual to a fracton tensor gauge theory, providing a concrete manifestation of the fracton phenomenon in an ordinary solid. The topological defects of elasticity theory map onto charges of the tensor gauge theory, with disclinations and dislocations corresponding to fractons and dipoles, respectively. The transverse and longitudinal phonons of crystals map onto the two gapless gauge modes of the gauge theory. The restricted dynamics of fractons matches with constraints on the mobility of lattice defects. The duality leads to numerous predictions for phases and phase transitions of the fracton system, such as the existence of gauge theory counterparts to the (commensurate) crystal, supersolid, hexatic, and isotropic fluid phases of elasticity theory. Extensions of this duality to generalized elasticity theories provide a route to the discovery of new fracton models. As a further consequence, the duality implies that fracton phases are relevant to the study of interacting topological crystalline insulators.

The thermalization of soft modes in non-expanding isotropic quark gluon plasmas

Energy Technology Data Exchange (ETDEWEB)

Blaizot, Jean-Paul, E-mail: jean-paul.blaizot@cea.fr [Institut de Physique Théorique, CNRS/UMR 3681, CEA Saclay, F-91191 Gif-sur-Yvette (France); Liao, Jinfeng [Physics Department and Center for Exploration of Energy and Matter, Indiana University, 2401 N Milo B. Sampson Lane, Bloomington, IN 47408 (United States); RIKEN BNL Research Center, Bldg. 510A, Brookhaven National Laboratory, Upton, NY 11973 (United States); Mehtar-Tani, Yacine [Institute for Nuclear Theory, University of Washington, Seattle, WA 98195-1550 (United States)

2017-05-15

We discuss the role of elastic and inelastic collisions and their interplay in the thermalization of the quark–gluon plasma. We consider a simplified situation of a static plasma, spatially uniform and isotropic in momentum space. We focus on the small momentum region, which equilibrates first, and on a short time scale. We obtain a simple kinetic equation that allows for an analytic description of the most important regimes. The present analysis suggests that the formation of a Bose condensate, expected when only elastic collisions are present, is strongly hindered by the inelastic, radiative, processes.

Zirconium elasticity modules

International Nuclear Information System (INIS)

Vavra, G.

1978-01-01

Considered are the limit and the intermediate values of the Young modulus E, modulus of shear G and of linear modulus of compression K obtainable at various temperatures (4.2 to 1133 K) for single crystals of α-zirconium. Determined and presented are the corrected isotropic elasticity characteristics of E, G, K over the above range of temperatures of textured and non-textured α-Zr

Uniqueness in inverse elastic scattering with finitely many incident waves

International Nuclear Information System (INIS)

Elschner, Johannes; Yamamoto, Masahiro

2009-01-01

We consider the third and fourth exterior boundary value problems of linear isotropic elasticity and present uniqueness results for the corresponding inverse scattering problems with polyhedral-type obstacles and a finite number of incident plane elastic waves. Our approach is based on a reflection principle for the Navier equation. (orig.)

Computational fluid dynamics incompressible turbulent flows

CERN Document Server

Kajishima, Takeo

2017-01-01

This textbook presents numerical solution techniques for incompressible turbulent flows that occur in a variety of scientific and engineering settings including aerodynamics of ground-based vehicles and low-speed aircraft, fluid flows in energy systems, atmospheric flows, and biological flows. This book encompasses fluid mechanics, partial differential equations, numerical methods, and turbulence models, and emphasizes the foundation on how the governing partial differential equations for incompressible fluid flow can be solved numerically in an accurate and efficient manner. Extensive discussions on incompressible flow solvers and turbulence modeling are also offered. This text is an ideal instructional resource and reference for students, research scientists, and professional engineers interested in analyzing fluid flows using numerical simulations for fundamental research and industrial applications. • Introduces CFD techniques for incompressible flow and turbulence with a comprehensive approach; • Enr...

Nearly incompressible fluids: Hydrodynamics and large scale inhomogeneity

International Nuclear Information System (INIS)

Hunana, P.; Zank, G. P.; Shaikh, D.

2006-01-01

A system of hydrodynamic equations in the presence of large-scale inhomogeneities for a high plasma beta solar wind is derived. The theory is derived under the assumption of low turbulent Mach number and is developed for the flows where the usual incompressible description is not satisfactory and a full compressible treatment is too complex for any analytical studies. When the effects of compressibility are incorporated only weakly, a new description, referred to as 'nearly incompressible hydrodynamics', is obtained. The nearly incompressible theory, was originally applied to homogeneous flows. However, large-scale gradients in density, pressure, temperature, etc., are typical in the solar wind and it was unclear how inhomogeneities would affect the usual incompressible and nearly incompressible descriptions. In the homogeneous case, the lowest order expansion of the fully compressible equations leads to the usual incompressible equations, followed at higher orders by the nearly incompressible equations, as introduced by Zank and Matthaeus. With this work we show that the inclusion of large-scale inhomogeneities (in this case time-independent and radially symmetric background solar wind) modifies the leading-order incompressible description of solar wind flow. We find, for example, that the divergence of velocity fluctuations is nonsolenoidal and that density fluctuations can be described to leading order as a passive scalar. Locally (for small lengthscales), this system of equations converges to the usual incompressible equations and we therefore use the term 'locally incompressible' to describe the equations. This term should be distinguished from the term 'nearly incompressible', which is reserved for higher-order corrections. Furthermore, we find that density fluctuations scale with Mach number linearly, in contrast to the original homogeneous nearly incompressible theory, in which density fluctuations scale with the square of Mach number. Inhomogeneous nearly

A micromechanics model of the elastic properties of human dentine

Energy Technology Data Exchange (ETDEWEB)

Kinney, J. H. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Balooch, M. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Marshall, G. W. [Univ. of California, San Francisco, CA (United States). Dept. of Restorative Dentistry; Marshall, S. J. [Univ. of California, San Francisco, CA (United States). Dept. of Restorative Dentistry

1999-10-01

A generalized self-consistent model of cylindrical inclusions in a homogeneous and isotropic matrix phase was used to study the effects of tubule orientation on the elastic properties of dentin. Closed form expressions for the five independent elastic constants of dentin were derived in terms of tubule concentration, and the Young's moduli and Poisson ratios of peri- and intertubular dentin. An atomic force microscope (AFM) indentation technique determined the Young's moduli of the peri- and intertubular dentin as approximately 30 GPa and 15 GPa, respectively. Over the natural variation in tubule density found in dentin, there was only a slight variation in the axial and transverse shear moduli with position in the tooth, and there was no measurable effect of tubule orientation. We conclude that tubule orientation has no appreciable effect on the elastic behavior of normal dentin, and that the elastic properties of healthy dentin can be modeled as an isotropic continuum with a Young's modulus of approximately 16 GPa and a shear modulus of 6.2 GPa.

The elastic response of composite materials

International Nuclear Information System (INIS)

Laws, N.

1980-01-01

The theory of linear elasticity is used to study the elastic response of composite materials. The main concern is the prediction of overall moduli. Some attention is paid to the problem of deciding upon when the idea of an overall modulus is meaningful. In addition it is shown how to calculate some rigorous bounds on the overall moduli, and some predictions of the self-consistent method are discussed. The paper mainly concentrates on isotropic dispersions of spheres, unidirectional fibre-reinforced materials and laminates. (author)

Lagrangian statistics in compressible isotropic homogeneous turbulence

Science.gov (United States)

Yang, Yantao; Wang, Jianchun; Shi, Yipeng; Chen, Shiyi

2011-11-01

In this work we conducted the Direct Numerical Simulation (DNS) of a forced compressible isotropic homogeneous turbulence and investigated the flow statistics from the Lagrangian point of view, namely the statistics is computed following the passive tracers trajectories. The numerical method combined the Eulerian field solver which was developed by Wang et al. (2010, J. Comp. Phys., 229, 5257-5279), and a Lagrangian module for tracking the tracers and recording the data. The Lagrangian probability density functions (p.d.f.'s) have then been calculated for both kinetic and thermodynamic quantities. In order to isolate the shearing part from the compressing part of the flow, we employed the Helmholtz decomposition to decompose the flow field (mainly the velocity field) into the solenoidal and compressive parts. The solenoidal part was compared with the incompressible case, while the compressibility effect showed up in the compressive part. The Lagrangian structure functions and cross-correlation between various quantities will also be discussed. This work was supported in part by the China's Turbulence Program under Grant No.2009CB724101.

Ultrasound estimation and FE analysis of elastic modulus of Kelvin foam

International Nuclear Information System (INIS)

Kim, Nohyu; Yang, Seung Yong

2016-01-01

The elastic modulus of a 3D-printed Kelvin foam plate is investigated by measuring the acoustic wave velocity of 1 MHz ultrasound. An isotropic tetrakaidecahedron foam with 3 mm unit cell is designed and printed layer upon layer to fabricate a Kelvin foam plate of 14 mm thickness with a 3D CAD/printer using ABS plastic. The Kelvin foam plate is completely filled with paraffin wax for impedance matching, so that the acoustic wave may propagate through the porous foam plate. The acoustic wave velocity of the foam plate is measured using the time-of-flight (TOF) method and is used to calculate the elastic modulus of the Kelvin foam plate based on acousto-elasticity. Finite element method (FEM) and micromechanics is applied to the Kelvin foam plate to calculate the theoretical elastic modulus using a non-isotropic tetrakaidecahedron model. The predicted elastic modulus of the Kelvin foam plate from FEM and micromechanics model is similar, which is only 3-4% of the bulk material. The experimental value of the elastic modulus from the ultrasonic method is approximately twice as that of the numerical and theoretical methods because of the flexural deformation of the cell edges neglected in the ultrasonic method

Ultrasound estimation and FE analysis of elastic modulus of Kelvin foam

Energy Technology Data Exchange (ETDEWEB)

Kim, Nohyu; Yang, Seung Yong [School of Mechatronics Engineering, Korea University of Technology and Education, Cheonan (Korea, Republic of)

2016-02-15

The elastic modulus of a 3D-printed Kelvin foam plate is investigated by measuring the acoustic wave velocity of 1 MHz ultrasound. An isotropic tetrakaidecahedron foam with 3 mm unit cell is designed and printed layer upon layer to fabricate a Kelvin foam plate of 14 mm thickness with a 3D CAD/printer using ABS plastic. The Kelvin foam plate is completely filled with paraffin wax for impedance matching, so that the acoustic wave may propagate through the porous foam plate. The acoustic wave velocity of the foam plate is measured using the time-of-flight (TOF) method and is used to calculate the elastic modulus of the Kelvin foam plate based on acousto-elasticity. Finite element method (FEM) and micromechanics is applied to the Kelvin foam plate to calculate the theoretical elastic modulus using a non-isotropic tetrakaidecahedron model. The predicted elastic modulus of the Kelvin foam plate from FEM and micromechanics model is similar, which is only 3-4% of the bulk material. The experimental value of the elastic modulus from the ultrasonic method is approximately twice as that of the numerical and theoretical methods because of the flexural deformation of the cell edges neglected in the ultrasonic method.

Error estimation and adaptivity for incompressible hyperelasticity

KAUST Repository

Whiteley, J.P.

2014-04-30

SUMMARY: A Galerkin FEM is developed for nonlinear, incompressible (hyper) elasticity that takes account of nonlinearities in both the strain tensor and the relationship between the strain tensor and the stress tensor. By using suitably defined linearised dual problems with appropriate boundary conditions, a posteriori error estimates are then derived for both linear functionals of the solution and linear functionals of the stress on a boundary, where Dirichlet boundary conditions are applied. A second, higher order method for calculating a linear functional of the stress on a Dirichlet boundary is also presented together with an a posteriori error estimator for this approach. An implementation for a 2D model problem with known solution, where the entries of the strain tensor exhibit large, rapid variations, demonstrates the accuracy and sharpness of the error estimators. Finally, using a selection of model problems, the a posteriori error estimate is shown to provide a basis for effective mesh adaptivity. © 2014 John Wiley & Sons, Ltd.

Stochastic isotropic hyperelastic materials: constitutive calibration and model selection

Science.gov (United States)

Mihai, L. Angela; Woolley, Thomas E.; Goriely, Alain

2018-03-01

Biological and synthetic materials often exhibit intrinsic variability in their elastic responses under large strains, owing to microstructural inhomogeneity or when elastic data are extracted from viscoelastic mechanical tests. For these materials, although hyperelastic models calibrated to mean data are useful, stochastic representations accounting also for data dispersion carry extra information about the variability of material properties found in practical applications. We combine finite elasticity and information theories to construct homogeneous isotropic hyperelastic models with random field parameters calibrated to discrete mean values and standard deviations of either the stress-strain function or the nonlinear shear modulus, which is a function of the deformation, estimated from experimental tests. These quantities can take on different values, corresponding to possible outcomes of the experiments. As multiple models can be derived that adequately represent the observed phenomena, we apply Occam's razor by providing an explicit criterion for model selection based on Bayesian statistics. We then employ this criterion to select a model among competing models calibrated to experimental data for rubber and brain tissue under single or multiaxial loads.

Elastic representation surfaces of unidirectional graphite/epoxy composites

International Nuclear Information System (INIS)

Kriz, R.D.; Ledbetter, H.M.

1985-01-01

Unidirectional graphite/epoxy composites exhibit high elastic anisotropy and unusual geometrical features in their elastic-property polar diagrams. From the five-component transverse-isotropic elastic-stiffness tensor we compute and display representation surfaces for Young's modulus, torsional modulus, linear compressibility, and Poisson's ratios. Based on Christoffel-equation solutions, we describe some unusual elastic-wave-surface topological features. Musgrave considered in detail the differences between phase-velocity and group-velocity surfaces arising from high elastic anisotropy. For these composites, we find effects similar to, but more dramatic than, Musgrave's. Some new, unexpected results for graphite/epoxy include: a shear-wave velocity that exceeds a longitudinal velocity in the plane transverse to the fiber; a wave that changes polarization character from longitudinal to transverse as the propagation direction sweeps from the fiber axis to the perpendicular axis

Uniqueness theorems in linear elasticity

CERN Document Server

Knops, Robin John

1971-01-01

The classical result for uniqueness in elasticity theory is due to Kirchhoff. It states that the standard mixed boundary value problem for a homogeneous isotropic linear elastic material in equilibrium and occupying a bounded three-dimensional region of space possesses at most one solution in the classical sense, provided the Lame and shear moduli, A and J1 respectively, obey the inequalities (3 A + 2 J1) > 0 and J1>O. In linear elastodynamics the analogous result, due to Neumann, is that the initial-mixed boundary value problem possesses at most one solution provided the elastic moduli satisfy the same set of inequalities as in Kirchhoffs theorem. Most standard textbooks on the linear theory of elasticity mention only these two classical criteria for uniqueness and neglect altogether the abundant literature which has appeared since the original publications of Kirchhoff. To remedy this deficiency it seems appropriate to attempt a coherent description ofthe various contributions made to the study of uniquenes...

Elastic constants of a Laves phase compound: C15 NbCr2

International Nuclear Information System (INIS)

Ormeci, A.; Chu, F.; Wills, J.M.; Chen, S.P.; Albers, R.C.; Thoma, D.J.; Mitchell, T.E.

1997-01-01

The single-crystal elastic constants of C15 NbCr 2 have been computed by using a first-principles, self-consistent, full-potential total energy method. From these single-crystal elastic constants the isotropic elastic moduli are calculated using the Voigt and Reuss averages. The calculated values are in fair agreement with the experimental values. The implications of the results are discussed with regards to Poisson's ratio and the direction dependence of Young's modulus

A Potential Method for Body and Surface Wave Propagation in Transversely Isotropic Half- and Full-Spaces

Directory of Open Access Journals (Sweden)

Mehdi Raoofian Naeeni

2016-12-01

Full Text Available The problem of propagation of plane wave including body and surface waves propagating in a transversely isotropic half-space with a depth-wise axis of material symmetry is investigated in details. Using the advantage of representation of displacement fields in terms of two complete scalar potential functions, the coupled equations of motion are uncoupled and reduced to two independent equations for potential functions. In this paper, the secular equations for determination of body and surface wave velocities are derived in terms of both elasticity coefficients and the direction of propagation. In particular, the longitudinal, transverse and Rayleigh wave velocities are determined in explicit forms. It is also shown that in transversely isotropic materials, a Rayleigh wave may propagate in different manner from that of isotropic materials. Some numerical results for synthetic transversely isotropic materials are also illustrated to show the behavior of wave motion due to anisotropic nature of the problem.

Large Deformation Constitutive Laws for Isotropic Thermoelastic Materials

Energy Technology Data Exchange (ETDEWEB)

Plohr, Bradley J. [Los Alamos National Laboratory; Plohr, Jeeyeon N. [Los Alamos National Laboratory

2012-07-25

We examine the approximations made in using Hooke's law as a constitutive relation for an isotropic thermoelastic material subjected to large deformation by calculating the stress evolution equation from the free energy. For a general thermoelastic material, we employ the volume-preserving part of the deformation gradient to facilitate volumetric/shear strain decompositions of the free energy, its first derivatives (the Cauchy stress and entropy), and its second derivatives (the specific heat, Grueneisen tensor, and elasticity tensor). Specializing to isotropic materials, we calculate these constitutive quantities more explicitly. For deformations with limited shear strain, but possibly large changes in volume, we show that the differential equations for the stress components involve new terms in addition to the traditional Hooke's law terms. These new terms are of the same order in the shear strain as the objective derivative terms needed for frame indifference; unless the latter terms are negligible, the former cannot be neglected. We also demonstrate that accounting for the new terms requires that the deformation gradient be included as a field variable

An isotropic suspension system for a biaxial accelerometer using electroplated thick metal with a HAR SU-8 mold

International Nuclear Information System (INIS)

Lee, Jin Seung; Lee, Seung S

2008-01-01

In this paper, a novel approach is developed to design an isotropic suspension system using thick metal freestanding micro-structures combining bulk micro-machining with electroplating based on a HAR SU-8 mold. An omega-shape isotropic suspension system composed of circular curved beams that have free switching of imaginary boundary conditions is proposed. This novel isotropic suspension design is not affected by geometric dimensional parameters and always achieves matching stiffness along the principle axes of elasticity. Using the finite element method, the isotropic suspension system was compared with an S-shaped meandering suspension system. In order to realize the suggested isotropic suspension system, a cost-effective fabrication process using electroplating with the SU-8 mold was developed to avoid expensive equipment and materials such as deep reactive-ion etching (DRIE) or a silicon-on-insulator (SOI) wafer. The fabricated isotropic suspension system was verified by electromagnetic actuation experiments. Finally, a biaxial accelerometer with isotropic suspension system was realized and tested using a vibration generator system. The proposed isotropic suspension system and the modified surface micro-machining technique based on electroplating with an SU-8 mold can contribute towards minimizing the system size, simplifying the system configuration, reducing the system price of and facilitating mass production of various types of low-cost sensors and actuators

On liquid vibration in elastic containers

International Nuclear Information System (INIS)

Priehn, F.

1984-01-01

Numerical methods of calculation for containers made of circular rings of any crossection are derived for containers which are filled with incompressible and also with compressible liquids. This is done neglecting the formation of waves on the liquid surface, and by using a simplified mechanical model for calculations for the elastic walls. Using a developed Fourier series in the circumferential direction, this leads to a plane model and one obtains a very compact system of equations, which give an opportunity of studying the individual effects very economically. (orig./HP) [de

Optimum shape design of incompressible hyperelastic structures with analytical sensitivity analysis

International Nuclear Information System (INIS)

Jarraya, A.; Wali, M.; Dammark, F.

2014-01-01

This paper is focused on the structural shape optimization of incompressible hyperelastic structures. An analytical sensitivity is developed for the rubber like materials. The whole shape optimization process is carried out by coupling a closed geometric shape in R 2 with boundaries, defined by B-splines curves, exact sensitivity analysis and mathematical programming method (S.Q.P: sequential quadratic programming). Design variables are the control points coordinate. The objective function is to minimize Von-Mises stress, constrained to the total material volume of the structure remains constant. In order to validate the exact Jacobian method, the sensitivity calculation is performed: numerically by an efficient finite difference scheme and by the exact Jacobian method. Numerical optimization examples are presented for elastic and hyperelastic materials using the proposed method.

Rayleigh waves in elastic medium with double porosity

Directory of Open Access Journals (Sweden)

Rajneesh KUMAR

2018-03-01

Full Text Available The present paper deals with the propagation of Rayleigh waves in isotropic homogeneous elastic half-space with double porosity whose surface is subjected to stress-free boundary conditions. The compact secular equations for elastic solid half-space with voids are deduced as special cases from the present analysis. In order to illustrate the analytical developments, the secular equations have been solved numerically. The computer simulated results for copper materials in respect of Rayleigh wave velocity and attenuation coe¢ cient have been presented graphically.

A high-order boundary integral method for surface diffusions on elastically stressed axisymmetric rods

OpenAIRE

Li, Xiaofan; Nie, Qing

2009-01-01

Many applications in materials involve surface diffusion of elastically stressed solids. Study of singularity formation and long-time behavior of such solid surfaces requires accurate simulations in both space and time. Here we present a high-order boundary integral method for an elastically stressed solid with axi-symmetry due to surface diffusions. In this method, the boundary integrals for isotropic elasticity in axi-symmetric geometry are approximated through modified alternating quadratu...

Algorithm of constructing hybrid effective modules for elastic isotropic composites

Science.gov (United States)

Svetashkov, A. A.; Miciński, J.; Kupriyanov, N. A.; Barashkov, V. N.; Lushnikov, A. V.

2017-02-01

The algorithm of constructing of new effective elastic characteristics of two-component composites based on the superposition of the models of Reiss and Voigt, Hashin and Strikman, as well as models of the geometric average for effective modules. These effective characteristics are inside forks Voigt and Reiss. Additionally, the calculations of the stress-strain state of composite structures with new effective characteristics give more accurate prediction than classical models do.

A Membrane Model from Implicit Elasticity Theory

Science.gov (United States)

Freed, A. D.; Liao, J.; Einstein, D. R.

2014-01-01

A Fungean solid is derived for membranous materials as a body defined by isotropic response functions whose mathematical structure is that of a Hookean solid where the elastic constants are replaced by functions of state derived from an implicit, thermodynamic, internal-energy function. The theory utilizes Biot’s (1939) definitions for stress and strain that, in 1-dimension, are the stress/strain measures adopted by Fung (1967) when he postulated what is now known as Fung’s law. Our Fungean membrane model is parameterized against a biaxial data set acquired from a porcine pleural membrane subjected to three, sequential, proportional, planar extensions. These data support an isotropic/deviatoric split in the stress and strain-rate hypothesized by our theory. These data also demonstrate that the material response is highly non-linear but, otherwise, mechanically isotropic. These data are described reasonably well by our otherwise simple, four-parameter, material model. PMID:24282079

Nonlinear electroelastic deformations of dielectric elastomer composites: II - Non-Gaussian elastic dielectrics

Science.gov (United States)

Lefèvre, Victor; Lopez-Pamies, Oscar

2017-02-01

This paper presents an analytical framework to construct approximate homogenization solutions for the macroscopic elastic dielectric response - under finite deformations and finite electric fields - of dielectric elastomer composites with two-phase isotropic particulate microstructures. The central idea consists in employing the homogenization solution derived in Part I of this work for ideal elastic dielectric composites within the context of a nonlinear comparison medium method - this is derived as an extension of the comparison medium method of Lopez-Pamies et al. (2013) in nonlinear elastostatics to the coupled realm of nonlinear electroelastostatics - to generate in turn a corresponding solution for composite materials with non-ideal elastic dielectric constituents. Complementary to this analytical framework, a hybrid finite-element formulation to construct homogenization solutions numerically (in three dimensions) is also presented. The proposed analytical framework is utilized to work out a general approximate homogenization solution for non-Gaussian dielectric elastomers filled with nonlinear elastic dielectric particles that may exhibit polarization saturation. The solution applies to arbitrary (non-percolative) isotropic distributions of filler particles. By construction, it is exact in the limit of small deformations and moderate electric fields. For finite deformations and finite electric fields, its accuracy is demonstrated by means of direct comparisons with finite-element solutions. Aimed at gaining physical insight into the extreme enhancement in electrostriction properties displayed by emerging dielectric elastomer composites, various cases wherein the filler particles are of poly- and mono-disperse sizes and exhibit different types of elastic dielectric behavior are discussed in detail. Contrary to an initial conjecture in the literature, it is found (inter alia) that the isotropic addition of a small volume fraction of stiff (semi

Elastic constants of a Laves phase compound: C15 NbCr{sub 2}

Energy Technology Data Exchange (ETDEWEB)

Ormeci, A. [Koc Univ., Istanbul (Turkey)]|[Los Alamos National Lab., NM (United States); Chu, F.; Wills, J.M.; Chen, S.P.; Albers, R.C.; Thoma, D.J.; Mitchell, T.E. [Los Alamos National Lab., NM (United States)

1997-04-01

The single-crystal elastic constants of C15 NbCr{sub 2} have been computed by using a first-principles, self-consistent, full-potential total energy method. From these single-crystal elastic constants the isotropic elastic moduli are calculated using the Voigt and Reuss averages. The calculated values are in fair agreement with the experimental values. The implications of the results are discussed with regards to Poisson`s ratio and the direction dependence of Young`s modulus.

Wavelets for the stimulation of turbulent incompressible flows

International Nuclear Information System (INIS)

Deriaz, E.

2006-02-01

This PhD thesis presents original wavelet methods aimed at simulating incompressible fluids. In order to construct 2D and 3D wavelets designed for incompressible flows, we resume P-G Lemarie-Rieussets and K. Urbans works on divergence free wavelets. We show the existence of associated fast algorithms. In the following, we use divergence-free wavelet construction to define the Helmholtz decomposition of 2D and 3D vector fields. All these algorithms provide a new method for the numerical resolution of the incompressible Navier-Stokes equations. (author)

Influence of Elastic Anisotropy on Extended Dislocation Nodes

Energy Technology Data Exchange (ETDEWEB)

Pettersson, B

1971-09-15

The interaction forces between the partial dislocations forming an extended dislocation node are calculated using elasticity theory for anisotropic media.s are carried out for nodes of screw, edge and mixed character in Ag, which has an anisotropy ratio A equal to 3, and in a hypothetic material with A = 1 and the same shear modulus as Ag. The results are compared with three previous theories using isotropic elasticity theory. As expected, in Ag the influence of anisotropy is of the same order as the uncertainty due to the dislocation core energy

Rayleigh wave effects in an elastic half-space.

Science.gov (United States)

Aggarwal, H. R.

1972-01-01

Consideration of Rayleigh wave effects in a homogeneous isotropic linearly elastic half-space subject to an impulsive uniform disk pressure loading. An approximate formula is obtained for the Rayleigh wave effects. It is shown that the Rayleigh waves near the center of loading arise from the portion of the dilatational and shear waves moving toward the axis, after they originate at the edge of the load disk. A study is made of the vertical displacement due to Rayleigh waves at points on the axis near the surface of the elastic half-space.

The generalized Cauchy relation: a probe for local structure in materials with isotropic symmetry

Energy Technology Data Exchange (ETDEWEB)

Bactavatchalou, R [Laboratoire Europeen de Recherche Universitaire Saarland- Lorraine- Luxembourg at Universitaet des Saarlandes (Luxembourg); Alnot, P [Universite Henri Poincare, Nancy I (France); Bailer, J [Universite du Luxembourg (Luxembourg); Kolle, M [Laboratoire Europeen de Recherche Universitaire Saarland- Lorraine- Luxembourg at Universitaet des Saarlandes (Luxembourg); Mueller, U [Laboratoire Europeen de Recherche Universitaire Saarland- Lorraine- Luxembourg at Universitaet des Saarlandes (Luxembourg); Philipp, M [Laboratoire Europeen de Recherche Universitaire Saarland- Lorraine- Luxembourg at Universitaet des Saarlandes (Luxembourg); Possart, W [Laboratoire Europeen de Recherche Universitaire Saarland- Lorraine- Luxembourg at Universitaet des Saarlandes (Luxembourg); Rouxel, D [Universite Henri Poincare, Nancy I (France); Sanctuary, R [Universite du Luxembourg (Luxembourg); Tschoepe, A [Laboratoire Europeen de Recherche Universitaire Saarland- Lorraine- Luxembourg at Universitaet des Saarlandes (Luxembourg); Vergnat, Ch [Laboratoire Europeen de Recherche Universitaire Saarland- Lorraine- Luxembourg at Universitaet des Saarlandes (Luxembourg); Wetzel, B [Institut fuer Verbundwerkstoffe TU Kaiserslautern 67663 Kaiserslautern (Germany); Krueger, J K [Laboratoire Europeen de Recherche Universitaire Saarland- Lorraine- Luxembourg at Universitaet des Saarlandes (Luxembourg)

2006-05-15

The elastic properties of the isotropic state of condensed matter are given by the elastic constants ell and c44. In the liquid state the static shear stiffness c44 vanishes whereas at sufficient high probe frequencies a dynamic shear stiffness may appear. In that latter case the question about the existence of a Cauchy relation appears. It will be shown that a pure Cauchy relation can appear only under special conditions which are rarely fulfilled. For all investigated materials, including ceramics, liquids and glasses, a linear relation between ell and c44 called generalized Cauchy relation is observed, which, surprisingly, follows a linear transformation.

Effect of nonlinear stress-strain relationship on bending strength of isotropic graphite

International Nuclear Information System (INIS)

Arai, Taketoshi; Oku, Tatsuo

1978-05-01

Four-point bending tests were made on rectangular isotropic 7477PT graphite specimens of different sizes to observe the relation between load and outermost fiber strain. Analytical methods, allowing for nonlinear stress-strain relationships different between tension and compression, were developed for calculating the fiber stress distribution in a beam and the failure probability based on the Weibull statistical theory for bending fracture. With increase of the stress, the stress-strain curves for tension deviate from the linearity and also from those for compression. The true bending strengths of the rectangular bars are 10 -- 20 percent lower than elastic bending strengths. Revised Weibull theory gives failure probability distributions agreeing with measured ones, compared with the theory based on elastic behavior. (auth.)

Elastic energy and metastable phase equilibria for coherent mixtures in cubic systems

International Nuclear Information System (INIS)

Williams, R.O.

1979-02-01

Expressions were derived for the elastic energy due to coherency for cubic systems for an isotropic structure and for (100) or (111) habit planes for a lamellar structure. For the metastable equilibria the usual tangent compositions are replaced by compositions that are tangent to the elastic energy curve. For a loss of coherency there is an energy decrease due to the elastic effects and a further decrease associated with compositional changes. Information contained within this treatment permits calculation of the x-ray diffraction effects for such structures

Microstructural evolution in inhomogeneous elastic media

International Nuclear Information System (INIS)

Jou, H.J.; Leo, P.H.; Lowengrub, J.S.

1997-01-01

We simulate the diffusional evolution of microstructures produced by solid state diffusional transformations in elastically stressed binary alloys in two dimensions. The microstructure consists of arbitrarily shaped precipitates embedded coherently in an infinite matrix. The precipitate and matrix are taken to be elastically isotropic, although they may have different elastic constants (elastically inhomogeneous). Both far-field applied strains and mismatch strains between the phases are considered. The diffusion and elastic fields are calculated using the boundary integral method, together with a small scale preconditioner to remove ill-conditioning. The precipitate-matrix interfaces are tracked using a nonstiff time updating method. The numerical method is spectrally accurate and efficient. Simulations of a single precipitate indicate that precipitate shapes depend strongly on the mass flux into the system as well as on the elastic fields. Growing shapes (positive mass flux) are dendritic while equilibrium shapes (zero mass flux) are squarish. Simulations of multiparticle systems show complicated interactions between precipitate morphology and the overall development of microstructure (i.e., precipitate alignment, translation, merging, and coarsening). In both single and multiple particle simulations, the details of the microstructural evolution depend strongly o the elastic inhomogeneity, misfit strain, and applied fields. 57 refs., 24 figs

Scalar evolution equations for shear waves in incompressible solids: a simple derivation of the Z, ZK, KZK and KP equations

OpenAIRE

Destrade, Michel; Goriely, Alain; Saccomandi, Giuseppe

2011-01-01

We study the propagation of two-dimensional finite-amplitude shear waves in a nonlinear pre-strained incompressible solid, and derive several asymptotic amplitude equations in a simple, consistent, and rigorous manner. The scalar Zabolotskaya (Z) equation is shown to be the asymptotic limit of the equations of motion for all elastic generalized neo-Hookean solids (with strain energy depending only on the first principal invariant of Cauchy-Green strain). However, we show that the Z equation c...

Progress in the analysis of non-axisymmetric wave propagation in a homogeneous solid circular cylinder of a piezoelectric transversely isotropic material

CSIR Research Space (South Africa)

Every, AG

2010-01-01

Full Text Available Non-axisymmetric waves in a free homogeneous piezoelectric cylinder of transversely isotropic material with axial polarization are investigated on the basis of the linear theory of elasticity and linear electromechanical coupling. The solution...

Effective stress law for anisotropic elastic deformation

International Nuclear Information System (INIS)

Carroll, M.M.

1979-01-01

An effective stress law is derived analytically to describe the effect of pore fluid pressure on the linearly elastic response of saturated porous rocks which exhibit anisotropy. For general anisotropy the difference between the effective stress and the applied stress is not hydrostatic. The effective stress law involves two constants for transversely isotropic response and three constants for orthotropic response; these constants can be expressed in terms of the moduli of the porous material and of the solid material. These expressions simplify considerably when the anisotropy is structural rather than intrinsic, i.e., in the case of an isotropic solid material with an anisotropic pore structure. In this case the effective stress law involves the solid or grain bulk modulus and two or three moduli of the porous material, for transverse isotropy and orthotropy, respectively. The law reduces, in the case of isotropic response, to that suggested by Geertsma (1957) and by Skempton (1961) and derived analytically by Nur and Byerlee

Quasi-elastic neutron scattering study of a re-entrant side-chain liquid-crystal polyacrylate

Science.gov (United States)

Benguigui, L.; Noirez, L.; Kahn, R.; Keller, P.; Lambert, M.; Cohen de Lara, E.

1991-04-01

We present a first investigation of the dynamics of a side chain liquid crystal polyacrylate in the isotropic (I), nematic (N), smectic A (SA), and re-entrant nematic (NRe) phases by means of quasi-elastic neutron scattering. The motion or/and the mobility of the mesogen protons decreases as soon as the temperature decreases after the isotropic-nematic transition. The I-N and SA-NRe transitions corrspond to a jump in the curve of the Elastic Incoherent Structure Factor (ratio: elastic scattering/ total scattering) versus temperature, on the other hand the transition N-SA occurs without any change of slope. We conclude that the local order is very similar in the nematic and the smectic A phases. Nous présentons une première étude dynamique par diffusion quasi-élastique des neutrons, d'un échantillon de polyacrylate mésomorphe en peigne dans chacune des phases : isotrope, nématique, smectique et nématique rentrante. On montre que le mouvement et/ou la mobilité des protons du mésogène se restreint à mesure que la température diminue après la transition isotrope-nématique. Contrairement à la transition N-SA, les transitions I-N et SA-NRe correspondent à une discontinuité dans la courbe du Facteur de Structure Incohérent Elastique (rapport : intensité élastique/intensité totale) en fonction de la température ; l'ordre local semble donc très proche pour les phases nématique et smectique.

Determination of elastic modulus for hollow spherical shells via resonant ultrasound spectroscopy

Energy Technology Data Exchange (ETDEWEB)

Ma, Xiaojun [Institute of Modern Physics, Fudan University, Shanghai 200433 (China); Research Center of Laser Fusion, CAEP, Mianyang 621900 (China); Tang, Xing; Wang, Zongwei [Research Center of Laser Fusion, CAEP, Mianyang 621900 (China); Chen, Qian; Qian, Menglu [Institute of Acoustic, Tongji University, Shanghai 200092 (China); Meng, Jie [Research Center of Laser Fusion, CAEP, Mianyang 621900 (China); Tang, Yongjian [Institute of Modern Physics, Fudan University, Shanghai 200433 (China); Research Center of Laser Fusion, CAEP, Mianyang 621900 (China); Shen, Hao [Institute of Modern Physics, Fudan University, Shanghai 200433 (China); Gao, Dangzhong, E-mail: dgaocn@163.com [Research Center of Laser Fusion, CAEP, Mianyang 621900 (China)

2017-04-15

Highlights: • The axisymmetric frequency equation of an isotropic hollow two-layer sphere is deduced by three dimension elasticity theory and global matrix method. • The simulated results demonstrate that the natural frequencies of a hollow sphere are more strongly dependent on Young’s modulus than Poisson's ratio. • The Young’s moduli of polymer capsules with an sub-millimeter inner radius are measured accurately with an uncertainty of ∼10%. - Abstract: The elastic property of a capsule is one of the essential parameters both in engineering applications and scientific understanding of material nature in inertial confinement fusion (ICF) experiments. The axisymmetric frequency equation of an isotropic hollow two-layer sphere is deduced by three dimension elasticity theory and global matrix method, and a combined resonant ultrasound spectroscopy(RUS), which consists of a piezoelectric-based resonant ultrasound spectroscopy(PZT-RUS) and a laser-based resonant ultrasound spectroscopy(LRUS), is developed for determining the elastic modulus of capsule. To understand the behavior of natural frequencies varying with elastic properties, the dependence of natural frequencies on Young’s modulus and Poisson’s ratio are calculated numerically. Some representative polymer capsules are measured using PZT-RUS and LRUS. Based on the theoretical and experimental results, the Young’s moduli of these capsules are measured accurately with an uncertainty of ∼10%.

Helical Birods: An Elastic Model of Helically Wound Double-Stranded Rods

KAUST Repository

Prior, Christopher

2014-01-01

as an isotropic inextensible elastic rod. An important consideration in this demonstration is the possible effect of varying the geometric boundary constraints; it is shown the effect of this choice becomes negligible in this limit in which the rope has dimensions

Constraints on light WIMP candidates from the isotropic diffuse gamma-ray emission

International Nuclear Information System (INIS)

Arina, Chiara; Tytgat, Michel H.G.

2011-01-01

Motivated by the measurements reported by direct detection experiments, most notably DAMA, CDMS-II, CoGeNT and Xenon10/100, we study further the constraints that might be set on some light dark matter candidates, M DM ∼ few GeV, using the Fermi-LAT data on the isotropic gamma-ray diffuse emission. In particular, we consider a Dirac fermion singlet interacting through a new Z' gauge boson, and a scalar singlet S interacting through the Higgs portal. Both candidates are WIMP (Weakly Interacting Massive Particles), i.e. they have an annihilation cross-section in the pbarn range. Also they may both have a spin-independent elastic cross section on nucleons in the range required by direct detection experiments. Although being generic WIMP candidates, because they have different interactions with Standard Model particles, their phenomenology regarding the isotropic diffuse gamma-ray emission is quite distinct. In the case of the scalar singlet, the one-to-one correspondence between its annihilation cross-section and its spin-independent elastic scattering cross-section permits to express the constraints from the Fermi-LAT data in the direct detection exclusion plot, σ n 0 −M DM . Depending on the astrophysics, we argue that it is possible to exclude the singlet scalar dark matter candidate at 95% confidence level. The constraints on the Dirac singlet interacting through a Z' are comparatively weaker

Aero-elastic stability of airfoil flow using 2-D CFD

Energy Technology Data Exchange (ETDEWEB)

Johansen, J [Risoe National Lab., Roskilde (Denmark)

1999-03-01

A three degrees-of-freedom structural dynamics model has been coupled to a two-dimensional incompressible CFD code. The numerical investigation considers aero-elastic stability for two different airfoils; the NACA0012 and the LM 2 18 % airfoils. Stable and unstable configurations and limit cycle oscillations are predicted in accordance with literature for the first airfoil. An attempt to predict stall induced edge-wise vibrations on a wind turbine airfoil fails using this two-dimensional approach. (au)

The role of an effective isotropic tissue modulus in the elastic properties of cancellous bone

NARCIS (Netherlands)

Kabel, J.; Rietbergen, van B.; Dalstra, M.; Odgaard, A.; Huiskes, H.W.J.

1999-01-01

Conceptually, the elastic characteristics of cancellous bone could be predicted directly from the trabecular morphology-or architecture-and by the elastic properties of the tissue itself. Although hardly any experimental evidence exists, it is often implicitly assumed that tissue anisotropy has a

A high-order boundary integral method for surface diffusions on elastically stressed axisymmetric rods.

Science.gov (United States)

Li, Xiaofan; Nie, Qing

2009-07-01

Many applications in materials involve surface diffusion of elastically stressed solids. Study of singularity formation and long-time behavior of such solid surfaces requires accurate simulations in both space and time. Here we present a high-order boundary integral method for an elastically stressed solid with axi-symmetry due to surface diffusions. In this method, the boundary integrals for isotropic elasticity in axi-symmetric geometry are approximated through modified alternating quadratures along with an extrapolation technique, leading to an arbitrarily high-order quadrature; in addition, a high-order (temporal) integration factor method, based on explicit representation of the mean curvature, is used to reduce the stability constraint on time-step. To apply this method to a periodic (in axial direction) and axi-symmetric elastically stressed cylinder, we also present a fast and accurate summation method for the periodic Green's functions of isotropic elasticity. Using the high-order boundary integral method, we demonstrate that in absence of elasticity the cylinder surface pinches in finite time at the axis of the symmetry and the universal cone angle of the pinching is found to be consistent with the previous studies based on a self-similar assumption. In the presence of elastic stress, we show that a finite time, geometrical singularity occurs well before the cylindrical solid collapses onto the axis of symmetry, and the angle of the corner singularity on the cylinder surface is also estimated.

Rayleigh-Taylor instability in accelerated elastic-solid slabs

Science.gov (United States)

Piriz, S. A.; Piriz, A. R.; Tahir, N. A.

2017-12-01

We develop the linear theory for the asymptotic growth of the incompressible Rayleigh-Taylor instability of an accelerated solid slab of density ρ2, shear modulus G , and thickness h , placed over a semi-infinite ideal fluid of density ρ110.1007/s000330050121] to arbitrary values of AT and unveil the singular feature of an instability threshold below which the slab is stable for any perturbation wavelength. As a consequence, an accelerated elastic-solid slab is stable if ρ2g h /G ≤2 (1 -AT) /AT .

Elastic full-waveform inversion of transmission data in 2D VTI media

KAUST Repository

Kamath, Nishant; Tsvankin, Ilya

2014-01-01

Full-waveform inversion (FWI) has been implemented mostly for isotropic media, with extensions to anisotropic models typically limited to acoustic approximations. Here, we develop elastic FWI for transmitted waves in 2D heterogeneous VTI (transversely isotropic with a vertical symmetry axis) media. The model is parameterized in terms of the P- and S-wave vertical velocities and the P-wave normal-moveout and horizontal velocities. To test the FWI algorithm, we introduce Gaussian anomalies in the Thomsen parameters of a homogeneous VTI medium and perform FWI of transmission data for different configurations of the source and receiver arrays. The inversion results strongly depend on the acquisition geometry and the aperture because of the parameter trade-offs. In contrast to acoustic FWI, the elastic inversion helps constrain the S-wave vertical velocity, which for our model is decoupled from the other parameters.

Elastic full-waveform inversion of transmission data in 2D VTI media

KAUST Repository

Kamath, Nishant

2014-08-05

Full-waveform inversion (FWI) has been implemented mostly for isotropic media, with extensions to anisotropic models typically limited to acoustic approximations. Here, we develop elastic FWI for transmitted waves in 2D heterogeneous VTI (transversely isotropic with a vertical symmetry axis) media. The model is parameterized in terms of the P- and S-wave vertical velocities and the P-wave normal-moveout and horizontal velocities. To test the FWI algorithm, we introduce Gaussian anomalies in the Thomsen parameters of a homogeneous VTI medium and perform FWI of transmission data for different configurations of the source and receiver arrays. The inversion results strongly depend on the acquisition geometry and the aperture because of the parameter trade-offs. In contrast to acoustic FWI, the elastic inversion helps constrain the S-wave vertical velocity, which for our model is decoupled from the other parameters.

Theory of reversal nonisothermal elastic-plastic deformation

International Nuclear Information System (INIS)

Shorr, B.F.

1979-01-01

Considered is approximated theory of nonisothermal elastic-plastic deformation at arbitrary laws of loading, permitting to describe nonisothermal isotropic and anisotropic strengthening of the material, Bauschinger effect and different tempo of plastic deformation development over different directions of loading depending on the deformation prehistory. The comparison of the theory with the experimental data showed good coincidence and sufficient simplicity permits to use it in technical calcualtions

thermoelastic waves without energy dissipation in an elastic plate ...

African Journals Online (AJOL)

cistvr

The first generalization, for isotropic bodies, is due to Lord & Shulman (1967) who obtained a wave-type heat equation by postulating a new law of heat conduction to replace the classical Fourier's law. ...... In this paper we have studied the thermoelastic interactions due to the punching of a cylindrical hole in an elastic plate ...

First-principles study of elastic and thermodynamic properties of orthorhombic OsB4 under high pressure

Science.gov (United States)

Yan, Hai-Yan; Zhang, Mei-Guang; Huang, Duo-Hui; Wei, Qun

2013-04-01

The first-principles study on the elastic properties, elastic anisotropy and thermodynamic properties of the orthorhombic OsB4 is reported using density functional theory method with the ultrasoft pseudopotential scheme in the frame of the generalized gradient approximation. The calculated equilibrium parameters are in good agreement with the available theoretical data. A complete elastic tensor and crystal anisotropies of the ultra-incompressible OsB4 are determined in the pressure range of 0-50 GPa. By the elastic stability criteria, it is predicted that the orthorhombic OsB4 is stable below 50 GPa. By using the quasi-harmonic Debye model, the heat capacity, the coefficient of thermal expansion, and the Grüneisen parameter of OsB4 are also successfully obtained in the present work.

Generation of discrete inelastic and elastic transfer matrix

International Nuclear Information System (INIS)

Garcia, R.D.M.; Santina, M.D.

1985-01-01

A technique developed for the calculation of the isotropic and linearly anisotropic components components of elastic and discrete inelastic transfer matrices is presented in this work. The implementation of the technique is discussed in detail and numerical results obtained for some examples are compared with results reported in the literature or generated with the use of several processing codes. (author) [pt

Simulation of Free Airfoil Vibrations in Incompressible Viscous Flow — Comparison of FEM and FVM

Directory of Open Access Journals (Sweden)

Petr Sváček

2012-01-01

Full Text Available This paper deals with a numerical solution of the interaction of two-dimensional (2-D incompressible viscous flow and a vibrating profile NACA 0012 with large amplitudes. The laminar flow is described by the Navier-Stokes equations in the arbitrary Lagrangian-Eulerian form. The profile with two degrees of freedom (2-DOF can rotate around its elastic axis and oscillate in the vertical direction. Its motion is described by a nonlinear system of two ordinary differential equations. Deformations of the computational domain due to the profile motion are treated by the arbitrary Lagrangian-Eulerianmethod. The finite volume method and the finite element method are applied, and the numerical results are compared.

Elastic interaction of hydrogen atoms on graphene: A multiscale approach from first principles to continuum elasticity

Science.gov (United States)

Branicio, Paulo S.; Vastola, Guglielmo; Jhon, Mark H.; Sullivan, Michael B.; Shenoy, Vivek B.; Srolovitz, David J.

2016-10-01

The deformation of graphene due to the chemisorption of hydrogen atoms on its surface and the long-range elastic interaction between hydrogen atoms induced by these deformations are investigated using a multiscale approach based on first principles, empirical interactions, and continuum modeling. Focus is given to the intrinsic low-temperature structure and interactions. Therefore, all calculations are performed at T =0 , neglecting possible temperature or thermal fluctuation effects. Results from different methods agree well and consistently describe the local deformation of graphene on multiple length scales reaching 500 Å . The results indicate that the elastic interaction mediated by this deformation is significant and depends on the deformation of the graphene sheet both in and out of plane. Surprisingly, despite the isotropic elasticity of graphene, within the linear elastic regime, atoms elastically attract or repel each other depending on (i) the specific site they are chemisorbed; (ii) the relative position of the sites; (iii) and if they are on the same or on opposite surface sides. The interaction energy sign and power-law decay calculated from molecular statics agree well with theoretical predictions from linear elasticity theory, considering in-plane or out-of-plane deformations as a superposition or in a coupled nonlinear approach. Deviations on the exact power law between molecular statics and the linear elastic analysis are evidence of the importance of nonlinear effects on the elasticity of monolayer graphene. These results have implications for the understanding of the generation of clusters and regular formations of hydrogen and other chemisorbed atoms on graphene.

Ultrabroadband elastic cloaking in thin plates.

Science.gov (United States)

Farhat, Mohamed; Guenneau, Sebastien; Enoch, Stefan

2009-07-10

Control of waves with metamaterials is of great topical interest, and is fueled by rapid progress in broadband acoustic and electromagnetic cloaks. We propose a design for a cloak to control bending waves propagating in isotropic heterogeneous thin plates. This is achieved through homogenization of a multilayered concentric coating filled with piecewise constant isotropic elastic material. Significantly, our cloak displays no phase shift for both backward and forward scattering. To foster experimental efforts, we provide a simplified design of the cloak which is shown to work in a more than two-octave frequency range (30 Hz to 150 Hz) when it consists of 10 layers using only 6 different materials overall. This metamaterial should be easy to manufacture, with potential applications ranging from car industry to anti-earthquake passive systems for smart buildings, depending upon the plate dimensions and wavelengths.

Real-Time Incompressible Fluid Simulation on the GPU

Directory of Open Access Journals (Sweden)

Xiao Nie

2015-01-01

Full Text Available We present a parallel framework for simulating incompressible fluids with predictive-corrective incompressible smoothed particle hydrodynamics (PCISPH on the GPU in real time. To this end, we propose an efficient GPU streaming pipeline to map the entire computational task onto the GPU, fully exploiting the massive computational power of state-of-the-art GPUs. In PCISPH-based simulations, neighbor search is the major performance obstacle because this process is performed several times at each time step. To eliminate this bottleneck, an efficient parallel sorting method for this time-consuming step is introduced. Moreover, we discuss several optimization techniques including using fast on-chip shared memory to avoid global memory bandwidth limitations and thus further improve performance on modern GPU hardware. With our framework, the realism of real-time fluid simulation is significantly improved since our method enforces incompressibility constraint which is typically ignored due to efficiency reason in previous GPU-based SPH methods. The performance results illustrate that our approach can efficiently simulate realistic incompressible fluid in real time and results in a speed-up factor of up to 23 on a high-end NVIDIA GPU in comparison to single-threaded CPU-based implementation.

In-Plane free Vibration Analysis of an Annular Disk with Point Elastic Support

OpenAIRE

Bashmal, S.; Bhat, R.; Rakheja, S.

2011-01-01

In-plane free vibrations of an elastic and isotropic annular disk with elastic constraints at the inner and outer boundaries, which are applied either along the entire periphery of the disk or at a point are investigated. The boundary characteristic orthogonal polynomials are employed in the Rayleigh-Ritz method to obtain the frequency parameters and the associated mode shapes. Boundary characteristic orthogonal polynomials are generated for the free boundary conditions of the disk while arti...

Identification of the parameters of an elastic material model using the constitutive equation gap method

KAUST Repository

Florentin, É ric; Lubineau, Gilles

2010-01-01

study resides in the application of these recent developments to the identification problem. The proposed CEGM is described in detail, then evaluated through the identification of heterogeneous isotropic elastic properties. The results obtained

First-principles elasticity of monocarboaluminate hydrates

KAUST Repository

Moon, J.; Yoon, S.; Wentzcovitch, R. M.; Monteiro, P. J. M.

2014-01-01

The elasticity of monocarboaluminate hydrates, 3CaO·Al2O3·CaCO3·xH2O (x = 11 or 8), has been investigated by first-principles calculations. Previous experimental study revealed that the fully hydrated monocarboaluminate (x = 11) exhibits exceptionally low compressibility compared to other reported calcium aluminate hydrates. This stiff hydration product can contribute to the strength of concrete made with Portland cements containing calcium carbonates. In this study, full elastic tensors and mechanical properties of the crystal structures with different water contents (x = 11 or 8) are computed by first-principles methods based on density functional theory. The results indicate that the compressibility of monocarboaluminate is highly dependent on the water content in the interlayer region. The structure also becomes more isotropic with the addition of water molecules in this region. Since the monocarboaluminate is a key hydration product of limestone added cement, elasticity of the crystal is important to understand its mechanical impact on concrete. Besides, it is put forth that this theoretical calculation will be useful in predicting the elastic properties of other complex cementitous materials and the influence of ion exchange on compressibility.

First-principles elasticity of monocarboaluminate hydrates

KAUST Repository

Moon, J.

2014-07-01

The elasticity of monocarboaluminate hydrates, 3CaO·Al2O3·CaCO3·xH2O (x = 11 or 8), has been investigated by first-principles calculations. Previous experimental study revealed that the fully hydrated monocarboaluminate (x = 11) exhibits exceptionally low compressibility compared to other reported calcium aluminate hydrates. This stiff hydration product can contribute to the strength of concrete made with Portland cements containing calcium carbonates. In this study, full elastic tensors and mechanical properties of the crystal structures with different water contents (x = 11 or 8) are computed by first-principles methods based on density functional theory. The results indicate that the compressibility of monocarboaluminate is highly dependent on the water content in the interlayer region. The structure also becomes more isotropic with the addition of water molecules in this region. Since the monocarboaluminate is a key hydration product of limestone added cement, elasticity of the crystal is important to understand its mechanical impact on concrete. Besides, it is put forth that this theoretical calculation will be useful in predicting the elastic properties of other complex cementitous materials and the influence of ion exchange on compressibility.

Toward in vivo lung's tissue incompressibility characterization for tumor motion modeling in radiation therapy

International Nuclear Information System (INIS)

Shirzadi, Zahra; Sadeghi-Naini, Ali; Samani, Abbas

2013-01-01

Purpose: A novel technique is proposed to characterize lung tissue incompressibility variation during respiration. Estimating lung tissue incompressibility parameter variations resulting from air content variation throughout respiration is critical for computer assisted tumor motion tracking. Continuous tumor motion is a major challenge in lung cancer radiotherapy, especially with external beam radiotherapy. If not accounted for, this motion may lead to areas of radiation overdosage for normal tissue. Given the unavailability of imaging modality that can be used effectively for real-time lung tumor tracking, computer assisted approach based on tissue deformation estimation can be a good alternative. This approach involves lung biomechanical model where its fidelity depends on input tissue properties. This investigation shows that considering variable tissue incompressibility parameter is very important for predicting tumor motion accurately, hence improving the lung radiotherapy outcome. Methods: First, an in silico lung phantom study was conducted to demonstrate the importance of employing variable Poisson's ratio for tumor motion predication. After it was established that modeling this variability is critical for accurate tumor motion prediction, an optimization based technique was developed to estimate lung tissue Poisson's ratio as a function of respiration cycle time. In this technique, the Poisson's ratio and lung pressure value were varied systematically until optimal values were obtained, leading to maximum similarity between acquired and simulated 4D CT lung images. This technique was applied in an ex vivo porcine lung study where simulated images were constructed using the end exhale CT image and deformation fields obtained from the lung's FE modeling of each respiration time increment. To model the tissue, linear elastic and Marlow hyperelastic material models in conjunction with variable Poisson's ratio were used. Results: The phantom study showed that

Molecular dynamics simulations of Gay-Berne nematic liquid crystal: Elastic properties from direct correlation functions

International Nuclear Information System (INIS)

Stelzer, J.; Trebin, H.R.; Longa, L.

1994-08-01

We report NVT and NPT molecular dynamics simulations of a Gay-Berne nematic liquid crystal using generalization of recently proposed algorithm by Toxvaerd [Phys. Rev. E47, 343, 1993]. On the basis of these simulations the Oseen-Zoher-Frank elastic constants K 11 , K 22 and K 33 as well as the surface constants K 13 and K 24 have been calculated within the framework of the direct correlation function approach of Lipkin et al. [J. Chem. Phys. 82, 472 (1985)]. The angular coefficients of the direct pair correlation function, which enter the final formulas, have been determined from the computer simulation data for the pair correlation function of the nematic by combining the Ornstein-Zernike relation and the Wienier-Hopf factorization scheme. The unoriented nematic approximation has been assumed when constructing the reference, isotropic state of Lipkin et al. By an extensive study of the model over a wide range of temperatures, densities and pressures a very detailed information has been provided about elastic behaviour of the Gay-Berne nematic. Interestingly, it is found that the results for the surface elastic constants are qualitatively different than those obtained with the help of analytical approximations for the isotropic, direct pair correlation function. For example, the values of the surface elastic constants are negative and an order of magnitude smaller than the bulk elasticity. (author). 30 refs, 9 figs

Propagation law of impact elastic wave based on specific materials

Directory of Open Access Journals (Sweden)

Chunmin CHEN

2017-02-01

Full Text Available In order to explore the propagation law of the impact elastic wave on the platform, the experimental platform is built by using the specific isotropic materials and anisotropic materials. The glass cloth epoxy laminated plate is used for anisotropic material, and an organic glass plate is used for isotropic material. The PVDF sensors adhered on the specific materials are utilized to collect data, and the elastic wave propagation law of different thick plates and laminated plates under impact conditions is analyzed. The Experimental results show that in anisotropic material, transverse wave propagation speed along the fiber arrangement direction is the fastest, while longitudinal wave propagation speed is the slowest. The longitudinal wave propagation speed in anisotropic laminates is much slower than that in the laminated thick plates. In the test channel arranged along a particular angle away from the central region of the material, transverse wave propagation speed is larger. Based on the experimental results, this paper proposes a material combination mode which is advantageous to elastic wave propagation and diffusion in shock-isolating materials. It is proposed to design a composite material with high acoustic velocity by adding regularly arranged fibrous materials. The overall design of the barrier material is a layered structure and a certain number of 90°zigzag structure.

Geometric Models for Isotropic Random Porous Media: A Review

Directory of Open Access Journals (Sweden)

Helmut Hermann

2014-01-01

Full Text Available Models for random porous media are considered. The models are isotropic both from the local and the macroscopic point of view; that is, the pores have spherical shape or their surface shows piecewise spherical curvature, and there is no macroscopic gradient of any geometrical feature. Both closed-pore and open-pore systems are discussed. The Poisson grain model, the model of hard spheres packing, and the penetrable sphere model are used; variable size distribution of the pores is included. A parameter is introduced which controls the degree of open-porosity. Besides systems built up by a single solid phase, models for porous media with the internal surface coated by a second phase are treated. Volume fraction, surface area, and correlation functions are given explicitly where applicable; otherwise numerical methods for determination are described. Effective medium theory is applied to calculate physical properties for the models such as isotropic elastic moduli, thermal and electrical conductivity, and static dielectric constant. The methods presented are exemplified by applications: small-angle scattering of systems showing fractal-like behavior in limited ranges of linear dimension, optimization of nanoporous insulating materials, and improvement of properties of open-pore systems by atomic layer deposition of a second phase on the internal surface.

Elastic stiffnesses of an Nb-Ti/Cu-composite superconductive wire

Science.gov (United States)

Kim, Sudook; Ledbetter, Hassel; Ogi, Hirotsugu

2000-09-01

Elastic-stiffness coefficients were determined on a 1.4-mm-diameter wire consisting of superconducting Nb-Ti fibers in a copper matrix, with a polyvinyl-resin coating. The matrix contained 324 Nb-Ti fibers. An electromagnetic-acoustic-resonance method was used to obtain five independent elastic-stiffness coefficients assuming transverse-isotropic symmetry. From these we calculated Young moduli, bulk modulus, and principal Poisson ratios. As a check, we used a mechanical-impulse-excitation method to directly measure the Young modulus in the fiber direction. The three-phase composite wire showed a 10% anisotropy in the Young modulus.

Structural, elastic, electronic and dynamical properties of OsB and ReB: Density functional calculations

Science.gov (United States)

Li, Yanling; Zeng, Zhi; Lin, Haiqing

2010-06-01

The structural, elastic, electronic and dynamical properties of ReB and OsB are investigated by first-principles calculations based on density functional theory. It turns out that ReB and OsB are metallic ultra-incompressible solids with small elastic anisotropy and high hardness. The change of c/ a ratio in OsB indicates that there is a structural phase transition at about 31 GPa. Phonon spectra calculations show that both OsB and ReB are stable dynamically and there are abnormal phonon dispersions along special directions in Brillouin zone. OsB and ReB do not show superconductivity due to very weak electron-phonon interactions in them.

Computer simulation of model cohesive powders: Plastic consolidation, structural changes and elasticity under isotropic loads

OpenAIRE

Gilabert, Francisco; Roux, Jean-Noël; Castellanos, Antonio

2008-01-01

International audience; The quasistatic behavior of a simple 2D model of a cohesive powder under isotropic loads is investigated by Discrete Element simulations. The loose packing states, as studied in a previous paper, undergo important structural changes under growing confining pressure P, while solid fraction \\Phi irreversibly increases by large amounts. The system state goes through three stages, with different forms of the plastic consolidation curve \\Phi(P*), under growing reduced press...

Axisymmetric ideal magnetohydrodynamic equilibria with incompressible flows

International Nuclear Information System (INIS)

Tasso, H.; Throumoulopoulos, G.N.

1997-12-01

It is shown that the ideal MHD equilibrium states of an axisymmetric plasma with incompressible flows are governed by an elliptic partial differential equation for the poloidal magnetic flux function ψ containing five surface quantities along with a relation for the pressure. Exact equilibria are constructed including those with non vanishing poloidal and toroidal flows and differentially varying radial electric fields. Unlike the case in cylindrical incompressible equilibria with isothermal magnetic surfaces which should have necessarily circular cross sections [G. N. Throumoulopoulos and H. Tasso, Phys. Plasmas 4, 1492 (1997)], no restriction appears on the shapes of the magnetic surfaces in the corresponding axisymmetric equilibria. The latter equilibria satisfy a set of six ordinary differential equations which for flows parallel to the magnetic field B can be solved semianalytically. In addition, it is proved the non existence of incompressible axisymmetric equilibria with (a) purely poloidal flows and (b) non-parallel flows with isothermal magnetic surfaces and vertical stroke B vertical stroke = vertical stroke B vertical stroke (ψ) (omnigenous equilibria). (orig.)

CFD simulation of flow-induced vibration of an elastically supported airfoil

Directory of Open Access Journals (Sweden)

Šidlof Petr

2016-01-01

Full Text Available Flow-induced vibration of lifting or control surfaces in aircraft may lead to catastrophic consequences. Under certain circumstances, the interaction between the airflow and the elastic structure may lead to instability with energy transferred from the airflow to the structure and with exponentially increasing amplitudes of the structure. In the current work, a CFD simulation of an elastically supported NACA0015 airfoil with two degrees of freedom (pitch and plunge coupled with 2D incompressible airflow is presented. The geometry of the airfoil, mass, moment of inertia, location of the centroid, linear and torsional stiffness was matched to properties of a physical airfoil model used for wind-tunnel measurements. The simulations were run within the OpenFOAM computational package. The results of the CFD simulations were compared with the experimental data.

Elastic properties of magnetostrictive rare-earth-iron alloys

International Nuclear Information System (INIS)

Cullen, J.R.; Blessing, G.; Rinaldi, S.

1978-01-01

The elastic properties of certain magnetostrictive rare-earth-iron alloys, namely polycrystalline Tbsub(0.3)Dysub(0.7)Fesub(2), Smsub(0.88)Dysub(0.12)Fesub(2)and amorphous TbFesub(2), were investigated ultrasonically. In all cases two shear waves were observed propagating simultaneously when a magnetic field was applied perpendicular to the direction of propagation. A model to explain this behaviour, based on magnetic-elastic coupling within local regions of these disordered materials, is developed and discussed in two limiting cases: (i) strongly coupled regions for which an effective isotropic magneto-elastic coupling is appropriate, and (ii) materials for which the elastic properties of the conglomerate are determined by averaging over those of independent regions. Experimental results up to fields of 25 kOe on the alloys mentioned above are exhibited and compared with the limiting cases (i) and (ii). In the case of polycrystalline Tbsub(0.3)Dysub(0.7)Fesub(2) further comparison is made between the determination of the magneto-elastic coupling constants using this model and the determination by using the results of a previous single-crystal study. (author)

Nearly incompressible MHD turbulence in the solar wind

International Nuclear Information System (INIS)

Matthaeus, W.H.; Zhou, Y.

1989-01-01

Observational studies indicate that solar wind plasma and magnetic field fluctuations may be meaningfully viewed as an example of magnetohydrodynamic turbulence. This paper presents a brief summary of some relevant results of turbulence theory and reviews a turbulence style description of 'typical' solar wind conditions. Recent results, particularly those regarding the radial evolution of inertial range cross helicity, support the viewpoint that interplanetary turbulence is active and evolving with heliocentric distance. A number of observed properties can be understood by appeal to incompressible turbulence mechanisms. This connection may be understood by appeal to incompressible turbulence mechanisms. This connection may be understood in terms of theories of pseudosound density fluctuations and nearly incompressible magnetohydrodynamics, which are also reviewed here. Finally, we summarize a recent two-scale dynamical theory of the radial and temporal evolution of the turbulence, which may provide an additional framework for understanding the observations. (author). 49 refs

The incompressibility assumption in computational simulations of nasal airflow.

Science.gov (United States)

Cal, Ismael R; Cercos-Pita, Jose Luis; Duque, Daniel

2017-06-01

Most of the computational works on nasal airflow up to date have assumed incompressibility, given the low Mach number of these flows. However, for high temperature gradients, the incompressibility assumption could lead to a loss of accuracy, due to the temperature dependence of air density and viscosity. In this article we aim to shed some light on the influence of this assumption in a model of calm breathing in an Asian nasal cavity, by solving the fluid flow equations in compressible and incompressible formulation for different ambient air temperatures using the OpenFOAM package. At low flow rates and warm climatological conditions, similar results were obtained from both approaches, showing that density variations need not be taken into account to obtain a good prediction of all flow features, at least for usual breathing conditions. This agrees with most of the simulations previously reported, at least as far as the incompressibility assumption is concerned. However, parameters like nasal resistance and wall shear stress distribution differ for air temperatures below [Formula: see text]C approximately. Therefore, density variations should be considered for simulations at such low temperatures.

Stress Distribution in Layered Elastic Creeping Array with a Vertical Cylindrical Shaft

Directory of Open Access Journals (Sweden)

Bobyleva Tatiana

2017-01-01

Full Text Available Construction should be taking into account the influence of time factor on the stability of the structures. In the paper hereditary creep and homogenization theories are used to determine stresses in the layered elastic creeping array with a vertical shaft. Volterra correspondence principle was applied. As a result, the reduction of a time-dependent elastic creeping problem to a corresponding elastic problem became possible. The method proposes a way to determine average (effective elastic creeping properties and homogenized stress field from known properties of the layers’ components. Creep kernels are of a convolution type and are taken in the exponential form. The problem of heterogeneous elastic creeping environment is reduced to a problem of homogeneous transversely isotropic medium. Different boundary conditions on the cylindrical shaft’s surface were considered. An analytical solution was obtained. These explicit expressions can be useful for the necessary calculations in the construction practice.

Effective thermoelastic properties of discrete-fiber reinforced materials with transversally-isotropic components

Science.gov (United States)

Nazarenko, Lidiya; Khoroshun, Leonid; Müller, Wolfgang H.; Wille, Ralf

2009-02-01

In the present paper, we will illustrate the application of the method of conditional moments by constructing the algorithm for determination of the effective elastic properties of composites from the given elastic constants of the components and geometrical parameters of inclusions. A special case of two-component matrix composite with randomly distributed unidirectional spheroidal inclusions is considered. To this end it is assumed that the components of the composite show transversally isotropic symmetry of thermoelastic properties and that the axes of symmetry of the thermoelastic properties of the matrix and inclusions coincide with the coordinate axis x 3. As a numerical example a composite based on carbon inclusions and epoxide matrix is investigated. The dependencies of Young’s moduli, Poisson’s ratios and shear modulus from the concentration of inclusions and for certain values which characterize the shape of inclusions are analyzed. The results are compared and discussed in context with other theoretical predictions and experimental data.

Surface effects on anti-plane shear waves propagating in magneto-electro-elastic nanoplates

International Nuclear Information System (INIS)

Wu, Bin; Zhang, Chunli; Chen, Weiqiu; Zhang, Chuanzeng

2015-01-01

Material surfaces may have a remarkable effect on the mechanical behavior of magneto-electro-elastic (or multiferroic) structures at nanoscale. In this paper, a surface magneto-electro-elasticity theory (or effective boundary condition formulation), which governs the motion of the material surface of magneto-electro-elastic nanoplates, is established by employing the state-space formalism. The properties of anti-plane shear (SH) waves propagating in a transversely isotropic magneto-electro-elastic plate with nanothickness are investigated by taking surface effects into account. The size-dependent dispersion relations of both antisymmetric and symmetric SH waves are presented. The thickness-shear frequencies and the asymptotic characteristics of the dispersion relations considering surface effects are determined analytically as well. Numerical results show that surface effects play a very pronounced role in elastic wave propagation in magneto-electro-elastic nanoplates, and the dispersion properties depend strongly on the chosen surface material parameters of magneto-electro-elastic nanoplates. As a consequence, it is possible to modulate the waves in magneto-electro-elastic nanoplates through surface engineering. (paper)

Computation of Viscous Incompressible Flows

CERN Document Server

Kwak, Dochan

2011-01-01

This monograph is intended as a concise and self-contained guide to practitioners and graduate students for applying approaches in computational fluid dynamics (CFD) to real-world problems that require a quantification of viscous incompressible flows. In various projects related to NASA missions, the authors have gained CFD expertise over many years by developing and utilizing tools especially related to viscous incompressible flows. They are looking at CFD from an engineering perspective, which is especially useful when working on real-world applications. From that point of view, CFD requires two major elements, namely methods/algorithm and engineering/physical modeling. As for the methods, CFD research has been performed with great successes. In terms of modeling/simulation, mission applications require a deeper understanding of CFD and flow physics, which has only been debated in technical conferences and to a limited scope. This monograph fills the gap by offering in-depth examples for students and engine...

Inverse design of an isotropic suspended Kirchhoff rod: theoretical and numerical results on the uniqueness of the natural shape

Science.gov (United States)

Bertails-Descoubes, Florence; Derouet-Jourdan, Alexandre; Romero, Victor; Lazarus, Arnaud

2018-04-01

Solving the equations for Kirchhoff elastic rods has been widely explored for decades in mathematics, physics and computer science, with significant applications in the modelling of thin flexible structures such as DNA, hair or climbing plants. As demonstrated in previous experimental and theoretical studies, the natural curvature plays an important role in the equilibrium shape of a Kirchhoff rod, even in the simple case where the rod is isotropic and suspended under gravity. In this paper, we investigate the reverse problem: can we characterize the natural curvature of a suspended isotropic rod, given an equilibrium curve? We prove that although there exists an infinite number of natural curvatures that are compatible with the prescribed equilibrium, they are all equivalent in the sense that they correspond to a unique natural shape for the rod. This natural shape can be computed efficiently by solving in sequence three linear initial value problems, starting from any framing of the input curve. We provide several numerical experiments to illustrate this uniqueness result, and finally discuss its potential impact on non-invasive parameter estimation and inverse design of thin elastic rods.

Isotropic oscillator: spheroidal wave functions

International Nuclear Information System (INIS)

Mardoyan, L.G.; Pogosyan, G.S.; Ter-Antonyan, V.M.; Sisakyan, A.N.

1985-01-01

Solutions of the Schroedinger equation are found for an isotropic oscillator (10) in prolate and oblate spheroidal coordinates. It is shown that the obtained solutions turn into spherical and cylindrical bases of the isotropic oscillator at R→0 and R→ infinity (R is the dimensional parameter entering into the definition of prolate and oblate spheroidal coordinates). The explicit form is given for both prolate and oblate basis of the isotropic oscillator for the lowest quantum states

X-ray elastic constants in textured Zr-base materials

International Nuclear Information System (INIS)

Ortiz, M.; Pochettino, A.A.; Lebrun, J.L.; Maeder, G.

1993-01-01

A general method for the calculation of the X-ray elastic constants (XREC) for textured hexagonal close-packed (hcp) materials was developed by using the orientation distribution function (ODF) and the Reuss hypothesis. This method was applied to textured zirconium (Zr) sheets and zircaloy 4 (Zry 4) extruded tubes. For these samples, where the elastic anisotropy is not very strong, an 'isotropic approximation' method is proposed using the ODF data. In that case, the classical XREC 1/2S 2 and S, values are calculated and experimentally verified for (10 bar 14) diffracting planes. Theoretical XREC values are also given for different (hkil) that could be chosen according to the experimental conditions, considering texture effects on diffracting peak intensities

The isotropic radio background revisited

Energy Technology Data Exchange (ETDEWEB)

Fornengo, Nicolao; Regis, Marco [Dipartimento di Fisica Teorica, Università di Torino, via P. Giuria 1, I–10125 Torino (Italy); Lineros, Roberto A. [Instituto de Física Corpuscular – CSIC/U. Valencia, Parc Científic, calle Catedrático José Beltrán, 2, E-46980 Paterna (Spain); Taoso, Marco, E-mail: fornengo@to.infn.it, E-mail: rlineros@ific.uv.es, E-mail: regis@to.infn.it, E-mail: taoso@cea.fr [Institut de Physique Théorique, CEA/Saclay, F-91191 Gif-sur-Yvette Cédex (France)

2014-04-01

We present an extensive analysis on the determination of the isotropic radio background. We consider six different radio maps, ranging from 22 MHz to 2.3 GHz and covering a large fraction of the sky. The large scale emission is modeled as a linear combination of an isotropic component plus the Galactic synchrotron radiation and thermal bremsstrahlung. Point-like and extended sources are either masked or accounted for by means of a template. We find a robust estimate of the isotropic radio background, with limited scatter among different Galactic models. The level of the isotropic background lies significantly above the contribution obtained by integrating the number counts of observed extragalactic sources. Since the isotropic component dominates at high latitudes, thus making the profile of the total emission flat, a Galactic origin for such excess appears unlikely. We conclude that, unless a systematic offset is present in the maps, and provided that our current understanding of the Galactic synchrotron emission is reasonable, extragalactic sources well below the current experimental threshold seem to account for the majority of the brightness of the extragalactic radio sky.

The isotropic radio background revisited

International Nuclear Information System (INIS)

Fornengo, Nicolao; Regis, Marco; Lineros, Roberto A.; Taoso, Marco

2014-01-01

We present an extensive analysis on the determination of the isotropic radio background. We consider six different radio maps, ranging from 22 MHz to 2.3 GHz and covering a large fraction of the sky. The large scale emission is modeled as a linear combination of an isotropic component plus the Galactic synchrotron radiation and thermal bremsstrahlung. Point-like and extended sources are either masked or accounted for by means of a template. We find a robust estimate of the isotropic radio background, with limited scatter among different Galactic models. The level of the isotropic background lies significantly above the contribution obtained by integrating the number counts of observed extragalactic sources. Since the isotropic component dominates at high latitudes, thus making the profile of the total emission flat, a Galactic origin for such excess appears unlikely. We conclude that, unless a systematic offset is present in the maps, and provided that our current understanding of the Galactic synchrotron emission is reasonable, extragalactic sources well below the current experimental threshold seem to account for the majority of the brightness of the extragalactic radio sky

Phase-field modeling of isothermal quasi-incompressible multicomponent liquids

Science.gov (United States)

Tóth, Gyula I.

2016-09-01

In this paper general dynamic equations describing the time evolution of isothermal quasi-incompressible multicomponent liquids are derived in the framework of the classical Ginzburg-Landau theory of first order phase transformations. Based on the fundamental equations of continuum mechanics, a general convection-diffusion dynamics is set up first for compressible liquids. The constitutive relations for the diffusion fluxes and the capillary stress are determined in the framework of gradient theories. Next the general definition of incompressibility is given, which is taken into account in the derivation by using the Lagrange multiplier method. To validate the theory, the dynamic equations are solved numerically for the quaternary quasi-incompressible Cahn-Hilliard system. It is demonstrated that variable density (i) has no effect on equilibrium (in case of a suitably constructed free energy functional) and (ii) can influence nonequilibrium pattern formation significantly.

Quasi-Rayleigh waves in transversely isotropic half-space with inclined axis of symmetry

International Nuclear Information System (INIS)

Yanovskaya, T.B.; Savina, L.S.

2003-09-01

A method for determination of characteristics of quasi-Rayleigh (qR) wave in a transversely isotropic homogeneous half-space with inclined axis of symmetry is outlined. The solution is obtained as a superposition of qP, qSV and qSH waves, and surface wave velocity is determined from the boundary conditions at the free surface and at infinity, as in the case of Rayleigh wave in isotropic half-space. Though the theory is simple enough, a numerical procedure for the calculation of surface wave velocity presents some difficulties. The difficulty is conditioned by necessity to calculate complex roots of a non-linear equation, which in turn contains functions determined as roots of nonlinear equations with complex coefficients. Numerical analysis shows that roots of the equation corresponding to the boundary conditions do not exist in the whole domain of azimuths and inclinations of the symmetry axis. The domain of existence of qR wave depends on the ratio of the elastic parameters: for some strongly anisotropic models the wave cannot exist at all. For some angles of inclination qR wave velocities deviate from those calculated on the basis of the perturbation method valid for weak anisotropy, though they have the same tendency of variation with azimuth. The phase of qR wave varies with depth unlike Rayleigh wave in isotropic half-space. Unlike Rayleigh wave in isotropic half-space, qR wave has three components - vertical, radial and transverse. Particle motion in horizontal plane is elliptic. Direction of the major axis of the ellipsis coincide with the direction of propagation only in azimuths 0 deg. (180 deg.) and 90 deg. (270 deg.). (author)

Integrating a logarithmic-strain based hyper-elastic formulation into a three-field mixed finite element formulation to deal with incompressibility in finite-strain elasto-plasticity

International Nuclear Information System (INIS)

Dina Al Akhrass; Bruchon, Julien; Drapier, Sylvain; Fayolle, Sebastien

2014-01-01

This paper deals with the treatment of incompressibility in solid mechanics in finite-strain elasto-plasticity. A finite-strain model proposed by Miehe, Apel and Lambrecht, which is based on a logarithmic strain measure and its work-conjugate stress tensor is chosen. Its main interest is that it allows for the adoption of standard constitutive models established in a small-strain framework. This model is extended to take into account the plastic incompressibility constraint intrinsically. In that purpose, an extension of this model to a three-field mixed finite element formulation is proposed, involving displacements, a strain variable and pressure as nodal variables with respect to standard finite element. Numerical examples of finite-strain problems are presented to assess the performance of the formulation. To conclude, an industrial case for which the classical under-integrated elements fail is considered. (authors)

Topological sensitivity based far-field detection of elastic inclusions

Directory of Open Access Journals (Sweden)

Tasawar Abbas

2018-03-01

Full Text Available The aim of this article is to present and rigorously analyze topological sensitivity based algorithms for detection of diametrically small inclusions in an isotropic homogeneous elastic formation using single and multiple measurements of the far-field scattering amplitudes. A L2-cost functional is considered and a location indicator is constructed from its topological derivative. The performance of the indicator is analyzed in terms of the topological sensitivity for location detection and stability with respect to measurement and medium noises. It is established that the location indicator does not guarantee inclusion detection and achieves only a low resolution when there is mode-conversion in an elastic formation. Accordingly, a weighted location indicator is designed to tackle the mode-conversion phenomenon. It is substantiated that the weighted function renders the location of an inclusion stably with resolution as per Rayleigh criterion. 2000 MSC: 35R30, 35L05, 74B05, 47A52, 65J20, Keywords: Inverse elastic scattering, Elasticity imaging, Topological derivative, Resolution analysis, Stability analysis

Multiparameter Elastic Full Waveform Inversion With Facies Constraints

KAUST Repository

Zhang, Zhendong

2017-08-17

Full waveform inversion (FWI) aims fully benefit from all the data characteristics to estimate the parameters describing the assumed physics of the subsurface. However, current efforts to utilize full waveform inversion as a tool beyond acoustic imaging applications, for example in reservoir analysis, faces inherent challenges related to the limited resolution and the potential trade-off between the elastic model parameters. Adding rock physics constraints does help to mitigate these issues, but current approaches to add such constraints are based on including them as a priori knowledge mostly valid around the well or as a boundary condition for the whole area. Since certain rock formations inside the Earth admit consistent elastic properties and relative values of elastic and anisotropic parameters (facies), utilizing such localized facies information in FWI can improve the resolution of inverted parameters. We propose a novel confidence map based approach to utilize the facies-based constraints in both isotropic and anisotropic elastic FWI. We invert for such a confidence map using Bayesian theory, in which the confidence map is updated at each iteration of the inversion using both the inverted models and a prior information. The numerical examples show that the proposed method can reduce the trade-offs and also can improve the resolution of the inverted elastic and anisotropic properties.

New developments in isotropic turbulent models for FENE-P fluids

Science.gov (United States)

Resende, P. R.; Cavadas, A. S.

2018-04-01

The evolution of viscoelastic turbulent models, in the last years, has been significant due to the direct numeric simulation (DNS) advances, which allowed us to capture in detail the evolution of the viscoelastic effects and the development of viscoelastic closures. New viscoelastic closures are proposed for viscoelastic fluids described by the finitely extensible nonlinear elastic-Peterlin constitutive model. One of the viscoelastic closure developed in the context of isotropic turbulent models, consists in a modification of the turbulent viscosity to include an elastic effect, capable of predicting, with good accuracy, the behaviour for different drag reductions. Another viscoelastic closure essential to predict drag reduction relates the viscoelastic term involving velocity and the tensor conformation fluctuations. The DNS data show the high impact of this term to predict correctly the drag reduction, and for this reason is proposed a simpler closure capable of predicting the viscoelastic behaviour with good performance. In addition, a new relation is developed to predict the drag reduction, quantity based on the trace of the tensor conformation at the wall, eliminating the need of the typically parameters of Weissenberg and Reynolds numbers, which depend on the friction velocity. This allows future developments for complex geometries.

Ultrasonic Determination of the Elastic Constants of Epoxy-natural Fiber Composites

Science.gov (United States)

Valencia, C. A. Meza; Pazos-Ospina, J. F.; Franco, E. E.; Ealo, Joao L.; Collazos-Burbano, D. A.; Garcia, G. F. Casanova

This paper shows the applications ultrasonic through-transmission technique to determine the elastic constants of two polymer-natural fiber composite materials with potential industrial application and economic and environmental advantages. The transversely isotropic coconut-epoxy and fique-epoxy samples were analyzed using an experimental setup which allows the sample to be rotated with respect to transducers faces and measures the time-of-flight at different angles of incidence. Then, the elastic properties of the material were obtained by fitting the experimental data to the Christoffel equation. Results show a good agreement between the measured elastic constants and the values predicted by an analytical model. The velocities as a function of the incidence angle are reported and the effect of the natural fiber on the stiffness of the composite is discussed.

Macroscopic simulation of isotropic permanent magnets

International Nuclear Information System (INIS)

Bruckner, Florian; Abert, Claas; Vogler, Christoph; Heinrichs, Frank; Satz, Armin; Ausserlechner, Udo; Binder, Gernot; Koeck, Helmut; Suess, Dieter

2016-01-01

Accurate simulations of isotropic permanent magnets require to take the magnetization process into account and consider the anisotropic, nonlinear, and hysteretic material behaviour near the saturation configuration. An efficient method for the solution of the magnetostatic Maxwell equations including the description of isotropic permanent magnets is presented. The algorithm can easily be implemented on top of existing finite element methods and does not require a full characterization of the hysteresis of the magnetic material. Strayfield measurements of an isotropic permanent magnet and simulation results are in good agreement and highlight the importance of a proper description of the isotropic material. - Highlights: • Simulations of isotropic permanent magnets. • Accurate calculation of remanence magnetization and strayfield. • Comparison with strayfield measurements and anisotropic magnet simulations. • Efficient 3D FEM–BEM coupling for solution of Maxwell equations.

Shock and rarefaction waves in a hyperbolic model of incompressible materials

Directory of Open Access Journals (Sweden)

Tommaso Ruggeri

2013-01-01

Full Text Available The aim of the present paper is to investigate shock and rarefaction waves in a hyperbolic model of incompressible materials. To this aim, we use the so-called extended quasi-thermal-incompressible (EQTI model, recently proposed by Gouin & Ruggeri (H. Gouin, T. Ruggeri, Internat. J. Non-Linear Mech. 47 688–693 (2012. In particular, we use as constitutive equation a variant of the well-known Bousinnesq approximation in which the specific volume depends not only on the temperature but also on the pressure. The limit case of ideal incompressibility, namely when the thermal expansion coefficient and the compressibility factor vanish, is also considered.

Mapping of moveout in tilted transversely isotropic media

KAUST Repository

Stovas, A.; Alkhalifah, Tariq Ali

2013-01-01

The computation of traveltimes in a transverse isotropic medium with a tilted symmetry axis tilted transversely isotropic is very important both for modelling and inversion. We develop a simple analytical procedure to map the traveltime function from a transverse isotropic medium with a vertical symmetry axis (vertical transversely isotropic) to a tilted transversely isotropic medium by applying point-by-point mapping of the traveltime function. This approach can be used for kinematic modelling and inversion in layered tilted transversely isotropic media. © 2013 European Association of Geoscientists & Engineers.

Mapping of moveout in tilted transversely isotropic media

KAUST Repository

Stovas, A.

2013-09-09

The computation of traveltimes in a transverse isotropic medium with a tilted symmetry axis tilted transversely isotropic is very important both for modelling and inversion. We develop a simple analytical procedure to map the traveltime function from a transverse isotropic medium with a vertical symmetry axis (vertical transversely isotropic) to a tilted transversely isotropic medium by applying point-by-point mapping of the traveltime function. This approach can be used for kinematic modelling and inversion in layered tilted transversely isotropic media. © 2013 European Association of Geoscientists & Engineers.

Modeling and analysis of waves in a heat conducting thermo-elastic plate of elliptical shape

Directory of Open Access Journals (Sweden)

R. Selvamani

Full Text Available Wave propagation in heat conducting thermo elastic plate of elliptical cross-section is studied using the Fourier expansion collocation method based on Suhubi's generalized theory. The equations of motion based on two-dimensional theory of elasticity is applied under the plane strain assumption of generalized thermo elastic plate of elliptical cross-sections composed of homogeneous isotropic material. The frequency equations are obtained by using the boundary conditions along outer and inner surface of elliptical cross-sectional plate using Fourier expansion collocation method. The computed non-dimensional frequency, velocity and quality factor are plotted in dispersion curves for longitudinal and flexural (symmetric and antisymmetric modes of vibrations.

Fibrillar structure and elasticity of hydrating collagen: a quantitative multiscale approach.

Science.gov (United States)

Morin, Claire; Hellmich, Christian; Henits, Peter

2013-01-21

It is well known that hydration of collagenous tissues leads to their swelling, as well as to softening of their elastic behavior. However, it is much less clear which microstructural and micromechanical "rules" are involved in this process. Here, we develop a theoretical approach cast in analytical mathematical formulations, which is experimentally validated by a wealth of independent tests on collagenous tissues, such as X-ray diffraction, vacuum drying, mass measurements, and Brillouin light scattering. The overall emerging picture is the following: air-drying leaves water only in the gap zones between the triple-helical collagen molecules; upon re-hydration, the extrafibrillar space is established at volumes directly proportional to the hydration-induced swelling of the (micro) fibrils, until the maximum equatorial distance between the long collagen molecules is reached. Thereafter, the volume of the fibrils stays constant, and only the extrafibrillar volume continues to grow. At all these hydration stages, the elastic behavior is governed by the same, hydration-invariant mechanical interaction pattern of only two, interpenetrating mechanical phases: transversely isotropic molecular collagen and isotropic water (or empty pores in the vacuum-dried case). Copyright © 2012 Elsevier Ltd. All rights reserved.

The buckling transition of two-dimensional elastic honeycombs: numerical simulation and Landau theory

International Nuclear Information System (INIS)

Jagla, E A

2004-01-01

I study the buckling transition under compression of a two-dimensional, hexagonal, regular elastic honeycomb. Under isotropic compression, the system buckles to a configuration consisting of a unit cell containing four of the original hexagons. This buckling pattern preserves the sixfold rotational symmetry of the original lattice but is chiral, and can be described as a combination of three different elemental distortions in directions rotated by 2π/3 from each other. Non-isotropic compression may induce patterns consisting of a single elemental distortion or a superposition of two of them. The numerical results compare very well with the outcome of a Landau theory of second-order phase transitions

Incompressibility of asymmetric nuclear matter

International Nuclear Information System (INIS)

Chen, Liewen; Cai, Baojun; Shen, Chun; Ko, Cheming; Xu, Jun; Li, Baoan

2010-01-01

Using an isospin- and momentum-dependent modified Gogny (MDI) interaction, the Skyrme-Hartree-Fock (SHF) approach, and a phenomenological modified Skyrme-like (MSL) model, we have studied the incompressibility K sat (δ) of isospin asymmetric nuclear matter at its saturation density. Our results show that in the expansion of K sat (δ) in powers of isospin asymmetry δ, i.e., K sat (δ) = K 0 + K sat,2 δ 2 + K sat,4 δ 4 + O(δ 6 ), the magnitude of the 4th-order K sat,4 parameter is generally small. The 2nd-order K sat,2 parameter thus essentially characterizes the isospin dependence of the incompressibility of asymmetric nuclear matter at saturation density. Furthermore, the K sat,2 can be expressed as K sat,2 = K sym – 6L – J 0 /K 0 L in terms of the slope parameter L and the curvature parameter K sym of the symmetry energy and the third-order derivative parameter J 0 of the energy of symmetric nuclear matter at saturation density, and we find the higher order J 0 contribution to K sat,2 generally cannot be neglected. Also, we have found a linear correlation between K sym and L as well as between J 0 /K 0 and K 0 . Using these correlations together with the empirical constraints on K 0 and L, the nuclear symmetry energy E sym (ρ0) at normal nuclear density, and the nucleon effective mass, we have obtained an estimated value of K sat,2 = -370 ± 120 MeV for the 2nd-order parameter in the isospin asymmetry expansion of the incompressibility of asymmetric nuclear matter at its saturation density. (author)

Fundamental topics for thermo-elastic stress analyses

International Nuclear Information System (INIS)

Biermann, M.

1989-01-01

This paper delivers a consistent collection of theoretical fundamentals needed to perform rather sound experimental stress analyses on thermo-elastic materials. An exposition of important concepts of symmetry and so-called peer groups, yielding the very base for a rational description of materials, goes ahead and is followed by an introduction to the constitutive theory of simple materials. Neat distinction is made between stress contributions determined by deformational and thermal impressions, on the one part, and stress constraints not accessible to strain gauging, on the other part. The mathematical formalism required for establishing constitutive equations is coherently developed from scratch and aided, albeit not subrogated, by intuition. The main intention goes to turning some of the recent advances in the nonlinear field theories of thermomechanics to practical account. A full success therein, obviously, results under the restriction to thermo-elasticity. In adverting to more particular subjects, the elementary static effects of nonlinear isotropic elasticity are pointed out. Due allowance is made for thermal effects likely to occur in heat conducting materials also beyond the isothermal or isentropic limit cases. Linearization of the constitutive equations for anisotropic thermo-elastic materials is then shown to entail the formulas of the classical theory. (orig./MM) [de

Computation of temperature-dependent legendre moments of a double-differential elastic cross section

International Nuclear Information System (INIS)

Arbanas, G.; Dunn, M.E.; Larson, N.M.; Leal, L.C.; Williams, M.L.; Becker, B.; Dagan, R.

2011-01-01

A general expression for temperature-dependent Legendre moments of a double-differential elastic scattering cross section was derived by Ouisloumen and Sanchez [Nucl. Sci. Eng. 107, 189-200 (1991)]. Attempts to compute this expression are hindered by the three-fold nested integral, limiting their practical application to just the zeroth Legendre moment of an isotropic scattering. It is shown that the two innermost integrals could be evaluated analytically to all orders of Legendre moments, and for anisotropic scattering, by a recursive application of the integration by parts method. For this method to work, the anisotropic angular distribution in the center of mass is expressed as an expansion in Legendre polynomials. The first several Legendre moments of elastic scattering of neutrons on 238 U are computed at T=1000 K at incoming energy 6.5 eV for isotropic scattering in the center of mass frame. Legendre moments of the anisotropic angular distribution given via Blatt-Biedenharn coefficients are computed at 1 keV. The results are in agreement with those computed by the Monte Carlo method. (author)

Some fundamental definitions of the elastic parameters for homogeneous isotropic linear elastic materials in pavement design and analysis

CSIR Research Space (South Africa)

De Beer, Morris

2008-07-01

Full Text Available - wave and ρ the material density. The elastic moduli P-wave modulus, M, is defined so that M = K + 4µ / 3 and M can then be determined by Equation 11, with a known speed Vp P MV 2 ρ = (11) It should however also... gas (such as air within compacted road materials), the adiabatic bulk modulus KS is approximately given by pKS κ= (4) Where: κ is the adiabatic index, (sometimes calledγ ); p is the pressure. In a fluid (such as moisture...

I-Love relations for incompressible stars and realistic stars

Science.gov (United States)

Chan, T. K.; Chan, AtMa P. O.; Leung, P. T.

2015-02-01

In spite of the diversity in the equations of state of nuclear matter, the recently discovered I-Love-Q relations [Yagi and Yunes, Science 341, 365 (2013), 10.1126/science.1236462], which relate the moment of inertia, tidal Love number (deformability), and the spin-induced quadrupole moment of compact stars, hold for various kinds of realistic neutron stars and quark stars. While the physical origin of such universality is still a current issue, the observation that the I-Love-Q relations of incompressible stars can well approximate those of realistic compact stars hints at a new direction to approach the problem. In this paper, by establishing recursive post-Minkowskian expansion for the moment of inertia and the tidal deformability of incompressible stars, we analytically derive the I-Love relation for incompressible stars and show that the so-obtained formula can be used to accurately predict the behavior of realistic compact stars from the Newtonian limit to the maximum mass limit.

Multi-component pre-stack time-imaging and migration-based velocity analysis in transversely isotropic media; Imagerie sismique multicomposante et analyse de vitesse de migration en milieu transverse isotrope

Energy Technology Data Exchange (ETDEWEB)

Gerea, C.V.

2001-06-01

Complementary to the recording of compressional (P-) waves, the observation of P-S converted waves has recently been receiving specific attention. This is mainly due to their tremendous potential as a tool for fracture and lithology characterization, imaging sediments in gas saturated rocks, and imaging shallow sediments with higher resolution than conventional P-P data. In a conventional marine seismic survey, we cannot record P-to-S converted-wave energy since the fluids cannot support shear-wave strain. Thus, to capture the converted-wave energy, we need to record it at the water-bottom casing an ocean-bottom cable (OBC). The S-waves recorded at the seabed are mainly converted from P to S (i.e., PS-waves or C-waves) at the subsurface reflectors. The most accurate way to image seismic data is pre-stack depth migration. In this thesis, I develop a numerically efficient 2.5-D true-amplitude elastic Kirchhoff pre-stack migration algorithm designed to handle OBC data gathered along a single line. All the kinematic and dynamic elastic Green's functions required in the computation of true-amplitude weight term of Kirchhoff summation, are based on the non-hyperbolic explicit approximations of P- and SV-wave travel-times in layered transversely isotropic (VTI) media. Hence, this elastic imaging algorithm is very well-suited for migration-based velocity analysis techniques, for which fast, robust and iterative pre-stack migration is desired. In this thesis, I approach also the topic of anisotropic velocity model building for elastic pre-stack time-imaging. and propose an original methodology for joint PP-PS migration-based velocity analysis (MVA) in layered VTI anisotropic media. Tests on elastic synthetic and real OBC seismic data ascertain the validity of the pre-stack migration algorithm and velocity analysis methodology. (author)

A blended pressure/density based method for the computation of incompressible and compressible flows

International Nuclear Information System (INIS)

Rossow, C.-C.

2003-01-01

An alternative method to low speed preconditioning for the computation of nearly incompressible flows with compressible methods is developed. For this approach the leading terms of the flux difference splitting (FDS) approximate Riemann solver are analyzed in the incompressible limit. In combination with the requirement of the velocity field to be divergence-free, an elliptic equation to solve for a pressure correction to enforce the divergence-free velocity field on the discrete level is derived. The pressure correction equation established is shown to be equivalent to classical methods for incompressible flows. In order to allow the computation of flows at all speeds, a blending technique for the transition from the incompressible, pressure based formulation to the compressible, density based formulation is established. It is found necessary to use preconditioning with this blending technique to account for a remaining 'compressible' contribution in the incompressible limit, and a suitable matrix directly applicable to conservative residuals is derived. Thus, a coherent framework is established to cover the discretization of both incompressible and compressible flows. Compared with standard preconditioning techniques, the blended pressure/density based approach showed improved robustness for high lift flows close to separation

Investigation of displacement, strain and stress in single step transversely isotropic elastic bonded joint

Science.gov (United States)

Apu, Md. Jakaria; Islam, Md. Shahidul

2016-07-01

Bi-material joint is often used in many advanced materials and structures. Determination of the bonding strength at the interface is very difficult because of the presence of the stress singularity. In this paper, the displacement and stress fields of a transversely isotropic bi-material joint around an interface edge are determined. Autodesk Simulation Mechanical 2015 is used to carry out the numerical computations. Stress and displacement fields demonstrate that the values near the edge of joint where the stress singularity occurs are larger than that at the inner portion. From the numerical results, it is suggested that de-bonding of the interface may occur at the interface edge of the joint due to the higher stress concentration at the free edge.

A Computational Model for Biomechanical Effects of Arterial Compliance Mismatch

Directory of Open Access Journals (Sweden)

Fan He

2015-01-01

Full Text Available Background. Compliance mismatch is a negative factor and it needs to be considered in arterial bypass grafting. Objective. A computational model was employed to investigate the effects of arterial compliance mismatch on blood flow, wall stress, and deformation. Methods. The unsteady blood flow was assumed to be laminar, Newtonian, viscous, and incompressible. The vessel wall was assumed to be linear elastic, isotropic, and incompressible. The fluid-wall interaction scheme was constructed using the finite element method. Results. The results show that there are identical wall shear stress waveforms, wall stress, and strain waveforms at different locations. The comparison of the results demonstrates that wall shear stresses and wall strains are higher while wall stresses are lower at the more compliant section. The differences promote the probability of intimal thickening at some locations. Conclusions. The model is effective and gives satisfactory results. It could be extended to all kinds of arteries with complicated geometrical and material factors.

Elastic full-waveform inversion and parameterization analysis applied to walk-away vertical seismic profile data for unconventional (heavy oil) reservoir characterization

Science.gov (United States)

Pan, Wenyong; Innanen, Kristopher A.; Geng, Yu

2018-03-01

Seismic full-waveform inversion (FWI) methods hold strong potential to recover multiple subsurface elastic properties for hydrocarbon reservoir characterization. Simultaneously updating multiple physical parameters introduces the problem of interparameter tradeoff, arising from the covariance between different physical parameters, which increases nonlinearity and uncertainty of multiparameter FWI. The coupling effects of different physical parameters are significantly influenced by model parameterization and acquisition arrangement. An appropriate choice of model parameterization is critical to successful field data applications of multiparameter FWI. The objective of this paper is to examine the performance of various model parameterizations in isotropic-elastic FWI with walk-away vertical seismic profile (W-VSP) dataset for unconventional heavy oil reservoir characterization. Six model parameterizations are considered: velocity-density (α, β and ρ΄), modulus-density (κ, μ and ρ), Lamé-density (λ, μ΄ and ρ‴), impedance-density (IP, IS and ρ″), velocity-impedance-I (α΄, β΄ and I_P^'), and velocity-impedance-II (α″, β″ and I_S^'). We begin analyzing the interparameter tradeoff by making use of scattering radiation patterns, which is a common strategy for qualitative parameter resolution analysis. In this paper, we discuss the advantages and limitations of the scattering radiation patterns and recommend that interparameter tradeoffs be evaluated using interparameter contamination kernels, which provide quantitative, second-order measurements of the interparameter contaminations and can be constructed efficiently with an adjoint-state approach. Synthetic W-VSP isotropic-elastic FWI experiments in the time domain verify our conclusions about interparameter tradeoffs for various model parameterizations. Density profiles are most strongly influenced by the interparameter contaminations; depending on model parameterization, the inverted density

Elastic full-waveform inversion and parametrization analysis applied to walk-away vertical seismic profile data for unconventional (heavy oil) reservoir characterization

Science.gov (United States)

Pan, Wenyong; Innanen, Kristopher A.; Geng, Yu

2018-06-01

Seismic full-waveform inversion (FWI) methods hold strong potential to recover multiple subsurface elastic properties for hydrocarbon reservoir characterization. Simultaneously updating multiple physical parameters introduces the problem of interparameter trade-off, arising from the simultaneous variations of different physical parameters, which increase the nonlinearity and uncertainty of multiparameter FWI. The coupling effects of different physical parameters are significantly influenced by model parametrization and acquisition arrangement. An appropriate choice of model parametrization is important to successful field data applications of multiparameter FWI. The objective of this paper is to examine the performance of various model parametrizations in isotropic-elastic FWI with walk-away vertical seismic profile (W-VSP) data for unconventional heavy oil reservoir characterization. Six model parametrizations are considered: velocity-density (α, β and ρ΄), modulus-density (κ, μ and ρ), Lamé-density (λ, μ΄ and ρ‴), impedance-density (IP, IS and ρ″), velocity-impedance-I (α΄, β΄ and I_P^' }) and velocity-impedance-II (α″, β″ and I_S^' }). We begin analysing the interparameter trade-off by making use of scattering radiation patterns, which is a common strategy for qualitative parameter resolution analysis. We discuss the advantages and limitations of the scattering radiation patterns and recommend that interparameter trade-offs be evaluated using interparameter contamination kernels, which provide quantitative, second-order measurements of the interparameter contaminations and can be constructed efficiently with an adjoint-state approach. Synthetic W-VSP isotropic-elastic FWI experiments in the time domain verify our conclusions about interparameter trade-offs for various model parametrizations. Density profiles are most strongly influenced by the interparameter contaminations; depending on model parametrization, the inverted density

Accurate solution algorithms for incompressible multiphase flows

International Nuclear Information System (INIS)

Rider, W.J.; Kothe, D.B.; Mosso, S.J.; Cerutti, J.H.; Hochstein, J.I.

1994-01-01

A number of advances in modeling multiphase incompressible flow are described. These advances include high-order Godunov projection methods, piecewise linear interface reconstruction and tracking and the continuum surface force model. Examples are given

Application of elasticity theory at Sandia Labortories

International Nuclear Information System (INIS)

Davison, L.

1975-01-01

Examples are given of the application of linear elasticity theory to the solution of practical problems encountered at Sandia Laboratories. It is being applied to a very broad range of problems: those in one, two, and three spatial dimensions, some involving static and some dynamic response, to materials having isotropic and anisotropic symmetry, to homogeneous and inhomogeneous bodies, etc. Various extensions of the theory to include electric, magnetic and thermal effects, to account for material microstructure, for radiation and spall damage, chemical reactions, and other phenomena have been developed and/or applied. In some applications linear elasticity represents the physics of a problem well and is the theory of choice. In others the theory was used because it lent insight into a larger problem that was also attacked by means of other theories and/or experiment, and in some cases it serves as a part of a more encompassing theory

Existence Results for Incompressible Magnetoelasticity

Czech Academy of Sciences Publication Activity Database

Kružík, Martin; Stefanelli, U.; Zeman, J.

2015-01-01

Roč. 35, č. 6 (2015), s. 2615-2623 ISSN 1078-0947 R&D Projects: GA ČR GA13-18652S Institutional support: RVO:67985556 Keywords : magnetoelasticity * magnetostrictive solids * incompressibility * existence of minimizers * quasistatic evolution * energetic solution Subject RIV: BA - General Mathematics Impact factor: 1.127, year: 2015 http://library.utia.cas.cz/separaty/2015/MTR/kruzik-0443017.pdf

Anisotropic elasticity of silicon and its application to the modelling of X-ray optics

International Nuclear Information System (INIS)

Zhang, Lin; Barrett, Raymond; Cloetens, Peter; Detlefs, Carsten; Sanchez del Rio, Manuel

2014-01-01

Anisotropic elasticity of single-crystal silicon, applications to modelling of a bent X-ray mirror, and thermal deformation of a liquid-nitrogen-cooled monochromator crystal are presented. The crystal lattice of single-crystal silicon gives rise to anisotropic elasticity. The stiffness and compliance coefficient matrix depend on crystal orientation and, consequently, Young’s modulus, the shear modulus and Poisson’s ratio as well. Computer codes (in Matlab and Python) have been developed to calculate these anisotropic elasticity parameters for a silicon crystal in any orientation. These codes facilitate the evaluation of these anisotropy effects in silicon for applications such as microelectronics, microelectromechanical systems and X-ray optics. For mechanically bent X-ray optics, it is shown that the silicon crystal orientation is an important factor which may significantly influence the optics design and manufacturing phase. Choosing the appropriate crystal orientation can both lead to improved performance whilst lowering mechanical bending stresses. The thermal deformation of the crystal depends on Poisson’s ratio. For an isotropic constant Poisson’s ratio, ν, the thermal deformation (RMS slope) is proportional to (1 + ν). For a cubic anisotropic material, the thermal deformation of the X-ray optics can be approximately simulated by using the average of ν 12 and ν 13 as an effective isotropic Poisson’s ratio, where the direction 1 is normal to the optic surface, and the directions 2 and 3 are two normal orthogonal directions parallel to the optical surface. This average is independent of the direction in the optical surface (the crystal plane) for Si(100), Si(110) and Si(111). Using the effective isotropic Poisson’s ratio for these orientations leads to an error in thermal deformation smaller than 5.5%

Anisotropic elasticity of silicon and its application to the modelling of X-ray optics

Energy Technology Data Exchange (ETDEWEB)

Zhang, Lin, E-mail: zhang@esrf.fr; Barrett, Raymond; Cloetens, Peter; Detlefs, Carsten; Sanchez del Rio, Manuel [European Synchrotron Radiation Facility, 6 Rue Jules Horowitz, BP 220, 38043 Grenoble (France)

2014-04-04

Anisotropic elasticity of single-crystal silicon, applications to modelling of a bent X-ray mirror, and thermal deformation of a liquid-nitrogen-cooled monochromator crystal are presented. The crystal lattice of single-crystal silicon gives rise to anisotropic elasticity. The stiffness and compliance coefficient matrix depend on crystal orientation and, consequently, Young’s modulus, the shear modulus and Poisson’s ratio as well. Computer codes (in Matlab and Python) have been developed to calculate these anisotropic elasticity parameters for a silicon crystal in any orientation. These codes facilitate the evaluation of these anisotropy effects in silicon for applications such as microelectronics, microelectromechanical systems and X-ray optics. For mechanically bent X-ray optics, it is shown that the silicon crystal orientation is an important factor which may significantly influence the optics design and manufacturing phase. Choosing the appropriate crystal orientation can both lead to improved performance whilst lowering mechanical bending stresses. The thermal deformation of the crystal depends on Poisson’s ratio. For an isotropic constant Poisson’s ratio, ν, the thermal deformation (RMS slope) is proportional to (1 + ν). For a cubic anisotropic material, the thermal deformation of the X-ray optics can be approximately simulated by using the average of ν{sub 12} and ν{sub 13} as an effective isotropic Poisson’s ratio, where the direction 1 is normal to the optic surface, and the directions 2 and 3 are two normal orthogonal directions parallel to the optical surface. This average is independent of the direction in the optical surface (the crystal plane) for Si(100), Si(110) and Si(111). Using the effective isotropic Poisson’s ratio for these orientations leads to an error in thermal deformation smaller than 5.5%.

Elastic reflection based waveform inversion with a nonlinear approach

KAUST Repository

Guo, Qiang

2017-08-16

Full waveform inversion (FWI) is a highly nonlinear problem due to the complex reflectivity of the Earth, and this nonlinearity only increases under the more expensive elastic assumption. In elastic media, we need a good initial P-wave velocity and even a better initial S-wave velocity models with accurate representation of the low model wavenumbers for FWI to converge. However, inverting for the low wavenumber components of P- and S-wave velocities using reflection waveform inversion (RWI) with an objective to fit the reflection shape, rather than produce reflections, may mitigate the limitations of FWI. Because FWI, performing as a migration operator, is in preference of the high wavenumber updates along reflectors. We propose a nonlinear elastic RWI that inverts for both the low wavenumber and perturbation components of the P- and S-wave velocities. To generate the full elastic reflection wavefields, we derive an equivalent stress source made up by the inverted model perturbations and incident wavefields. We update both the perturbation and propagation parts of the velocity models in a nested fashion. Applications on synthetic isotropic models and field data show that our method can efficiently update the low and high wavenumber parts of the models.

Elastic reflection based waveform inversion with a nonlinear approach

KAUST Repository

Guo, Qiang; Alkhalifah, Tariq Ali

2017-01-01

Full waveform inversion (FWI) is a highly nonlinear problem due to the complex reflectivity of the Earth, and this nonlinearity only increases under the more expensive elastic assumption. In elastic media, we need a good initial P-wave velocity and even a better initial S-wave velocity models with accurate representation of the low model wavenumbers for FWI to converge. However, inverting for the low wavenumber components of P- and S-wave velocities using reflection waveform inversion (RWI) with an objective to fit the reflection shape, rather than produce reflections, may mitigate the limitations of FWI. Because FWI, performing as a migration operator, is in preference of the high wavenumber updates along reflectors. We propose a nonlinear elastic RWI that inverts for both the low wavenumber and perturbation components of the P- and S-wave velocities. To generate the full elastic reflection wavefields, we derive an equivalent stress source made up by the inverted model perturbations and incident wavefields. We update both the perturbation and propagation parts of the velocity models in a nested fashion. Applications on synthetic isotropic models and field data show that our method can efficiently update the low and high wavenumber parts of the models.

Direct numerical simulation of droplet-laden isotropic turbulence

Science.gov (United States)

Dodd, Michael S.

Interaction of liquid droplets with turbulence is important in numerous applications ranging from rain formation to oil spills to spray combustion. The physical mechanisms of droplet-turbulence interaction are largely unknown, especially when compared to that of solid particles. Compared to solid particles, droplets can deform, break up, coalesce and have internal fluid circulation. The main goal of this work is to investigate using direct numerical simulation (DNS) the physical mechanisms of droplet-turbulence interaction, both for non-evaporating and evaporating droplets. To achieve this objective, we develop and couple a new pressure-correction method with the volume-of-fluid (VoF) method for simulating incompressible two-fluid flows. The method's main advantage is that the variable coefficient Poisson equation that arises in solving the incompressible Navier-Stokes equations for two-fluid flows is reduced to a constant coefficient equation. This equation can then be solved directly using, e.g., the FFT-based parallel Poisson solver. For a 10243 mesh, our new pressure-correction method using a fast Poisson solver is ten to forty times faster than the standard pressure-correction method using multigrid. Using the coupled pressure-correction and VoF method, we perform direct numerical simulations (DNS) of 3130 finite-size, non-evaporating droplets of diameter approximately equal to the Taylor lengthscale and with 5% droplet volume fraction in decaying isotropic turbulence at initial Taylor-scale Reynolds number Relambda = 83. In the droplet-laden cases, we vary one of the following three parameters: the droplet Weber number based on the r.m.s. velocity of turbulence (0.1 ≤ Werms ≤ 5), the droplet- to carrier-fluid density ratio (1 ≤ rhod/rho c ≤ 100) or the droplet- to carrier-fluid viscosity ratio (1 ≤ mud/muc ≤ 100). We derive the turbulence kinetic energy (TKE) equations for the two-fluid, carrier-fluid and droplet-fluid flow. These equations allow

Three-dimensional nonlinear ideal MHD equilibria with field-aligned incompressible and compressible flows

International Nuclear Information System (INIS)

Moawad, S. M.; Ibrahim, D. A.

2016-01-01

The equilibrium properties of three-dimensional ideal magnetohydrodynamics (MHD) are investigated. Incompressible and compressible flows are considered. The governing equations are taken in a steady state such that the magnetic field is parallel to the plasma flow. Equations of stationary equilibrium for both of incompressible and compressible MHD flows are derived and described in a mathematical mode. For incompressible MHD flows, Alfvénic and non-Alfvénic flows with constant and variable magnetofluid density are investigated. For Alfvénic incompressible flows, the general three-dimensional solutions are determined with the aid of two potential functions of the velocity field. For non-Alfvénic incompressible flows, the stationary equilibrium equations are reduced to two differential constraints on the potential functions, flow velocity, magnetofluid density, and the static pressure. Some examples which may be of some relevance to axisymmetric confinement systems are presented. For compressible MHD flows, equations of the stationary equilibrium are derived with the aid of a single potential function of the velocity field. The existence of three-dimensional solutions for these MHD flows is investigated. Several classes of three-dimensional exact solutions for several cases of nonlinear equilibrium equations are presented.

Thermalization vs. isotropization and azimuthal fluctuations

International Nuclear Information System (INIS)

Mrowczynski, Stanislaw

2005-01-01

Hydrodynamic description requires a local thermodynamic equilibrium of the system under study but an approximate hydrodynamic behaviour is already manifested when a momentum distribution of liquid components is not of equilibrium form but merely isotropic. While the process of equilibration is relatively slow, the parton system becomes isotropic rather fast due to the plasma instabilities. Azimuthal fluctuations observed in relativistic heavy-ion collisions are argued to distinguish between a fully equilibrated and only isotropic parton system produced in the collision early stage

Rayleigh Waves in a Rotating Orthotropic Micropolar Elastic Solid Half-Space

Directory of Open Access Journals (Sweden)

Baljeet Singh

2013-01-01

Full Text Available A problem on Rayleigh wave in a rotating half-space of an orthotropic micropolar material is considered. The governing equations are solved for surface wave solutions in the half space of the material. These solutions satisfy the boundary conditions at free surface of the half-space to obtain the frequency equation of the Rayleigh wave. For numerical purpose, the frequency equation is approximated. The nondimensional speed of Rayleigh wave is computed and shown graphically versus nondimensional frequency and rotation-frequency ratio for both orthotropic micropolar elastic and isotropic micropolar elastic cases. The numerical results show the effects of rotation, orthotropy, and nondimensional frequency on the nondimensional speed of the Rayleigh wave.

On the isotropic elastic constants of graphite nodules in ductile cast iron: Analytical and numerical micromechanical investigations

DEFF Research Database (Denmark)

Andriollo, Tito; Hattel, Jesper

2016-01-01

A comprehensive description of the mechanical behavior of nodules in ductile iron is still missing in the published literature. Nevertheless, experimental evidence exists for the importance of such graphite particles during macroscopic material deformation, especially under compressive loading...... mesoscopic moduli in agreement with Young's modulus and Poisson's ratio recorded for common ferritic ductile iron grades. This suggests that graphite nodules may not be considered isotropic at the microscopic scale, at least from a mechanical viewpoint....

Regularity criteria for incompressible magnetohydrodynamics equations in three dimensions

International Nuclear Information System (INIS)

Lin, Hongxia; Du, Lili

2013-01-01

In this paper, we give some new global regularity criteria for three-dimensional incompressible magnetohydrodynamics (MHD) equations. More precisely, we provide some sufficient conditions in terms of the derivatives of the velocity or pressure, for the global regularity of strong solutions to 3D incompressible MHD equations in the whole space, as well as for periodic boundary conditions. Moreover, the regularity criterion involving three of the nine components of the velocity gradient tensor is also obtained. The main results generalize the recent work by Cao and Wu (2010 Two regularity criteria for the 3D MHD equations J. Diff. Eqns 248 2263–74) and the analysis in part is based on the works by Cao C and Titi E (2008 Regularity criteria for the three-dimensional Navier–Stokes equations Indiana Univ. Math. J. 57 2643–61; 2011 Gobal regularity criterion for the 3D Navier–Stokes equations involving one entry of the velocity gradient tensor Arch. Rational Mech. Anal. 202 919–32) for 3D incompressible Navier–Stokes equations. (paper)

Extreme non-linear elasticity and transformation optics

DEFF Research Database (Denmark)

Gersborg, Allan Roulund; Sigmund, Ole

2010-01-01

realizations correspond to minimizers of elastic energy potentials for extreme values of the mechanical Poisson's ratio ν . For TE (Hz) polarized light an incompressible transformation ν = 1/2 is ideal and for TM (E z) polarized light one should use a compressible transformation with negative Poissons's ratio......Transformation optics is a powerful concept for designing novel optical components such as high transmission waveguides and cloaking devices. The selection of specific transformations is a non-unique problem. Here we reveal that transformations which allow for all dielectric and broadband optical...... ν = -1. For the TM polarization the mechanical analogy corresponds to a modified Liao functional known from the transformation optics literature. Finally, the analogy between ideal transformations and solid mechanical material models automates and broadens the concept of transformation optics...

Weyl geometry and the nonlinear mechanics of distributed point defects

KAUST Repository

Yavari, A.

2012-09-05

The residual stress field of a nonlinear elastic solid with a spherically symmetric distribution of point defects is obtained explicitly using methods from differential geometry. The material manifold of a solid with distributed point defects-where the body is stress-free-is a flat Weyl manifold, i.e. a manifold with an affine connection that has non-metricity with vanishing traceless part, but both its torsion and curvature tensors vanish. Given a spherically symmetric point defect distribution, we construct its Weyl material manifold using the method of Cartan\\'s moving frames. Having the material manifold, the anelasticity problem is transformed to a nonlinear elasticity problem and reduces the problem of computing the residual stresses to finding an embedding into the Euclidean ambient space. In the case of incompressible neo-Hookean solids, we calculate explicitly this residual stress field. We consider the example of a finite ball and a point defect distribution uniform in a smaller ball and vanishing elsewhere. We show that the residual stress field inside the smaller ball is uniform and hydrostatic. We also prove a nonlinear analogue of Eshelby\\'s celebrated inclusion problem for a spherical inclusion in an isotropic incompressible nonlinear solid. © 2012 The Royal Society.

The Theory of Nearly Incompressible Magnetohydrodynamic Turbulence: Homogeneous Description

Science.gov (United States)

Zank, G. P.; Adhikari, L.; Hunana, P.; Shiota, D.; Bruno, R.; Telloni, D.; Avinash, K.

2017-09-01

The theory of nearly incompressible magnetohydrodynamics (NI MHD) was developed to understand the apparent incompressibility of the solar wind and other plasma environments, particularly the relationship of density fluctuations to incompressible manifestations of turbulence in the solar wind and interstellar medium. Of interest was the identification of distinct leading-order incompressible descriptions for plasma beta β ≫ 1 and β ∼ 1 or ≪ 1 environments. In the first case, the “dimensionality” of the MHD description is 3D whereas for the latter two, there is a collapse of dimensionality in that the leading-order incompressible MHD description is 2D in a plane orthogonal to the large-scale or mean magnetic field. Despite the success of NI MHD in describing fluctuations in a low-frequency plasma environment such as the solar wind, a basic turbulence description has not been developed. Here, we rewrite the NI MHD system in terms of Elsässer variables. We discuss the distinction that emerges between the three cases. However, we focus on the β ∼ 1 or ≪ 1 regimes since these are appropriate to the solar wind and solar corona. In both cases, the leading-order turbulence model describes 2D turbulence and the higher-order description corresponds to slab turbulence, which forms a minority component. The Elsäasser β ∼ 1 or ≪ 1 formulation exhibits the nonlinear couplings between 2D and slab components very clearly, and shows that slab fluctuations respond in a passive scalar sense to the turbulently evolving majority 2D component fluctuations. The coupling of 2D and slab fluctuations through the β ∼ 1 or ≪ 1 NI MHD description leads to a very natural emergence of the “Goldreich-Sridhar” critical balance scaling parameter, although now with a different interpretation. Specifically, the critical balance parameter shows that the energy flux in wave number space is a consequence of the intensity of Alfvén wave sweeping versus passive scalar

Parametric study of the deformation of transversely isotropic discs under diametral compression

Directory of Open Access Journals (Sweden)

Christos F. Markides

2017-07-01

Full Text Available The displacement field in a circular disc made of a transversely isotropic material is explored in a parametric manner. The disc is assumed to be loaded by a parabolic distribution of compressive radial stresses along two finite arcs of its periphery in the absence of any tangential (frictional stresses. Advantage is here taken of a recently introduced closed-form analytic solution for the displacement field developed in an orthotropic disc under diametral compression which was achieved adopting the complex potentials technique for rectilinear anisotropic materials as it was formulated in the pioneering work of S.G. Lekhnitskii. The analytic nature of this solution permits thorough, indepth exploration of the influence of some crucial parameters on the qualitative and quantitative characteristics of the deformation of transversely isotropic circular discs compressed between the jaws of the devise suggested by the International Society for Rock Mechanics for the standardized implementation of the Brazilian-disc test. The parameters considered include the anisotropy ratio (i.e., the ratio of the two elastic moduli characterizing the disc material, the angle between the loading axis and the planes of transverse isotropy and the length of the loaded arcs. Strongly non-linear relationships between these parameters and the components of the displacement field are revealed.

Elastic Properties of Tricalcium Aluminate from High-Pressure Experiments and First-Principles Calculations

KAUST Repository

Moon, Juhyuk

2012-06-04

The structure and elasticity of tricalcium aluminate (C 3A) have been experimentally and theoretically studied. From high-pressure X-ray diffraction experiments, the bulk modulus of 102(6) and 110(3) GPa were obtained by fitting second- and third-order finite strain equation of state, respectively. First-principles calculations with a generalized gradient approximation gave an isotropic bulk modulus of 102.1 GPa and an isothermal bulk modulus of 106.0 GPa. The static calculations using the exchange-correlation functional show an excellent agreement with the experimental measurements. Based on the agreement, accurate elastic constants and other elastic moduli were computed. The slight difference of behavior at high pressure can be explained by the infiltration of pressure-transmitting silicone oil into structural holes in C 3A. The computed elastic and mechanical properties will be useful in understanding structural and mechanical properties of cementitious materials, particularly with the increasing interest in the advanced applications at the nanoscale. © 2012 The American Ceramic Society.

Elastic Properties of Tricalcium Aluminate from High-Pressure Experiments and First-Principles Calculations

KAUST Repository

Moon, Juhyuk; Yoon, Seyoon; Wentzcovitch, Renata M.; Clark, Simon M.; Monteiro, Paulo J.M.

2012-01-01

The structure and elasticity of tricalcium aluminate (C 3A) have been experimentally and theoretically studied. From high-pressure X-ray diffraction experiments, the bulk modulus of 102(6) and 110(3) GPa were obtained by fitting second- and third-order finite strain equation of state, respectively. First-principles calculations with a generalized gradient approximation gave an isotropic bulk modulus of 102.1 GPa and an isothermal bulk modulus of 106.0 GPa. The static calculations using the exchange-correlation functional show an excellent agreement with the experimental measurements. Based on the agreement, accurate elastic constants and other elastic moduli were computed. The slight difference of behavior at high pressure can be explained by the infiltration of pressure-transmitting silicone oil into structural holes in C 3A. The computed elastic and mechanical properties will be useful in understanding structural and mechanical properties of cementitious materials, particularly with the increasing interest in the advanced applications at the nanoscale. © 2012 The American Ceramic Society.

A stable partitioned FSI algorithm for incompressible flow and deforming beams

International Nuclear Information System (INIS)

Li, L.; Henshaw, W.D.; Banks, J.W.; Schwendeman, D.W.; Main, A.

2016-01-01

An added-mass partitioned (AMP) algorithm is described for solving fluid–structure interaction (FSI) problems coupling incompressible flows with thin elastic structures undergoing finite deformations. The new AMP scheme is fully second-order accurate and stable, without sub-time-step iterations, even for very light structures when added-mass effects are strong. The fluid, governed by the incompressible Navier–Stokes equations, is solved in velocity-pressure form using a fractional-step method; large deformations are treated with a mixed Eulerian-Lagrangian approach on deforming composite grids. The motion of the thin structure is governed by a generalized Euler–Bernoulli beam model, and these equations are solved in a Lagrangian frame using two approaches, one based on finite differences and the other on finite elements. The key AMP interface condition is a generalized Robin (mixed) condition on the fluid pressure. This condition, which is derived at a continuous level, has no adjustable parameters and is applied at the discrete level to couple the partitioned domain solvers. Special treatment of the AMP condition is required to couple the finite-element beam solver with the finite-difference-based fluid solver, and two coupling approaches are described. A normal-mode stability analysis is performed for a linearized model problem involving a beam separating two fluid domains, and it is shown that the AMP scheme is stable independent of the ratio of the mass of the fluid to that of the structure. A traditional partitioned (TP) scheme using a Dirichlet–Neumann coupling for the same model problem is shown to be unconditionally unstable if the added mass of the fluid is too large. A series of benchmark problems of increasing complexity are considered to illustrate the behavior of the AMP algorithm, and to compare the behavior with that of the TP scheme. The results of all these benchmark problems verify the stability and accuracy of the AMP scheme. Results for

A stable partitioned FSI algorithm for incompressible flow and deforming beams

Energy Technology Data Exchange (ETDEWEB)

Li, L., E-mail: lil19@rpi.edu [Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180 (United States); Henshaw, W.D., E-mail: henshw@rpi.edu [Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180 (United States); Banks, J.W., E-mail: banksj3@rpi.edu [Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180 (United States); Schwendeman, D.W., E-mail: schwed@rpi.edu [Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180 (United States); Main, A., E-mail: amain8511@gmail.com [Department of Civil and Environmental Engineering, Duke University, Durham, NC 27708 (United States)

2016-05-01

An added-mass partitioned (AMP) algorithm is described for solving fluid–structure interaction (FSI) problems coupling incompressible flows with thin elastic structures undergoing finite deformations. The new AMP scheme is fully second-order accurate and stable, without sub-time-step iterations, even for very light structures when added-mass effects are strong. The fluid, governed by the incompressible Navier–Stokes equations, is solved in velocity-pressure form using a fractional-step method; large deformations are treated with a mixed Eulerian-Lagrangian approach on deforming composite grids. The motion of the thin structure is governed by a generalized Euler–Bernoulli beam model, and these equations are solved in a Lagrangian frame using two approaches, one based on finite differences and the other on finite elements. The key AMP interface condition is a generalized Robin (mixed) condition on the fluid pressure. This condition, which is derived at a continuous level, has no adjustable parameters and is applied at the discrete level to couple the partitioned domain solvers. Special treatment of the AMP condition is required to couple the finite-element beam solver with the finite-difference-based fluid solver, and two coupling approaches are described. A normal-mode stability analysis is performed for a linearized model problem involving a beam separating two fluid domains, and it is shown that the AMP scheme is stable independent of the ratio of the mass of the fluid to that of the structure. A traditional partitioned (TP) scheme using a Dirichlet–Neumann coupling for the same model problem is shown to be unconditionally unstable if the added mass of the fluid is too large. A series of benchmark problems of increasing complexity are considered to illustrate the behavior of the AMP algorithm, and to compare the behavior with that of the TP scheme. The results of all these benchmark problems verify the stability and accuracy of the AMP scheme. Results for

On preconditioning incompressible non-Newtonian flow problems

NARCIS (Netherlands)

He, X.; Neytcheva, M.; Vuik, C.

2013-01-01

This paper deals with fast and reliable numerical solution methods for the incompressible non-Newtonian Navier-Stokes equations. To handle the nonlinearity of the governing equations, the Picard and Newton methods are used to linearize these coupled partial differential equations. For space

Elastic Anisotropy of Basalt

Science.gov (United States)

Becker, K.; Shapiro, S.; Stanchits, S.; Dresen, G.; Kaselow, A.; Vinciguerra, S.

2005-12-01

Elastic properties of rocks are sensitive to changes of the in-situ stress and damage state. In particular, seismic velocities are strongly affected by stress-induced formation and deformation of cracks or shear-enhanced pore collapse. The effect of stress on seismic velocities as a result of pore space deformation in isotropic rock at isostatic compression may be expressed by the equation: A+K*P-B*exp (-D*P) (1), where P=Pc-Pp is the effective pressure, the pure difference between confining pressure and pore pressure. The parameter A, K, B and D describe material constants determined using experimental data. The physical meaning of the parameters is given by Shapiro (2003, in Geophysics Vol.68(Nr.2)). Parameter D is related to the stress sensitivity of the rock. A similar relation was derived by Shapiro and Kaselow (2005, in Geophysics in press) for weak anisotropic rocks under arbitrary load. They describe the stress dependent anisotropy in terms of Thomson's (1986, in Geophysics, Vol. 51(Nr.10)) anisotropy parameters ɛ and γ as a function of stress in the case of an initially isotropic rock: ɛ ∝ E2-E3, γ ∝ E3-E2 (2) with Ei=exp (D*Pi). The exponential terms Ei are controlled by the effective stress components Pi. To test this relation, we have conducted a series of triaxial compression tests on dry samples of initially isotropic Etnean Basalt in a servo-controlled MTS loading frame equipped with a pressure cell. Confining pressure was 60, 40 and 20 MPa. Samples were 5 cm in diameter and 10 cm in length. Elastic anisotropy was induced by axial compression of the samples through opening and growth of microcracks predominantly oriented parallel to the sample axis. Ultrasonic P- and S- wave velocities were monitored parallel and normal to the sample axis by an array of 20 piezoceramic transducers glued to the surface. Preamplified full waveform signals were stored in two 12 channel transient recorders. According to equation 2 the anisotropy parameters are

An analytical solution for the elastic response to surface loads imposed on a layered, transversely isotropic and self-gravitating Earth

DEFF Research Database (Denmark)

Pan, E.; Chen, J.Y.; Bevis, M.

2015-01-01

to a linear system of equations for the expansion coefficients. We then solve for the expansion coefficients analytically under the assumption (i.e. approximation) that in the mantle, the density in each layer varies as 1/r (where r is the radial coordinate) while the gravity is constant and that in the core...... the gravity in each layer varies linearly in r with constant density. These approximations dramatically simplify the subsequent mathematical analysis and render closed-form expressions for the expansion coefficients. We implement our solution in a MATLAB code and perform a benchmark which shows both...... the correctness of our solution and the implementation. We also calculate the load Love numbers (LLNs) of the PREM Earth for different degrees of the Legendre function for both isotropic and transversely isotropic, layered mantles with different core models, demonstrating for the first time the effect of Earth...

Inviscid incompressible limits on expanding domains

Czech Academy of Sciences Publication Activity Database

Feireisl, Eduard; Nečasová, Šárka; Sun, Y.

2014-01-01

Roč. 27, č. 10 (2014), s. 2465-2477 ISSN 0951-7715 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : compressible Navier-Stokes system * large domain * inviscid limit * incompressible limit Subject RIV: BA - General Mathematics Impact factor: 1.208, year: 2014 http://iopscience.iop.org/0951-7715/27/10/2465/

ACOUSTIC WAVES EMISSION IN THE TWO-COMPONENT HEREDITARY-ELASTIC MEDIUM

Directory of Open Access Journals (Sweden)

V. S. Polenov

2014-01-01

Full Text Available Summary. On the dynamics of two-component media a number of papers, which address the elastic waves in a homogeneous, unbounded fluid-saturated porous medium. In other studies address issues of dissipative processes in harmonic deformation hereditary elastic medium. In the article the dissipative processes of the viscoelastic porous medium, which hereditary properties are described by the core relaxation fractional exponential function U.N. Rabotnova integro-differential Boltzmann-Volterr ratio, harmonic deformation by the straining saturated incompressible liquid are investigated. Speed of wave propagation, absorption coefficient, mechanical loss tangent, logarithmic decrement, depending on fractional parameter γ, determining formulas received. The frequency logarithm and temperature graph dependences with the goal fractional parameter are constructed. Shows the dependences velocity and attenuation coefficient of the tangent of the phase angle of the logarithm of the temperature, and the dependence of the attenuation coefficient of the logarithm of the frequency. Dependencies the speed and the tangent of the phase angle of the frequency identical function of the logarithm of temperature.

Nuclear incompressibility: from finite nuclei to nuclear matter

International Nuclear Information System (INIS)

Treiner, J.; Krivine, H.; Bohigas, O.

1981-01-01

The recent increase of experimental data concerning the Giant Monopole Resonance Energy Esub(M) gives information on the incompressibility modulus of nuclear matter, provided one can extrapolate the incompressibility of a nucleus Ksub(A) defined by Esub(M)=[h 2 /m KA/ 2 >]sup(1/2), to the infinite medium. We discuss the theoretical interpretation of the coefficients of an Asup(-1/3) - expansion of Ksub(A) by studying the asymptotic behaviour of two RPA sum rules (corresponding to the scaling and the constrained model), evaluated using self-consistent Thomas-Fermi calculations. We show that the scaling model is the most suitable one as it leads to a rapidly converging Asup(-1/3)-expansion of the corresponding incompressibility Ksub(A)sup(S), whereas this is not the case with the constrained model. Some semi-empirical relations between the coefficients of the expansion of Ksub(A)sup(S) are established, which reduce to one the number of free-parameters in a best fit analysis of the experimental data. This reduction is essential due to the still limited number and accuracy of experimental data. We then show the compatibility of the data given by the various experimental groups with this parametrization and obtain a value of Ksub(nm)=220+-20 MeV, in good agreement with more microscopic analysis

Wave chaos in the elastic disk.

Science.gov (United States)

Sondergaard, Niels; Tanner, Gregor

2002-12-01

The relation between the elastic wave equation for plane, isotropic bodies and an underlying classical ray dynamics is investigated. We study, in particular, the eigenfrequencies of an elastic disk with free boundaries and their connection to periodic rays inside the circular domain. Even though the problem is separable, wave mixing between the shear and pressure component of the wave field at the boundary leads to an effective stochastic part in the ray dynamics. This introduces phenomena typically associated with classical chaos as, for example, an exponential increase in the number of periodic orbits. Classically, the problem can be decomposed into an integrable part and a simple binary Markov process. Similarly, the wave equation can, in the high-frequency limit, be mapped onto a quantum graph. Implications of this result for the level statistics are discussed. Furthermore, a periodic trace formula is derived from the scattering matrix based on the inside-outside duality between eigenmodes and scattering solutions and periodic orbits are identified by Fourier transforming the spectral density.

Direct differentiation of the quasi-incompressible fluid formulation of fluid-structure interaction using the PFEM

Science.gov (United States)

Zhu, Minjie; Scott, Michael H.

2017-07-01

Accurate and efficient response sensitivities for fluid-structure interaction (FSI) simulations are important for assessing the uncertain response of coastal and off-shore structures to hydrodynamic loading. To compute gradients efficiently via the direct differentiation method (DDM) for the fully incompressible fluid formulation, approximations of the sensitivity equations are necessary, leading to inaccuracies of the computed gradients when the geometry of the fluid mesh changes rapidly between successive time steps or the fluid viscosity is nonzero. To maintain accuracy of the sensitivity computations, a quasi-incompressible fluid is assumed for the response analysis of FSI using the particle finite element method and DDM is applied to this formulation, resulting in linearized equations for the response sensitivity that are consistent with those used to compute the response. Both the response and the response sensitivity can be solved using the same unified fractional step method. FSI simulations show that although the response using the quasi-incompressible and incompressible fluid formulations is similar, only the quasi-incompressible approach gives accurate response sensitivity for viscous, turbulent flows regardless of time step size.

Compression modes and the nuclear matter incompressibility ...

Indian Academy of Sciences (India)

We review the current status of the nuclear matter ( = and no Coulomb interaction) incompressibility coefficient, , and describe the theoretical and the experimental methods used to determine from properties of compression modes in nuclei. In particular we consider the long standing problem of the conflicting ...

NASA-VOF2D, 2-D Transient Free Surface Incompressible Fluid Dynamic

International Nuclear Information System (INIS)

Torrey, M.D.

1988-01-01

1 - Description of program or function: NASA-VOF2D is a two- dimensional, transient, free surface incompressible fluid dynamics program. It allows multiple free surfaces with surface tension and wall adhesion forces and has a partial cell treatment which allows curved boundaries and interior obstacles. 2 - Method of solution: NASA-VOF2D simulates incompressible flows with free surfaces using the volume-of-fluid (VOF) algorithm. This technique is based on the use of donor-acceptor differencing to track the free surface across an Eulerian grid. The complete Navier-Stokes equations in primitive variables for an incompressible fluid are solved by finite differences with surface tension and wall adhesion included. Optionally the pressure equation can be solved by a conjugate residual method rather than the successive over-relaxation (SOR) method

3D elastic inversion of vertical seismic profiles in horizontally stratified media; Inversion elastique 3D de profils sismiques verticaux en milieux stratifies horizontalement

Energy Technology Data Exchange (ETDEWEB)

Petit, J.L.

1997-07-21

This thesis is devoted to the inversion of VSP (vertical seismic profile) seismic data in order to determine the elastic properties of horizontally stratified media. The VSP records are computed using the full wave elastic modelling in isotropic and transversely isotropic media using Hankel transform, a finite difference scheme and an inverse Hankel transform algorithm, and the propagation equations are determined and numerically solved; the importance of considering a 3D wave propagation model instead of a 1 D one is emphasized. The theoretical VSP inverse problem is then considered, with the seismic waveform inversion set as a least-squares problem, consisting in recovering the distribution of physical parameters which minimize the misfit between calculated and observed VSP. The corresponding problem requires the knowledge of the source function

Elasto-plastic model for transversely isotropic Tournemire shale based on microstructure approach

International Nuclear Information System (INIS)

Abdi, H.; Evgin, E.; Fall, M.; Nguyen, T.S.; Labrie, D.; Barnichon, J.D.; Su, G.; Simon, R.

2012-01-01

Document available in extended abstract form only. Argillaceous formations being considered as potential host rocks for the geological disposal of nuclear wastes are usually characterized by the presence of bedding planes, resulting in anisotropy of their strength and deformation properties. A laboratory program of uniaxial tests, triaxial tests, cyclic tests, and Brazilian tests with concurrent monitoring of acoustic emission was performed in order to determine the above properties. The experimental results and their interpretation are presented in detail in a companion paper (Abdi et al., 2012, in these proceedings). Typical results from triaxial tests indicate the following behaviour: 1. There is a strong dependence of the stress-strain behaviour with the loading orientation with respect to the bedding planes. 2. There are four distinct zones of the stress strain curve: a crack and/or bedding closure zone; an elastic zone, a plastic zone with strain hardening, and a collapse zone after the peak that leads abruptly to a residual strength value. 3. There is damage, especially after the peak, resulting in the degradation of the stiffness as shown by unloading-reloading cycles. In order to reproduce the above behaviour, we adopted a classical elasto-plastic framework. In the elastic range, the transversely isotropic nature of the material is taken into account by the adoption of an elastic stiffness matrix that requires five independent elastic constants. These elastic constants show degradation with the accumulated damage. Using the deviatoric plastic strain as a measure of damage, we expressed functional relationships for these constants, using the results of cyclic triaxial tests. For the plastic behaviour, we used a Mohr-Coulomb yield criterion which takes into account the relative orientation of the applied stress and the bedding planes, and also strain hardening and softening. In this work we used the deviatoric plastic strain as the hardening parameter in

Elastic Properties of Synthetic Pyrope (Mg3Al2Si3O12) to 9 GPa and 1000°C

Science.gov (United States)

Gwanmesia, G. D.; Zhang, J.; Li, B.; Darling, K.; Kung, J.; Neuville, D.; Raterron, P.; Sullivan, S.; Liebermann, R. C.

2003-04-01

We have measured the elastic wave velocities of polycrystalline pyrope (Mg_3Al_2Si_3O12) to 9 GPa and 1000^oC by ultrasonic interferometry, combined with in-situ synchrotron x-ray diffraction and imaging techniques. Fine-grained polycrystalline specimens (99.5% of theoretical density) were hot-pressed from a homogeneous glass starting material in the USSA-2000 apparatus at Stony Brook; the physical properties of the recovered specimens were characterized with density measurements, x-ray diffraction and transmission electron microscopy. Bench-top elastic wave velocities were in excellent agreement with the isotropic averages calculated from single-crystal elastic moduli of Leitner et al. (1980) by the Hashin-Shtrikman method. Travel times of acoustic compressional (P) and shear (S) waves, specimen lengths and PVT equations of state for the specimen and a NaCl standard were measured to 9 GPa and 1000^oC in a DIA-type high pressure apparatus (SAM-85), installed on the superconducting wiggler beamline (X17B) at the National Synchrotron Light Source of the Brookhaven National Laboratory. These data enabled us to determine the pressure and temperature derivatives of the elastic wave velocities and moduli for isotropic pyrope. We compare our new values with those of previous investigators and discuss the implications of these data for interpreting the seismic velocity gradients in the transition zone of the Earth's mantle.

Traveltime dispersion in an isotropic elastic mantle: strong lower-mantle signal in differential-frequency residuals

Science.gov (United States)

Schuberth, Bernhard S. A.; Zaroli, Christophe; Nolet, Guust

2015-12-01

We study wavefield effects of direct P- and S-waves in elastic and isotropic 3-D seismic structures derived from the temperature field of a high-resolution mantle circulation model. More specifically, we quantify the dispersion of traveltime residuals caused by diffraction in structures with dynamically constrained length scales and magnitudes of the lateral variations in seismic velocities and density. 3-D global wave propagation is simulated using a spectral element method. Intrinsic attenuation (i.e. dissipation of seismic energy) is deliberately neglected, so that any variation of traveltimes with frequency can be attributed to structural effects. Traveltime residuals are measured at 15, 22.5, 34 and 51 s dominant periods by cross-correlation of 3-D and 1-D synthetic waveforms. Additional simulations are performed for a model in which 3-D structure is removed in the upper 800 km to isolate the dispersion signal of the lower mantle. We find that the structural length scales inherent to a vigorously convecting mantle give rise to significant diffraction-induced body-wave traveltime dispersion. For both P- and S-waves, the difference between long-period and short-period residuals for a given source-receiver pair can reach up to several seconds for the period bands considered here. In general, these `differential-frequency' residuals tend to increase in magnitude with increasing short-period delay. Furthermore, the long-period signal typically is smaller in magnitude than the short-period one; that is, wave-front healing is efficient independent of the sign of the residuals. Unlike the single-frequency residuals, the differential-frequency residuals are surprisingly similar between the `lower-mantle' and the `whole-mantle' model for corresponding source-receiver pairs. The similarity is more pronounced in case of S-waves and varies between different combinations of period bands. The traveltime delay acquired in the upper mantle seems to cancel in these differential

Preconditioned augmented Lagrangian formulation for nearly incompressible cardiac mechanics.

Science.gov (United States)

Campos, Joventino Oliveira; Dos Santos, Rodrigo Weber; Sundnes, Joakim; Rocha, Bernardo Martins

2018-04-01

Computational modeling of the heart is a subject of substantial medical and scientific interest, which may contribute to increase the understanding of several phenomena associated with cardiac physiological and pathological states. Modeling the mechanics of the heart have led to considerable insights, but it still represents a complex and a demanding computational problem, especially in a strongly coupled electromechanical setting. Passive cardiac tissue is commonly modeled as hyperelastic and is characterized by quasi-incompressible, orthotropic, and nonlinear material behavior. These factors are known to be very challenging for the numerical solution of the model. The near-incompressibility is known to cause numerical issues such as the well-known locking phenomenon and ill-conditioning of the stiffness matrix. In this work, the augmented Lagrangian method is used to handle the nearly incompressible condition. This approach can potentially improve computational performance by reducing the condition number of the stiffness matrix and thereby improving the convergence of iterative solvers. We also improve the performance of iterative solvers by the use of an algebraic multigrid preconditioner. Numerical results of the augmented Lagrangian method combined with a preconditioned iterative solver for a cardiac mechanics benchmark suite are presented to show its improved performance. Copyright © 2017 John Wiley & Sons, Ltd.

Traveltime Dispersion in an Isotropic Elastic Mantle: Dominance of the Lower Mantle Signal in Differential-frequency Time Residuals

Science.gov (United States)

Schuberth, B. S. A.; Zaroli, C.; Nolet, G.

2014-12-01

We study wavefield effects in elastic isotropic 3-D seismic structures derived from the temperature field of a high resolution mantle circulation model. More specifically, we quantify the structural dispersion of traveltime residuals of direct P- and S-waves in a model with realistic length-scales and magnitudes of the variations in seismic velocities and density. 3-D global wave propagation is simulated using a spectral element method, and traveltime residuals are measured in four different frequency bands by cross-correlation of 3-D and 1-D synthetic waveforms. Intrinsic (dissipative) attenuation is deliberately neglected, so that any variation of traveltimes with frequency can be attributed to structural effects. Additional simulations are performed for a model in which 3-D structure is removed in the upper 800 km to isolate the dispersion signal of the lower mantle. One question that we address is whether the structural length-scales inherent to a vigorously convecting mantle give rise to significant body-wave dispersion. In our synthetic dataset, the difference between long-period and short-period traveltime residuals generally increases with increasing short-period residual. However, we do not find an exact linear dependence, and in case of P-waves even non-monotonic behaviour. At largest short-period residuals, average dispersion is on the order of 2 s for both P- and S-waves and even larger when structure is confined to the lower mantle. Dispersion also appears to be asymmetric; that is, larger for negative than for positive residuals. The standard deviations of both P- and S-wave residuals also increase with increasing period and we discuss possible explanations for this behaviour. Overall, wavefield effects in both models are generally stronger for P-waves than for S-waves at the same frequencies. We also find that for certain combinations of periods, the difference between the respective residuals is very similar between the "whole mantle" and the "lower

Theory and Transport of Nearly Incompressible Magnetohydrodynamic Turbulence

Energy Technology Data Exchange (ETDEWEB)

Zank, G. P.; Adhikari, L.; Hunana, P. [Center for Space Plasma and Aeronomic Research (CSPAR), University of Alabama in Huntsville, Huntsville, AL 35805 (United States); Shiota, D. [Institute for Space-Earth Environmental Research, Nagoya University, Nagoya, Aichi 464-8601 (Japan); Bruno, R. [INAF-IAPS Istituto di Astrofisica e Planetologia Spaziali, Via del Fosso del Cavaliere 100, I-00133 Roma (Italy); Telloni, D. [INAF—Astrophysical Observatory of Torino, Via Osservatorio 20, I-10025 Pino Torinese (Italy)

2017-02-01

The theory of nearly incompressible magnetohydrodynamics (NI MHD) was developed largely in the early 1990s, together with an important extension to inhomogeneous flows in 2010. Much of the focus in the earlier work was to understand the apparent incompressibility of the solar wind and other plasma environments, and the relationship of density fluctuations to apparently incompressible manifestations of turbulence in the solar wind and interstellar medium. Further important predictions about the “dimensionality” of solar wind turbulence and its relationship to the plasma beta were made and subsequently confirmed observationally. However, despite the initial success of NI MHD in describing fluctuations in the solar wind, a detailed application to solar wind turbulence has not been undertaken. Here, we use the equations of NI MHD to describe solar wind turbulence, rewriting the NI MHD system in terms of Elsässer variables. Distinct descriptions of 2D and slab turbulence emerge naturally from the Elsässer formulation, as do the nonlinear couplings between 2D and slab components. For plasma beta order 1 or less regions, predictions for 2D and slab spectra result from the NI MHD description, and predictions for the spectral characteristics of density fluctuations can be made. We conclude by presenting a NI MHD formulation describing the transport of majority 2D and minority slab turbulence throughout the solar wind. A preliminary comparison of theory and observations is presented.

Leptodermous expansion of finite-nucleus incompressibility

International Nuclear Information System (INIS)

Nayak, R.C.

1990-01-01

We consider the influence of higher-order terms in the leptodermous expansion used to extract the incompressibility K v of infinite nuclear matter from data on the breathing mode of finite nuclei. The terms we calculate are the curvature term K cv A -2/3 , the surface-symmetry term K ss I 2 A -1/3 , the quartic volume-symmetry term K 4 I 4 , and a Coulomb-exchange term. Working within the framework of the scaling model we derive expressions for their coefficients in terms of quantities that are defined for infinite and semi-infinite nuclear matter. We calculate these coefficients for four different Skyrme-type forces, using the extended Thomas-Fermi (ETF) approximation. With the same forces we also calculate the incompressibility K (A, I) for a number of finite nuclei, fit the results to the leptodermous expansion, and thereby extract new results for the same coefficients. The comparison of the two calculations shows that the leptodermous expansion is converging rapidly. Of the new terms, the term K 4 I 4 is quite negligible, the curvature term should be included, and we discuss to what extent the other higher-order terms are significant. (orig.)

Simulating propagation of decoupled elastic waves using low-rank approximate mixed-domain integral operators for anisotropic media

KAUST Repository

Cheng, Jiubing; Alkhalifah, Tariq Ali; Wu, Zedong; Zou, Peng; Wang, Chenlong

2016-01-01

In elastic imaging, the extrapolated vector fields are decoupled into pure wave modes, such that the imaging condition produces interpretable images. Conventionally, mode decoupling in anisotropic media is costly because the operators involved are dependent on the velocity, and thus they are not stationary. We have developed an efficient pseudospectral approach to directly extrapolate the decoupled elastic waves using low-rank approximate mixed-domain integral operators on the basis of the elastic displacement wave equation. We have applied k-space adjustment to the pseudospectral solution to allow for a relatively large extrapolation time step. The low-rank approximation was, thus, applied to the spectral operators that simultaneously extrapolate and decompose the elastic wavefields. Synthetic examples on transversely isotropic and orthorhombic models showed that our approach has the potential to efficiently and accurately simulate the propagations of the decoupled quasi-P and quasi-S modes as well as the total wavefields for elastic wave modeling, imaging, and inversion.

Simulating propagation of decoupled elastic waves using low-rank approximate mixed-domain integral operators for anisotropic media

KAUST Repository

Cheng, Jiubing

2016-03-15

In elastic imaging, the extrapolated vector fields are decoupled into pure wave modes, such that the imaging condition produces interpretable images. Conventionally, mode decoupling in anisotropic media is costly because the operators involved are dependent on the velocity, and thus they are not stationary. We have developed an efficient pseudospectral approach to directly extrapolate the decoupled elastic waves using low-rank approximate mixed-domain integral operators on the basis of the elastic displacement wave equation. We have applied k-space adjustment to the pseudospectral solution to allow for a relatively large extrapolation time step. The low-rank approximation was, thus, applied to the spectral operators that simultaneously extrapolate and decompose the elastic wavefields. Synthetic examples on transversely isotropic and orthorhombic models showed that our approach has the potential to efficiently and accurately simulate the propagations of the decoupled quasi-P and quasi-S modes as well as the total wavefields for elastic wave modeling, imaging, and inversion.

Thermal stress state of laminated shells of revolution made of isotropic and linearly orthotropic materials

International Nuclear Information System (INIS)

Savchenko, V.G.

1995-01-01

In this investigation, we will use a cylindrical coordinate system to study the stress state of laminated shells of revolution made of inelastically deforming isotropic materials and elastic materials with linear orthotropy. One of the principal directions of anisotropy coincides with the axis of revolution of the body. The shells will be subjected to nonaxisymmetric loading by body bar K (K Z , K r , K var-phi ) and surface bar t n (t nz , t nr , t nvar-phi ) forces and heating. The level of loading is such that the rheological properties of the materials of the layers are not a factor, although their thermomechanical characteristics depend on temperature. In addition, the loading and heating of the body occur in such a way that simple (or close to simple) deformation processes take place in its isotropic elements. These processes are accompanied by inelastic strains and the formation of unloading regions in which plastic strains having the sign opposite the initial strains develop. It is assumed that the layers of the body are secured to one another without interference and that conditions corresponding to ideal contact prevail at their interfaces

Finite element method with quadratic quadrilateral unit for solving two dimensional incompressible N-S equation

International Nuclear Information System (INIS)

Tao Ganqiang; Yu Qing; Xiao Xiao

2011-01-01

Viscous and incompressible fluid flow is important for numerous engineering mechanics problems. Because of high non linear and incompressibility for Navier-Stokes equation, it is very difficult to solve Navier-Stokes equation by numerical method. According to its characters of Navier-Stokes equation, quartic derivation controlling equation of the two dimensional incompressible Navier-Stokes equation is set up firstly. The method solves the problem for dealing with vorticity boundary and automatically meets incompressibility condition. Then Finite Element equation for Navier-Stokes equation is proposed by using quadratic quadrilateral unit with 8 nodes in which the unit function is quadratic and non linear.-Based on it, the Finite Element program of quadratic quadrilateral unit with 8 nodes is developed. Lastly, numerical experiment proves the accuracy and dependability of the method and also shows the method has good application prospect in computational fluid mechanics. (authors)

Inviscid incompressible limits for rotating fluids

Czech Academy of Sciences Publication Activity Database

Caggio, Matteo; Nečasová, Šárka

2017-01-01

Roč. 163, November (2017), s. 1-18 ISSN 0362-546X R&D Projects: GA ČR GA16-03230S Institutional support: RVO:67985840 Keywords : compressible Navier -Stokces system * rotating fluids * incompressible limit Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.192, year: 2016 http://www.sciencedirect.com/science/article/pii/S0362546X17301815?via%3Dihub

Inviscid incompressible limits for rotating fluids

Czech Academy of Sciences Publication Activity Database

Caggio, Matteo; Nečasová, Šárka

2017-01-01

Roč. 163, November (2017), s. 1-18 ISSN 0362-546X R&D Projects: GA ČR GA16-03230S Institutional support: RVO:67985840 Keywords : compressible Navier-Stokces system * rotating fluids * incompressible limit Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.192, year: 2016 http://www.sciencedirect.com/science/article/pii/S0362546X17301815?via%3Dihub

Ultrasound elasticity imaging of human posterior tibial tendon

Science.gov (United States)

Gao, Liang

Posterior tibial tendon dysfunction (PTTD) is a common degenerative condition leading to a severe impairment of gait. There is currently no effective method to determine whether a patient with advanced PTTD would benefit from several months of bracing and physical therapy or ultimately require surgery. Tendon degeneration is closely associated with irreversible degradation of its collagen structure, leading to changes to its mechanical properties. If these properties could be monitored in vivo, it could be used to quantify the severity of tendonosis and help determine the appropriate treatment. Ultrasound elasticity imaging (UEI) is a real-time, noninvasive technique to objectively measure mechanical properties in soft tissue. It consists of acquiring a sequence of ultrasound frames and applying speckle tracking to estimate displacement and strain at each pixel. The goals of my dissertation were to 1) use acoustic simulations to investigate the performance of UEI during tendon deformation with different geometries; 2) develop and validate UEI as a potentially noninvasive technique for quantifying tendon mechanical properties in human cadaver experiments; 3) design a platform for UEI to measure mechanical properties of the PTT in vivo and determine whether there are detectable and quantifiable differences between healthy and diseased tendons. First, ultrasound simulations of tendon deformation were performed using an acoustic modeling program. The effects of different tendon geometries (cylinder and curved cylinder) on the performance of UEI were investigated. Modeling results indicated that UEI accurately estimated the strain in the cylinder geometry, but underestimated in the curved cylinder. The simulation also predicted that the out-of-the-plane motion of the PTT would cause a non-uniform strain pattern within incompressible homogeneous isotropic material. However, to average within a small region of interest determined by principal component analysis (PCA

Numerical implementation of a transverse-isotropic inelastic, work-hardening constitutive model

International Nuclear Information System (INIS)

Baladi, G.Y.

1977-01-01

This paper documents the numerical implementation of a model, specifically a transverse-isotropic, inelastic, work-hardening constitutive model. A brief overview of the mathematical formulation of the model is presented to facilitate the understanding of its numerical implementation. The model is based on incremental flow theories for materials which have time- and temperature-independent properties and which are capable of undergoing small plastic as well as small elastic strain at each loading increment. In addition, the model is written in terms of 'pseudo' stress invariants so that the incremental anisotropic stress-strain relationship can be readily incorporated into existing finite-difference or finite-element computer codes. The isotropic version of the model is retrieved without any changes in the mathematical formulation or in the numerical implementation (algorithm) of the model. Various methods exist for incorporating inelastic constitutive models into computer programs. The method presented in this paper is appropriate for both finite-difference and finite-element codes, and is applicable for solving static as wall as dynamic problems. This method expresses the material constitutive properties as a matrix of coefficients, C (generalized tangent moduli), which relates incremental stresses to incremental strains. It possesses desirable convergence properties. In either finite-difference or finite-element applications the input quantities are the initial stress components, obtained at the end of the previous strain increment, and the new strain increments. The output quantities are the new values of the stress components

Elastic scattering and ω meson production near the threshold of π-p → ω + n

International Nuclear Information System (INIS)

Karami, H.; Carr, J.; Debenham, N.C.; Garbutt, D.A.; Jones, W.G.; Binnie, D.M.; Keyne, J.; Moissidis, P.; Sarma, H.N.; Siotis, I.

1979-01-01

Measurements are reported of the differential cross section for the reaction π - +p → ω + n from threshold to a final-state c.m. momentum P* of 200 MeV/c. The previously reported fall in total cross section sigma/P* below about 100 MeV/c is again seen. The differential cross section remains close to isotropic over the entire range. A parallel experiment on the variation in the elastic differential cross section across the threshold shows evidence of this threshold. The elastic data cover a range of incident moments from 1010 to 1180 MeV/c in steps of 5 MeV/c. (Auth.)

Discrete Exterior Calculus Discretization of Incompressible Navier-Stokes Equations

KAUST Repository

Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi

2017-01-01

A conservative discretization of incompressible Navier-Stokes equations over surface simplicial meshes is developed using discrete exterior calculus (DEC). Numerical experiments for flows over surfaces reveal a second order accuracy

Efficient Parallel Algorithms for Unsteady Incompressible Flows

KAUST Repository

Guermond, Jean-Luc; Minev, Peter D.

2013-01-01

The objective of this paper is to give an overview of recent developments on splitting schemes for solving the time-dependent incompressible Navier–Stokes equations and to discuss possible extensions to the variable density/viscosity case. A particular attention is given to algorithms that can be implemented efficiently on large parallel clusters.

A new approach to determine geomechanical parameters of Vertical Transverse Isotropic media using VSP data

Science.gov (United States)

Gholami, Raoof; Moradzadeh, Ali; Rasouli, Vamegh; Hanachi, Javid

2014-12-01

Conventionally, high frequency Dipole Shear sonic Imager (DSI) logs are used for anisotropic modeling where fast and slow shear wave's velocities are required. However, the results obtained from a DSI log are restricted to a specific and possibly short interval of the wellbore. The aims of this paper are to use Vertical Seismic Profile (VSP) data and show its application in geomechanical analysis of subsurface layers under anisotropic condition. After processing and separating upgoing and downgoing P- and S-waves, a methodology based Vertical Transverse Isotropic (VTI) condition was presented to determine elastic stiffness parameters. Having stiffness parameters determined, elastic modulus, strength and in-situ stress parameters were estimated and calibrated against the field and core sample data. Although the VSP based geomechanical parameters were calibrated against the real field data, the accuracy of the method cannot be as much as that of the well logs. However, the method presented in this paper may become a very good asset for geomechanical evaluation of the intervals where well log data are not available.

Elastic-plastic behaviour of thick-walled containers considering plastic compressibility

International Nuclear Information System (INIS)

Betten, J.; Frosch, H.G.

1983-01-01

In this paper the elastic-plastic behaviour of thick-walled pressure vessels with internal and external pressure is studied. To describe the mechanical behaviour of isotropic, plastic compressible materials we use a plastic potential which is a single-valued function of the principle stresses. For cylinders and spheres an analytic expression for the computation of stresses and residual stresses is specified. Afterwards the strains are calculated by using the finite difference method. Some examples will high-light the influence of the plastic compressibility on the behaviour of pressure vessels. (orig.) [de

Self-similarity in incompressible Navier-Stokes equations.

Science.gov (United States)

Ercan, Ali; Kavvas, M Levent

2015-12-01

The self-similarity conditions of the 3-dimensional (3D) incompressible Navier-Stokes equations are obtained by utilizing one-parameter Lie group of point scaling transformations. It is found that the scaling exponents of length dimensions in i = 1, 2, 3 coordinates in 3-dimensions are not arbitrary but equal for the self-similarity of 3D incompressible Navier-Stokes equations. It is also shown that the self-similarity in this particular flow process can be achieved in different time and space scales when the viscosity of the fluid is also scaled in addition to other flow variables. In other words, the self-similarity of Navier-Stokes equations is achievable under different fluid environments in the same or different gravity conditions. Self-similarity criteria due to initial and boundary conditions are also presented. Utilizing the proposed self-similarity conditions of the 3D hydrodynamic flow process, the value of a flow variable at a specified time and space can be scaled to a corresponding value in a self-similar domain at the corresponding time and space.

Elastic and Mechanical Properties of the MAX Phases

Science.gov (United States)

Barsoum, Michel W.; Radovic, Miladin

2011-08-01

The more than 60 ternary carbides and nitrides, with the general formula Mn+1AXn—where n = 1, 2, or 3; M is an early transition metal; A is an A-group element (a subset of groups 13-16); and X is C and/or N—represent a new class of layered solids, where Mn+1Xn layers are interleaved with pure A-group element layers. The growing interest in the Mn+1AXn phases lies in their unusual, and sometimes unique, set of properties that can be traced back to their layered nature and the fact that basal dislocations multiply and are mobile at room temperature. Because of their chemical and structural similarities, the MAX phases and their corresponding MX phases share many physical and chemical properties. In this paper we review our current understanding of the elastic and mechanical properties of bulk MAX phases where they differ significantly from their MX counterparts. Elastically the MAX phases are in general quite stiff and elastically isotropic. The MAX phases are relatively soft (2-8 GPa), are most readily machinable, and are damage tolerant. Some of them are also lightweight and resistant to thermal shock, oxidation, fatigue, and creep. In addition, they behave as nonlinear elastic solids, dissipating 25% of the mechanical energy during compressive cycling loading of up to 1 GPa at room temperature. At higher temperatures, they undergo a brittle-to-plastic transition, and their mechanical behavior is a strong function of deformation rate.

Elastic-Plastic Constitutive Equation of WC-Co Cemented Carbides with Anisotropic Damage

International Nuclear Information System (INIS)

Hayakawa, Kunio; Nakamura, Tamotsu; Tanaka, Shigekazu

2007-01-01

Elastic-plastic constitutive equation of WC-Co cemented carbides with anisotropic damage is proposed to predict a precise service life of cold forging tools. A 2nd rank symmetric tensor damage tensor is introduced in order to express the stress unilaterality; a salient difference in uniaxial behavior between tension and compression. The conventional framework of irreversible thermodynamics is used to derive the constitutive equation. The Gibbs potential is formulated as a function of stress, damage tensor, isotropic hardening variable and kinematic hardening variable. The elastic-damage constitutive equation, conjugate forces of damage, isotropic hardening and kinematic hardening variable is derived from the potential. For the kinematic hardening variable, the superposition of three kinematic hardening laws is employed in order to improve the cyclic behavior of the material. For the evolution equation of the damage tensor, the damage is assumed to progress by fracture of the Co matrix - WC particle interface and by the mechanism of fatigue, i.e. the accumulation of microscopic plastic strain in matrix and particles. By using the constitutive equations, calculation of uniaxial tensile and compressive test is performed and the results are compared with the experimental ones in the literature. Furthermore, finite element analysis on cold forward extrusion was carried out, in which the proposed constitutive equation was employed as die insert material

Elastic-plastic analysis using an efficient formulation of the finite element method

International Nuclear Information System (INIS)

Aamodt, B.; Mo, O.

1975-01-01

Based on the flow theory of plasticity, the von Mises or the Tresca yield criterion and the isotropic hardening law, an incremental stiffness relationship can be established for a finite element model of the elasto-plastic structure. However, instead of including all degrees of freedom and all finite elements of the total model in a nonlinear solution process, a separation of elastic and plastic parts of the structure can be carried out. Such a separation can be obtained by identifying elastic parts of the structure as 'elastic' superelements and elasto-plastic parts of the structure as 'elasto-plastic' superelements. Also, it may be of advantage to use several levels of superelements in modelling the elastic parts of the structure. For the 'elasto-plastic' superelements the specific plastic computations such as updating of the incremental stiffness matrix and subsequent reduction (i.e. static condensation of all degrees of freedom being local to the superelements) have to be carried out repeatedly during the nonlinear solution process. The solution of the nonlinear equations is performed utilizing a combination of load incrementation and equilibrium interations. The present method of analysis is demonstrated for two larger examples of elasto-plastic analysis. (Auth.)

Calculation of incompressible fluid flow through cambered blades

Science.gov (United States)

Hsu, C. C.

1970-01-01

Conformal mapping technique yields linear, approximate solutions for calculating flow of an incompressible fluid through staggered array of cambered blades for the cases of flow with partial cavitation and supercavitation. Lift and drag coefficients, cavitation number, cavity shape, and exit flow conditions can be determined.

On an incompressible model in radiation hydrodynamics

Czech Academy of Sciences Publication Activity Database

Ducomet, B.; Nečasová, Šárka

2015-01-01

Roč. 38, č. 4 (2015), s. 765-774 ISSN 0170-4214 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : radiation hydrodynamics * incompressible Navier-Stokes-Fourier system * weak solution Subject RIV: BA - General Mathematics Impact factor: 1.002, year: 2015 http://onlinelibrary.wiley.com/doi/10.1002/mma.3107/abstract

Effect of inertia on laminar swimming and flying of an assembly of rigid spheres in an incompressible viscous fluid

Science.gov (United States)

Felderhof, B. U.

2015-11-01

A mechanical model of swimming and flying in an incompressible viscous fluid in the absence of gravity is studied on the basis of assumed equations of motion. The system is modeled as an assembly of rigid spheres subject to elastic direct interactions and to periodic actuating forces which sum to zero. Hydrodynamic interactions are taken into account in the virtual mass matrix and in the friction matrix of the assembly. An equation of motion is derived for the velocity of the geometric center of the assembly. The mean power is calculated as the mean rate of dissipation. The full range of viscosity is covered, so that the theory can be applied to the flying of birds, as well as to the swimming of fish or bacteria. As an example a system of three equal spheres moving along a common axis is studied.

Reflection and refraction of elastic waves at a corrugated interface in a bi-material transversely isotropic full-space

International Nuclear Information System (INIS)

Shad-Manamen, N.; Eskandari-Ghadi, M.

2008-01-01

The existing theory for wave propagation through a soil layer are not compatible with the real soil layers because in the theory the layers are flat and the sub-layers are parallel, while in real the soil layers are not flat and they may not be parallel. Thus, wave propagations through a corrugated interface are so important. In this paper, a two dimensional SH-wave propagation through a corrugated interface between two linear transversely isotropic half-spaces is assessed. In order to do this, Lord Rayleigh's method is accepted to express the non-flat surface by a Fourier series. In this way, the amplitude of the reflected and transmitted waves is analytically determined in terms of the incident SH-wave amplitude. It is shown that except for the regular reflected and refracted waves, some irregular reflected and refracted waves are exist, and the amplitudes of these waves vary in terms of the angle and frequency of incident wave, equation of surface, and the material properties of the domains. The numerical computations for some cases of different amplitude/wave-length ratio of the interface are done. This work is an extension of Asano's paper (1960) for a more complicated interface, where more non-zero coefficients are considered in expressing the equation of surface in the form of Fourier series. The analytical results for some simpler case of isotropic domain are collapsed on Asano's results (1960). In addition, the numerical evaluation is in good agreement with Asano's.

Intra-connected three-dimensionally isotropic bulk negative index photonic metamaterial

International Nuclear Information System (INIS)

Guney, Durdu; Koschny, Thomas; Soukoulis, Costas

2010-01-01

Isotropic negative index metamaterials (NIMs) are highly desired, particularly for the realization of ultra-high resolution lenses. However, existing isotropic NIMs function only two-dimensionally and cannot be miniaturized beyond microwaves. Direct laser writing processes can be a paradigm shift toward the fabrication of three-dimensionally (3D) isotropic bulk optical metamaterials, but only at the expense of an additional design constraint, namely connectivity. Here, we demonstrate with a proof-of-principle design that the requirement connectivity does not preclude fully isotropic left-handed behavior. This is an important step towards the realization of bulk 3D isotropic NIMs at optical wavelengths.

Rocking Rotation of a Rigid Disk Embedded in a Transversely Isotropic Half-Space

Directory of Open Access Journals (Sweden)

Seyed Ahmadi

2014-06-01

Full Text Available The asymmetric problem of rocking rotation of a circular rigid disk embedded in a finite depth of a transversely isotropic half-space is analytically addressed. The rigid disk is assumed to be in frictionless contact with the elastic half-space. By virtue of appropriate Green's functions, the mixed boundary value problem is written as a dual integral equation. Employing further mathematical techniques, the integral equation is reduced to a well-known Fredholm integral equation of the second kind. The results related to the contact stress distribution across the disk region and the equivalent rocking stiffness of the system are expressed in terms of the solution of the obtained Fredholm  integral  equation. When the rigid disk is located on the surface or at the remote boundary, the exact closed-form solutions are presented. For verification purposes, the limiting case of an isotropic half-space is considered and the results are verified with those available in the literature. The jump behavior in the results at the edge of the rigid disk for the case of an infinitesimal embedment is highlighted analytically for the first time. Selected numerical results are depicted for the contact stress distribution across the disk region, rocking stiffness of the system, normal stress, and displacement components along the radial axis. Moreover, effects of anisotropy on the rocking stiffness factor are discussed in detail.

A numerical approximation to the elastic properties of sphere-reinforced composites

Science.gov (United States)

Segurado, J.; Llorca, J.

2002-10-01

Three-dimensional cubic unit cells containing 30 non-overlapping identical spheres randomly distributed were generated using a new, modified random sequential adsortion algorithm suitable for particle volume fractions of up to 50%. The elastic constants of the ensemble of spheres embedded in a continuous and isotropic elastic matrix were computed through the finite element analysis of the three-dimensional periodic unit cells, whose size was chosen as a compromise between the minimum size required to obtain accurate results in the statistical sense and the maximum one imposed by the computational cost. Three types of materials were studied: rigid spheres and spherical voids in an elastic matrix and a typical composite made up of glass spheres in an epoxy resin. The moduli obtained for different unit cells showed very little scatter, and the average values obtained from the analysis of four unit cells could be considered very close to the "exact" solution to the problem, in agreement with the results of Drugan and Willis (J. Mech. Phys. Solids 44 (1996) 497) referring to the size of the representative volume element for elastic composites. They were used to assess the accuracy of three classical analytical models: the Mori-Tanaka mean-field analysis, the generalized self-consistent method, and Torquato's third-order approximation.

Methods of Investigation of Equations that Describe Waves in Tubes with Elastic Walls and Application of the Theory of Reversible and Weak Dissipative Shocks

Science.gov (United States)

Bakholdin, Igor

2018-02-01

Various models of a tube with elastic walls are investigated: with controlled pressure, filled with incompressible fluid, filled with compressible gas. The non-linear theory of hyperelasticity is applied. The walls of a tube are described with complete membrane model. It is proposed to use linear model of plate in order to take the bending resistance of walls into account. The walls of the tube were treated previously as inviscid and incompressible. Compressibility of material of walls and viscosity of material, either gas or liquid are considered. Equations are solved numerically. Three-layer time and space centered reversible numerical scheme and similar two-layer space reversible numerical scheme with approximation of time derivatives by Runge-Kutta method are used. A method of correction of numerical schemes by inclusion of terms with highorder derivatives is developed. Simplified hyperbolic equations are derived.

On elastic waves in an thinly-layered laminated medium with stress couples under initial stress

Directory of Open Access Journals (Sweden)

P. Pal Roy

1988-01-01

Full Text Available The present work is concerned with a simple transformation rule in finding out the composite elastic coefficients of a thinly layered laminated medium whose bulk properties are strongly anisotropic with a microelastic bending rigidity. These elastic coefficients which were not known completely for a layered laminated structure, are obtained suitably in terms of initial stress components and Lame's constants λi, μi of initially isotropic solids. The explicit solutions of the dynamical equations for a prestressed thinly layered laminated medium under horizontal compression in a gravity field are derived. The results are discussed specifying the effects of hydrostatic, deviatoric and couple stresses upon the characteristic propagation velocities of shear and compression wave modes.

On PDE analysis of flows of quasi-incompressible fluids

Czech Academy of Sciences Publication Activity Database

Feireisl, Eduard; Lu, Y.; Málek, J.

2016-01-01

Roč. 96, č. 4 (2016), s. 491-508 ISSN 0044-2267 Keywords : quasi-incompressible fluids * weak solution Subject RIV: BA - General Mathematics Impact factor: 1.332, year: 2016 http://onlinelibrary.wiley.com/doi/10.1002/zamm.201400229

Qualitative behaviour of incompressible two-phase flows with phase ...

Indian Academy of Sciences (India)

Jan Prüss

2017-11-07

Nov 7, 2017 ... Qualitative behaviour of incompressible two-phase flows with phase ... Germany. 2Graduate School of Human and Environmental Studies, Kyoto University, ... Note that j is a dummy variable as it can be eliminated from the ...

Lattice Boltzmann model for three-dimensional decaying homogeneous isotropic turbulence

International Nuclear Information System (INIS)

Xu Hui; Tao Wenquan; Zhang Yan

2009-01-01

We implement a lattice Boltzmann method (LBM) for decaying homogeneous isotropic turbulence based on an analogous Galerkin filter and focus on the fundamental statistical isotropic property. This regularized method is constructed based on orthogonal Hermite polynomial space. For decaying homogeneous isotropic turbulence, this regularized method can simulate the isotropic property very well. Numerical studies demonstrate that the novel regularized LBM is a promising approximation of turbulent fluid flows, which paves the way for coupling various turbulent models with LBM

Torsion of a Cosserat elastic bar with square cross section: theory and experiment

Science.gov (United States)

Drugan, W. J.; Lakes, R. S.

2018-04-01

An approximate analytical solution for the displacement and microrotation vector fields is derived for pure torsion of a prismatic bar with square cross section comprised of homogeneous, isotropic linear Cosserat elastic material. This is accomplished by analytical simplification coupled with use of the principle of minimum potential energy together with polynomial representations for the desired field components. Explicit approximate expressions are derived for cross section warp and for applied torque versus angle of twist of the bar. These show that torsional rigidity exceeds the classical elasticity value, the difference being larger for slender bars, and that cross section warp is less than the classical amount. Experimental measurements on two sets of 3D printed square cross section polymeric bars, each set having a different microstructure and four different cross section sizes, revealed size effects not captured by classical elasticity but consistent with the present analysis for physically sensible values of the Cosserat moduli. The warp can allow inference of Cosserat elastic constants independently of any sensitivity the material may have to dilatation gradients; warp also facilitates inference of Cosserat constants that are difficult to obtain via size effects.

Change in physical properties of high density isotropic graphites irradiated in the ?JOYO? fast reactor

Science.gov (United States)

Maruyama, T.; Kaito, T.; Onose, S.; Shibahara, I.

1995-08-01

Thirteen kinds of isotropic graphites with different density and maximum grain size were irradiated in the experimental fast reactor "JOYO" to fluences from 2.11 to 2.86 × 10 26 n/m 2 ( E > 0.1 MeV) at temperatures from 549 to 597°C. Postirradiation examination was carried out on the dimensional changes, elastic modulus, and thermal conductivity of these materials. Dimensional change results indicate that the graphites irradiated at lower fluences showed shrinkage upon neutron irradiation followed by increase with increasing neutron fluences, irrespective of differences in material parameters. The Young's modulus and Poisson's ratio increased by two to three times the unirradiated values. The large scatter found in Poisson's ratio of unirradiated materials became very small and a linear dependence on density was obtained after irradiation. The thermal conductivity decreased to one-fifth to one-tenth of unirradiated values, with a negligible change in specific heat. The results of postirradiation examination indicated that the changes in physical properties of high density, isotropic graphites were mainly dominated by the irradiation condition rather than their material parameters. Namely, the effects of irradiation induced defects on physical properties of heavily neutron-irradiated graphites are much larger than that of defects associated with as-fabricated specimens.

Change in physical properties of high density isotropic graphites irradiated in the ''JOYO'' fast reactor

International Nuclear Information System (INIS)

Maruyama, T.; Kaito, T.; Onose, S.; Shibahara, I.

1995-01-01

Thirteen kinds of isotropic graphites with different density and maximum grain size were irradiated in the experimental fast reactor ''JOYO'' to fluences from 2.11 to 2.86x10 26 n/m 2 (E>0.1 MeV) at temperatures from 549 to 597 C. Postirradiation examination was carried out on the dimensional changes, elastic modulus, and thermal conductivity of these materials. Dimensional change results indicate that the graphites irradiated at lower fluences showed shrinkage upon neutron irradiation followed by increase with increasing neutron fluences, irrespective of differences in material parameters. The Young's modulus and Poisson's ratio increased by two to three times the unirradiated values. The large scatter found in Poisson's ratio of unirradiated materials became very small and a linear dependence on density was obtained after irradiation. The thermal conductivity decreased to one-fifth to one-tenth of unirradiated values, with a negligible change in specific heat. The results of postirradiation examination indicated that the changes in physical properties of high density, isotropic graphites were mainly dominated by the irradiation condition rather than their material parameters. Namely, the effects of irradiation induced defects on physical properties of heavily neutron-irradiated graphites are much larger than that of defects associated with as-fabricated specimens. (orig.)

Sudden Relaminarization and Lifetimes in Forced Isotropic Turbulence.

Science.gov (United States)

Linkmann, Moritz F; Morozov, Alexander

2015-09-25

We demonstrate an unexpected connection between isotropic turbulence and wall-bounded shear flows. We perform direct numerical simulations of isotropic turbulence forced at large scales at moderate Reynolds numbers and observe sudden transitions from a chaotic dynamics to a spatially simple flow, analogous to the laminar state in wall bounded shear flows. We find that the survival probabilities of turbulence are exponential and the typical lifetimes increase superexponentially with the Reynolds number. Our results suggest that both isotropic turbulence and wall-bounded shear flows qualitatively share the same phase-space dynamics.

Local mesh refinement for incompressible fluid flow with free surfaces

Energy Technology Data Exchange (ETDEWEB)

Terasaka, H.; Kajiwara, H.; Ogura, K. [Tokyo Electric Power Company (Japan)] [and others

1995-09-01

A new local mesh refinement (LMR) technique has been developed and applied to incompressible fluid flows with free surface boundaries. The LMR method embeds patches of fine grid in arbitrary regions of interest. Hence, more accurate solutions can be obtained with a lower number of computational cells. This method is very suitable for the simulation of free surface movements because free surface flow problems generally require a finer computational grid to obtain adequate results. By using this technique, one can place finer grids only near the surfaces, and therefore greatly reduce the total number of cells and computational costs. This paper introduces LMR3D, a three-dimensional incompressible flow analysis code. Numerical examples calculated with the code demonstrate well the advantages of the LMR method.

Isotropic Growth of Graphene toward Smoothing Stitching.

Science.gov (United States)

Zeng, Mengqi; Tan, Lifang; Wang, Lingxiang; Mendes, Rafael G; Qin, Zhihui; Huang, Yaxin; Zhang, Tao; Fang, Liwen; Zhang, Yanfeng; Yue, Shuanglin; Rümmeli, Mark H; Peng, Lianmao; Liu, Zhongfan; Chen, Shengli; Fu, Lei

2016-07-26

The quality of graphene grown via chemical vapor deposition still has very great disparity with its theoretical property due to the inevitable formation of grain boundaries. The design of single-crystal substrate with an anisotropic twofold symmetry for the unidirectional alignment of graphene seeds would be a promising way for eliminating the grain boundaries at the wafer scale. However, such a delicate process will be easily terminated by the obstruction of defects or impurities. Here we investigated the isotropic growth behavior of graphene single crystals via melting the growth substrate to obtain an amorphous isotropic surface, which will not offer any specific grain orientation induction or preponderant growth rate toward a certain direction in the graphene growth process. The as-obtained graphene grains are isotropically round with mixed edges that exhibit high activity. The orientation of adjacent grains can be easily self-adjusted to smoothly match each other over a liquid catalyst with facile atom delocalization due to the low rotation steric hindrance of the isotropic grains, thus achieving the smoothing stitching of the adjacent graphene. Therefore, the adverse effects of grain boundaries will be eliminated and the excellent transport performance of graphene will be more guaranteed. What is more, such an isotropic growth mode can be extended to other types of layered nanomaterials such as hexagonal boron nitride and transition metal chalcogenides for obtaining large-size intrinsic film with low defect.

Point force singularities outside a drop covered with an incompressible surfactant: Image systems and their applications

Science.gov (United States)

Shaik, Vaseem A.; Ardekani, Arezoo M.

2017-11-01

In this work we derive the image flow fields for point force singularities placed outside a stationary drop covered with an insoluble, nondiffusing, and incompressible surfactant. We assume the interface to be Newtonian and use the Boussinesq-Scriven constitutive law for the interfacial stress tensor. We use this analytical solution to investigate two different problems. First, we derive the mobility matrix for two drops of arbitrary sizes covered with an incompressible surfactant. In the second example, we calculate the velocity of a swimming microorganism (modeled as a Stokes dipole) outside a drop covered with an incompressible surfactant.

Effect of hydrostatic pressure in the ground state on the perturbed elastic deformable bodies in first post-Newtonian approximation

International Nuclear Information System (INIS)

Song Guoxuan

2009-01-01

Based on the dynamical equations for a nonrotating elastic deformable astronomical body in the first post-Newtonian approximation of Einstein's theory of gravity, we re-examined the boundary(junction) conditions and have proven that a term, which is missing in the customary boundary(junction) conditions, is found. This term is induced by the existence of initial equilibrium hydrostatic pressure. A physical explanation of this term is given in the Newtonian approximation as well. By using the correcting boundary conditions the relation of the free spherically symmetrical radial oscillation frequency of a nonrotating homogeneously and isotropically elastic sphere with constant density is derived.

Time-asymptotic interaction of flocking particles and an incompressible viscous fluid

International Nuclear Information System (INIS)

Bae, Hyeong-Ohk; Choi, Young-Pil; Ha, Seung-Yeal; Kang, Moon-Jin

2012-01-01

We present a new coupled kinetic-fluid model for the interactions between Cucker–Smale (C–S) flocking particles and incompressible fluid on the periodic spatial domain T d . Our coupled system consists of the kinetic C–S equation and the incompressible Navier–Stokes equations, and these two systems are coupled through the drag force. For the proposed model, we provide a global existence of weak solutions and a priori time-asymptotic exponential flocking estimates for any smooth flow, when the kinematic viscosity of the fluid is sufficiently large. The velocity of individual C–S particles and fluid velocity tend to the averaged time-dependent particle velocities exponentially fast

An Ab-initio study of structural, elastic, electronic and thermodynamic properties of triclinic Cu{sub 7}In{sub 3}

Energy Technology Data Exchange (ETDEWEB)

Yu, Ching-Feng [Department of Power Mechanical Engineering, National Tsing Hua University, Hsinchu 30013, Taiwan (China); Cheng, Hsien-Chie, E-mail: hccheng@fcu.edu.tw [Department of Aerospace and Systems Engineering, Feng Chia University, Taichung 40724, Taiwan (China); Chen, Wen-Hwa, E-mail: whchen@pme.nthu.edu.tw [Department of Power Mechanical Engineering, National Tsing Hua University, Hsinchu 30013, Taiwan (China)

2016-05-01

First principles density functional theory calculations within the generalized gradient approximation are performed to comprehensively study the structural, elastic, electronic and thermodynamic properties of triclinic single and polycrystalline Cu{sub 7}In{sub 3}. The polycrystalline elastic properties are predicted using the Voigt–Reuss–Hill approximation and the thermodynamic properties are evaluated based on the quasi-harmonic Debye model. Their temperature, hydrostatic pressure or crystal orientation dependences are also addressed, and the predicted physical properties are compared with the literature experimental and theoretical data and also with those of three other Cu–In compounds, i.e., CuIn, Cu{sub 2}In and Cu{sub 11}In{sub 9}. The present calculations show that in addition to being a much better conductor compared to Cu{sub 2}In and Cu{sub 11}In{sub 9}, Cu{sub 7}In{sub 3} crystal reveals weak elastic anisotropy, high ductility and low stiffness, and tends to become more elastically isotropic at very high hydrostatic pressure. Moreover, the Cu{sub 7}In{sub 3} holds the largest high-temperature heat capacity among the four Cu–In compounds. - Highlights: • The physical property of Cu{sub 7}In{sub 3} is reported by first-principles calculations. • Pressure effect on the physical property of Cu{sub 7}In{sub 3} is presented. • The calculated lattice constants of Cu{sub 7}In{sub 3} agree well with the experimental data. • Cu{sub 7}In{sub 3} tends to become more elastically isotropic at very high pressure. • The heat capacity of Cu{sub 7}In{sub 3} is much larger than that of CuIn, Cu{sub 2}In and Cu{sub 11}In{sub 9}.

Multiparameter elastic full waveform inversion with facies-based constraints

Science.gov (United States)

Zhang, Zhen-dong; Alkhalifah, Tariq; Naeini, Ehsan Zabihi; Sun, Bingbing

2018-06-01

Full waveform inversion (FWI) incorporates all the data characteristics to estimate the parameters described by the assumed physics of the subsurface. However, current efforts to utilize FWI beyond improved acoustic imaging, like in reservoir delineation, faces inherent challenges related to the limited resolution and the potential trade-off between the elastic model parameters. Some anisotropic parameters are insufficiently updated because of their minor contributions to the surface collected data. Adding rock physics constraints to the inversion helps mitigate such limited sensitivity, but current approaches to add such constraints are based on including them as a priori knowledge mostly valid around the well or as a global constraint for the whole area. Since similar rock formations inside the Earth admit consistent elastic properties and relative values of elasticity and anisotropy parameters (this enables us to define them as a seismic facies), utilizing such localized facies information in FWI can improve the resolution of inverted parameters. We propose a novel approach to use facies-based constraints in both isotropic and anisotropic elastic FWI. We invert for such facies using Bayesian theory and update them at each iteration of the inversion using both the inverted models and a priori information. We take the uncertainties of the estimated parameters (approximated by radiation patterns) into consideration and improve the quality of estimated facies maps. Four numerical examples corresponding to different acquisition, physical assumptions and model circumstances are used to verify the effectiveness of the proposed method.

Multiparameter Elastic Full Waveform Inversion with Facies-based Constraints

Science.gov (United States)

Zhang, Zhen-dong; Alkhalifah, Tariq; Naeini, Ehsan Zabihi; Sun, Bingbing

2018-03-01

Full waveform inversion (FWI) incorporates all the data characteristics to estimate the parameters described by the assumed physics of the subsurface. However, current efforts to utilize full waveform inversion beyond improved acoustic imaging, like in reservoir delineation, faces inherent challenges related to the limited resolution and the potential trade-off between the elastic model parameters. Some anisotropic parameters are insufficiently updated because of their minor contributions to the surface collected data. Adding rock physics constraints to the inversion helps mitigate such limited sensitivity, but current approaches to add such constraints are based on including them as a priori knowledge mostly valid around the well or as a global constraint for the whole area. Since similar rock formations inside the Earth admit consistent elastic properties and relative values of elasticity and anisotropy parameters (this enables us to define them as a seismic facies), utilizing such localized facies information in FWI can improve the resolution of inverted parameters. We propose a novel approach to use facies-based constraints in both isotropic and anisotropic elastic FWI. We invert for such facies using Bayesian theory and update them at each iteration of the inversion using both the inverted models and a prior information. We take the uncertainties of the estimated parameters (approximated by radiation patterns) into consideration and improve the quality of estimated facies maps. Four numerical examples corresponding to different acquisition, physical assumptions and model circumstances are used to verify the effectiveness of the proposed method.

Multiparameter Elastic Full Waveform Inversion with Facies-based Constraints

KAUST Repository

Zhang, Zhendong

2018-03-20

Full waveform inversion (FWI) incorporates all the data characteristics to estimate the parameters described by the assumed physics of the subsurface. However, current efforts to utilize full waveform inversion beyond improved acoustic imaging, like in reservoir delineation, faces inherent challenges related to the limited resolution and the potential trade-off between the elastic model parameters. Some anisotropic parameters are insufficiently updated because of their minor contributions to the surface collected data. Adding rock physics constraints to the inversion helps mitigate such limited sensitivity, but current approaches to add such constraints are based on including them as a priori knowledge mostly valid around the well or as a global constraint for the whole area. Since similar rock formations inside the Earth admit consistent elastic properties and relative values of elasticity and anisotropy parameters (this enables us to define them as a seismic facies), utilizing such localized facies information in FWI can improve the resolution of inverted parameters. We propose a novel approach to use facies-based constraints in both isotropic and anisotropic elastic FWI. We invert for such facies using Bayesian theory and update them at each iteration of the inversion using both the inverted models and a prior information. We take the uncertainties of the estimated parameters (approximated by radiation patterns) into consideration and improve the quality of estimated facies maps. Four numerical examples corresponding to different acquisition, physical assumptions and model circumstances are used to verify the effectiveness of the proposed method.

Diffusion-limited mixing by incompressible flows

Science.gov (United States)

Miles, Christopher J.; Doering, Charles R.

2018-05-01

Incompressible flows can be effective mixers by appropriately advecting a passive tracer to produce small filamentation length scales. In addition, diffusion is generally perceived as beneficial to mixing due to its ability to homogenize a passive tracer. However we provide numerical evidence that, in cases where advection and diffusion are both actively present, diffusion may produce negative effects by limiting the mixing effectiveness of incompressible optimal flows. This limitation appears to be due to the presence of a limiting length scale given by a generalised Batchelor length (Batchelor 1959 J. Fluid Mech. 5 113–33). This length scale limitation may in turn affect long-term mixing rates. More specifically, we consider local-in-time flow optimisation under energy and enstrophy flow constraints with the objective of maximising the mixing rate. We observe that, for enstrophy-bounded optimal flows, the strength of diffusion may not impact the long-term mixing rate. For energy-constrained optimal flows, however, an increase in the strength of diffusion can decrease the mixing rate. We provide analytical lower bounds on mixing rates and length scales achievable under related constraints (point-wise bounded speed and rate-of-strain) by extending the work of Lin et al (2011 J. Fluid Mech. 675 465–76) and Poon (1996 Commun. PDE 21 521–39).

Mathematical modeling of the crack growth in linear elastic isotropic materials by conventional fracture mechanics approaches and by molecular dynamics method: crack propagation direction angle under mixed mode loading

Science.gov (United States)

Stepanova, Larisa; Bronnikov, Sergej

2018-03-01

The crack growth directional angles in the isotropic linear elastic plane with the central crack under mixed-mode loading conditions for the full range of the mixity parameter are found. Two fracture criteria of traditional linear fracture mechanics (maximum tangential stress and minimum strain energy density criteria) are used. Atomistic simulations of the central crack growth process in an infinite plane medium under mixed-mode loading using Large-scale Molecular Massively Parallel Simulator (LAMMPS), a classical molecular dynamics code, are performed. The inter-atomic potential used in this investigation is Embedded Atom Method (EAM) potential. The plane specimens with initial central crack were subjected to Mixed-Mode loadings. The simulation cell contains 400000 atoms. The crack propagation direction angles under different values of the mixity parameter in a wide range of values from pure tensile loading to pure shear loading in a wide diapason of temperatures (from 0.1 К to 800 К) are obtained and analyzed. It is shown that the crack propagation direction angles obtained by molecular dynamics method coincide with the crack propagation direction angles given by the multi-parameter fracture criteria based on the strain energy density and the multi-parameter description of the crack-tip fields.

Geometric method for stability of non-linear elastic thin shells

CERN Document Server

Ivanova, Jordanka

2002-01-01

PREFACE This book deals with the new developments and applications of the geometric method to the nonlinear stability problem for thin non-elastic shells. There are no other published books on this subject except the basic ones of A. V. Pogorelov (1966,1967,1986), where variational principles defined over isometric surfaces, are postulated, and applied mainly to static and dynamic problems of elastic isotropic thin shells. A. V. Pogorelov (Harkov, Ukraine) was the first to provide in his monographs the geometric construction of the deformed shell surface in a post-critical stage and deriving explicitely the asymptotic formulas for the upper and lower critical loads. In most cases, these formulas were presented in a closed analytical form, and confirmed by experimental data. The geometric method by Pogorelov is one of the most important analytical methods developed during the last century. Its power consists in its ability to provide a clear geometric picture of the postcritical form of a deformed shell surfac...

Observation of elastic scattering effects on photoelectron angular distributions in free Xe clusters

International Nuclear Information System (INIS)

Oehrwall, G; Tchaplyguine, M; Gisselbrecht, M; Lundwall, M; Feifel, R; Rander, T; Schulz, J; Marinho, R R T; Lindgren, A; Sorensen, S L; Svensson, S; Bjoerneholm, O

2003-01-01

We report an observation of substantial deviations in the photoelectron angular distribution for photoionization of atoms in free Xe clusters compared to the case of photoionization of free atoms. The cross section, however, seems not to vary between the cluster and free atoms. This observation was made in the vicinity of the Xe 4d Cooper minimum, where the atomic angular distribution is known to vary dramatically. The angular distribution of electrons emitted from atoms in the clusters is more isotropic than that of free atoms over the entire kinetic energy range studied. Furthermore, the angular distribution is more isotropic for atoms in the interior of the clusters than for atoms at the surface. We attribute this deviation to elastic scattering of the outgoing photoelectrons. We have investigated two average cluster sizes, ≥ 4000 and 1000 and found no significant differences between these two cases

Theories for Elastic Plates via Orthogonal Polynomials

DEFF Research Database (Denmark)

Krenk, Steen

1981-01-01

A complementary energy functional is used to derive an infinite system of two-dimensional differential equations and appropriate boundary conditions for stresses and displacements in homogeneous anisotropic elastic plates. Stress boundary conditions are imposed on the faces a priori......, and this introduces a weight function in the variations of the transverse normal and shear stresses. As a result the coupling between the two-dimensional differential equations is described in terms of a single difference operator. Special attention is given to a truncated system of equations for bending...... of transversely isotropic plates. This theory has three boundary conditions, like Reissner's, but includes the effect of transverse normal strain, essentially through a reinterpretation of the transverse displacement function. Full agreement with general integrals to the homogeneous three-dimensional equations...

Conformal Field Theory as Microscopic Dynamics of Incompressible Euler and Navier-Stokes Equations

International Nuclear Information System (INIS)

Fouxon, Itzhak; Oz, Yaron

2008-01-01

We consider the hydrodynamics of relativistic conformal field theories at finite temperature. We show that the limit of slow motions of the ideal hydrodynamics leads to the nonrelativistic incompressible Euler equation. For viscous hydrodynamics we show that the limit of slow motions leads to the nonrelativistic incompressible Navier-Stokes equation. We explain the physical reasons for the reduction and discuss the implications. We propose that conformal field theories provide a fundamental microscopic viewpoint of the equations and the dynamics governed by them

Conformal field theory as microscopic dynamics of incompressible Euler and Navier-Stokes equations.

Science.gov (United States)

Fouxon, Itzhak; Oz, Yaron

2008-12-31

We consider the hydrodynamics of relativistic conformal field theories at finite temperature. We show that the limit of slow motions of the ideal hydrodynamics leads to the nonrelativistic incompressible Euler equation. For viscous hydrodynamics we show that the limit of slow motions leads to the nonrelativistic incompressible Navier-Stokes equation. We explain the physical reasons for the reduction and discuss the implications. We propose that conformal field theories provide a fundamental microscopic viewpoint of the equations and the dynamics governed by them.

The incompressible non-relativistic Navier-Stokes equation from gravity

International Nuclear Information System (INIS)

Bhattacharyya, Sayantani; Minwalla, Shiraz; Wadia, Spenta R.

2009-01-01

We note that the equations of relativistic hydrodynamics reduce to the incompressible Navier-Stokes equations in a particular scaling limit. In this limit boundary metric fluctuations of the underlying relativistic system turn into a forcing function identical to the action of a background electromagnetic field on the effectively charged fluid. We demonstrate that special conformal symmetries of the parent relativistic theory descend to 'accelerated boost' symmetries of the Navier-Stokes equations, uncovering a conformal symmetry structure of these equations. Applying our scaling limit to holographically induced fluid dynamics, we find gravity dual descriptions of an arbitrary solution of the forced non-relativistic incompressible Navier-Stokes equations. In the holographic context we also find a simple forced steady state shear solution to the Navier-Stokes equations, and demonstrate that this solution turns unstable at high enough Reynolds numbers, indicating a possible eventual transition to turbulence.

Isotropic nuclear graphites; the effect of neutron irradiation

International Nuclear Information System (INIS)

Lore, J.; Buscaillon, A.; Mottet, P.; Micaud, G.

1977-01-01

Several isotropic graphites have been manufactured using different forming processes and fillers such as needle coke, regular coke, or pitch coke. Their properties are described in this paper. Specimens of these products have been irradiated in the fast reactor Rapsodie between 400 to 1400 0 C, at fluences up to 1,7.10 21 n.cm -2 PHI.FG. The results show an isotropic behavior under neutron irradiation, but the induced dimensional changes are higher than those of isotropic coke graphites although they are lower than those of conventional extruded graphites made with the same coke

Process for the preparation of isotropic petroleum coke

International Nuclear Information System (INIS)

Kegler, W.H.; Huyser, M.E.

1975-01-01

A description is given of a process for preparing isotropic coke from oil residue charge. It includes blowing air into the residue until it reaches a softening temperature of around 49 to 116 deg C, the deferred coking of the residue having undergone blowing at a temperature of around 247 to 640 deg C, at a pressure between around 1.38x10 5 and 1.72x10 6 Pa, and the recovery of isotropic coke with a thermal expansion coefficient ratio under 1.5 approximately. The isotropic coke is used for preparing hexagonal graphite bars for nuclear reactor moderators [fr

Finite element methods for incompressible flow problems

CERN Document Server

John, Volker

2016-01-01

This book explores finite element methods for incompressible flow problems: Stokes equations, stationary Navier-Stokes equations, and time-dependent Navier-Stokes equations. It focuses on numerical analysis, but also discusses the practical use of these methods and includes numerical illustrations. It also provides a comprehensive overview of analytical results for turbulence models. The proofs are presented step by step, allowing readers to more easily understand the analytical techniques.

Ab initio study of the elastic properties of sodium chloride at high pressure

International Nuclear Information System (INIS)

Liu Lei; Bi Yan; Xu Jian; Chen Xiangrong

2010-01-01

The equation of state and elastic properties for B1- and B2-NaCl up to 160 GPa have been studied by using the density functional simulation within the generalized gradient approximation (GGA). The calculated lattice constants of NaCl agree well with experimental values in a precision of 0.1% over the pressure range studied. It is found that the cell volume decreases 5.5% at the phase transition point. All three independent elastic stiffness coefficients, c 11 , c 12 and c 44 for B1- and B2-NaCl are evaluated by a calculated stress tensor which was generated by forcing small strain to the optimized unit cell. The calculated zero-pressure elastic moduli, wave velocities, and their initial pressure dependences of B1-NaCl are in excellent agreement with experiments. Systematic investigation on the elasticity of NaCl has been done through four parameters, the Zener anisotropy ratio (A Z ), the acoustic anisotropy factor (A a ), the Cauchy deviation (δ), and the normalized elastic constants (c ij '). With the pressure, the Zener anisotropy ratio A Z decreases in the B1-phase, but increases in the B2-phase and reaches 1 at about 174 GPa, it suggests that NaCl would become elastic isotropic at this pressure range. The acoustic anisotropy factor A a shows the similar pressure behavior as A Z . The Cauchy deviation (δ)) increases with pressures, it demonstrates that in the interatomic interaction, the many-body contribution becomes more important at higher pressures. A discussion on the normalized elastic constants is also presented.

Texture of low temperature isotropic pyrocarbons

International Nuclear Information System (INIS)

Pelissier, Joseph; Lombard, Louis.

1976-01-01

Isotropic pyrocarbon deposited on fuel particles was studied by transmission electron microscopy in order to determine its texture. The material consists of an agglomerate of spherical growth features similar to those of carbon black. The spherical growth features are formed from the cristallites of turbostratic carbon and the distribution gives an isotropic structure. Neutron irradiation modifies the morphology of the pyrocarbon. The spherical growth features are deformed and the coating becomes strongly anisotropic. The transformation leads to the rupture of the coating caused by strong irradiation doses [fr

Calculation of the RPA response function of nuclei to quasi-elastic electron scattering with a density-dependent NN interaction

International Nuclear Information System (INIS)

Caillon, J-C.; Labarsouque, J.

1997-01-01

So far, the non-relativistic longitudinal and transverse functions in electron quasi-elastic scattering on the nuclei failed in reproducing satisfactorily the existent experimental data. The calculations including relativistic RPA correlations utilize until now the relativistic Hartree approximation to describe the nuclear matter. But, this provides an incompressibility module two times higher than its experimental value what is an important drawback for the calculation of realistic relativistic RPA correlations. Hence, we have determined the RPA response functions of nuclei by utilising a description of the relativistic nuclear matter leading to an incompressibility module in agreement with the empirical value. To do that we have utilized an interaction in the relativistic Hartree approximation in which we have determined the coupling constants σ-N and ω-N as a function of the density in order to reproduce the saturation curve obtained by a Dirac-Brueckner calculation. The results which we have obtained show that the longitudinal response function and the Coulomb sum generally overestimated when one utilizes the pure relativistic Hartree approximation, are here in good agreement with the experimental data for several nuclei

On singularity formation of a 3D model for incompressible Navier–Stokes equations

OpenAIRE

Hou, Thomas Y.; Shi, Zuoqiang; Wang, Shu

2012-01-01

We investigate the singularity formation of a 3D model that was recently proposed by Hou and Lei (2009) in [15] for axisymmetric 3D incompressible Navier–Stokes equations with swirl. The main difference between the 3D model of Hou and Lei and the reformulated 3D Navier–Stokes equations is that the convection term is neglected in the 3D model. This model shares many properties of the 3D incompressible Navier–Stokes equations. One of the main results of this paper is that we prove rigorously th...

Elastic-plastic code in the static regime for two-dimensional structures

International Nuclear Information System (INIS)

Giuliani, S.

1976-07-01

The finite-element computer code STEP-2D, which was conceived as a numerical tool for basic research in fracture mechanics presently under way in the Materials Division of JRC Ispra is described. The code employs 8-node isoparametric elements for calculating elastic-plastic stress and strain distributions in 2-D geometries. The von Mises yield criterion is used. Material strain hardening is described by means of either the isotropic or the so-called 'overlay' model. An incremental solution is employed in the plastic range. The program has been written in Fortran IV and compiled on an IBM 370-165

Incompressible Navier-Stokes equations. Theory and practice

Energy Technology Data Exchange (ETDEWEB)

Gjesdal, T.

1996-12-31

This paper contains notes from a seminar presented at the Dept. of Mathematics in the University of Bergen, Norway, Oct. 1996. It first introduces the theory of existence and uniqueness of solutions to the incompressible Navier-Stokes equation and defines a well-posed initial-boundary value problem. It then discusses different methods for solving numerically the Navier-Stokes equations in velocity-pressure formulation. The emphasis is on pressure correction methods. 19 refs.

A study of self-propelled elastic cylindrical micro-swimmers using modeling and computation

Science.gov (United States)

Shi, Lingling; Čanić, Sunčica; Quaini, Annalisa; Pan, Tsorng-Whay

2016-06-01

We study propulsion of micro-swimmers in 3D creeping flow. The swimmers are assumed to be made of elastic cylindrical hollow tubes. The swimming is generated by the contractions of the tube's elastic membrane walls producing a traveling wave in the form of a ;step-function; traversing the swimmer from right to left, propelling the swimmer from left to right. The problem is motivated by medical applications such as drug delivery. The influence of several non-dimensional design parameters on the velocity of the swimmer is investigated, including the swimmer aspect ratio, and the amplitude of the traveling wave relative to the swimmer radius. An immersed boundary method based on a finite element method approach is successfully combined with an elastic spring network model to simulate the two-way fluid-structure interaction coupling between the elastic cylindrical tube and the flow of a 3D viscous, incompressible fluid. To gain a deeper insight into the influence of various parameters on the swimmer speed, a reduced 1D fluid-structure interaction model was derived and validated. It was found that fast swimmers are those with large tube aspect ratios, and with the amplitude of the traveling wave which is roughly 50% of the reference swimmer radius. It was shown that the speed of our ;optimal swimmer; is around 1.5 swimmer lengths per second, which is at the top of the class of all currently manufactured micro-swimmers swimming in low Reynolds number flows (Re =10-6), reported in [11].

A Note on an Analytic Solution for an Incompressible Fluid-Conveying Pipeline System

Directory of Open Access Journals (Sweden)

Vincent O. S. Olunloyo

2017-01-01

Full Text Available This paper presents an integral transform analytic solution to the equations governing a fluid-conveying pipeline segment where a gyroscopic or Coriolis force effect is taken into consideration. The mathematical model idealizes a segment of the pipeline as an elastic beam conveying an incompressible fluid. It is clearly shown that when such a system is supported at both ends and in a free motion, the Coriolis force dissipates no energy (or simply does not work as it generates conjugate complex vibratory components for all flow velocities. It is demonstrated that the modal natural frequencies can be computed from the algebraic products of the complex frequency pairs. Clearly, the patterns of the characteristics of the system’s natural frequencies are seen partly when the real and imaginary components are plotted, as widely seen in the literature. Nonetheless, results from this study revealed that a continuity profile exists to connect the subcritical, critical, and postcritical vibratory behaviours when the absolute values are plotted for any velocity. In the meantime, the efficacy and versatility of this method against the usual assumed spatial or temporal modal solutions are demonstrated by confirming the predictions and validity of results of earlier workers such as Paidoussis, Ziegler, and others where pre- and postdivergence behaviours are exhibited.

Prediction of elastic and acoustic behaviors of calcarenite used for construction of historical monuments of Rabat, Morocco

Directory of Open Access Journals (Sweden)

Abdelaali Rahmouni

2017-02-01

Full Text Available Natural materials (e.g. rocks and soils are porous media, whose microstructures present a wide diversity. They generally consist of a heterogeneous solid phase and a porous phase which may be fully or partially saturated with one or more fluids. The prediction of elastic and acoustic properties of porous materials is very important in many fields, such as physics of rocks, reservoir geophysics, civil engineering, construction field and study of the behavior of historical monuments. The aim of this work is to predict the elastic and acoustic behaviors of isotropic porous materials of a solid matrix containing dry, saturated and partially saturated spherical pores. For this, a homogenization technique based on the Mori–Tanaka model is presented to connect the elastic and acoustic properties to porosity and degree of water saturation. Non-destructive ultrasonic technique is used to determine the elastic properties from measurements of P-wave velocities. The results obtained show the influence of porosity and degree of water saturation on the effective properties. The various predictions of Mori–Tanaka model are then compared with experimental results for the elastic and acoustic properties of calcarenite.

Topology optimization for elastic base under rectangular plate subjected to moving load

Directory of Open Access Journals (Sweden)

Jilavyan Samvel H.

2015-09-01

Full Text Available Distribution optimization of elastic material under elastic isotropic rectangular thin plate subjected to concentrated moving load is investigated in the present paper. The aim of optimization is to damp its vibrations in finite (fixed time. Accepting Kirchhoff hypothesis with respect to the plate and Winkler hypothesis with respect to the base, the mathematical model of the problem is constructed as two-dimensional bilinear equation, i.e. linear in state and control function. The maximal quantity of the base material is taken as optimality criterion to be minimized. The Fourier distributional transform and the Bubnov-Galerkin procedures are used to reduce the problem to integral equality type constraints. The explicit solution in terms of two- dimensional Heaviside‘s function is obtained, describing piecewise-continuous distribution of the material. The determination of the switching points is reduced to a problem of nonlinear programming. Data from numerical analysis are presented.

Isotropic compression of cohesive-frictional particles with rolling resistance

NARCIS (Netherlands)

Luding, Stefan; Benz, Thomas; Nordal, Steinar

2010-01-01

Cohesive-frictional and rough powders are the subject of this study. The behavior under isotropic compression is examined for different material properties involving Coulomb friction, rolling-resistance and contact-adhesion. Under isotropic compression, the density continuously increases according

Wrinkles and creases in the bending, unbending and eversion of soft sectors

Science.gov (United States)

Sigaeva, Taisiya; Mangan, Robert; Vergori, Luigi; Destrade, Michel; Sudak, Les

2018-04-01

We study what is clearly one of the most common modes of deformation found in nature, science and engineering, namely the large elastic bending of curved structures, as well as its inverse, unbending, which can be brought beyond complete straightening to turn into eversion. We find that the suggested mathematical solution to these problems always exists and is unique when the solid is modelled as a homogeneous, isotropic, incompressible hyperelastic material with a strain-energy satisfying the strong ellipticity condition. We also provide explicit asymptotic solutions for thin sectors. When the deformations are severe enough, the compressed side of the elastic material may buckle and wrinkles could then develop. We analyse, in detail, the onset of this instability for the Mooney-Rivlin strain energy, which covers the cases of the neo-Hookean model in exact nonlinear elasticity and of third-order elastic materials in weakly nonlinear elasticity. In particular, the associated theoretical and numerical treatment allows us to predict the number and wavelength of the wrinkles. Guided by experimental observations, we finally look at the development of creases, which we simulate through advanced finite-element computations. In some cases, the linearized analysis allows us to predict correctly the number and the wavelength of the creases, which turn out to occur only a few per cent of strain earlier than the wrinkles.

Wind turbine aerodynamics using an incompressible overset grid method

DEFF Research Database (Denmark)

Zahle, Frederik; Johansen, Jeppe; Sørensen, Niels N.

2007-01-01

In this paper 3D Navier-Stokes simulations of the unsteady flow over the NREL Phase VI turbine are presented. The computations are carried out using the structured grid, incompressible, finite volume flow solver EllipSys3D, which has been extended to include the use of overset grids. Computations...

Interactively variable isotropic resolution in computed tomography

International Nuclear Information System (INIS)

Lapp, Robert M; Kyriakou, Yiannis; Kachelriess, Marc; Wilharm, Sylvia; Kalender, Willi A

2008-01-01

An individual balancing between spatial resolution and image noise is necessary to fulfil the diagnostic requirements in medical CT imaging. In order to change influencing parameters, such as reconstruction kernel or effective slice thickness, additional raw-data-dependent image reconstructions have to be performed. Therefore, the noise versus resolution trade-off is time consuming and not interactively applicable. Furthermore, isotropic resolution, expressed by an equivalent point spread function (PSF) in every spatial direction, is important for the undistorted visualization and quantitative evaluation of small structures independent of the viewing plane. Theoretically, isotropic resolution can be obtained by matching the in-plane and through-plane resolution with the aforementioned parameters. Practically, however, the user is not assisted in doing so by current reconstruction systems and therefore isotropic resolution is not commonly achieved, in particular not at the desired resolution level. In this paper, an integrated approach is presented for equalizing the in-plane and through-plane spatial resolution by image filtering. The required filter kernels are calculated from previously measured PSFs in x/y- and z-direction. The concepts derived are combined with a variable resolution filtering technique. Both approaches are independent of CT raw data and operate only on reconstructed images which allows for their application in real time. Thereby, the aim of interactively variable, isotropic resolution is achieved. Results were evaluated quantitatively by measuring PSFs and image noise, and qualitatively by comparing the images to direct reconstructions regarded as the gold standard. Filtered images matched direct reconstructions with arbitrary reconstruction kernels with standard deviations in difference images of typically between 1 and 17 HU. Isotropic resolution was achieved within 5% of the selected resolution level. Processing times of 20-100 ms per frame

POD-Galerkin Model for Incompressible Single-Phase Flow in Porous Media

KAUST Repository

Wang, Yi; Yu, Bo; Sun, Shuyu

2017-01-01

Fast prediction modeling via proper orthogonal decomposition method combined with Galerkin projection is applied to incompressible single-phase fluid flow in porous media. Cases for different configurations of porous media, boundary conditions

Incompressible limit of the degenerate quantum compressible Navier-Stokes equations with general initial data

Science.gov (United States)

Kwon, Young-Sam; Li, Fucai

2018-03-01

In this paper we study the incompressible limit of the degenerate quantum compressible Navier-Stokes equations in a periodic domain T3 and the whole space R3 with general initial data. In the periodic case, by applying the refined relative entropy method and carrying out the detailed analysis on the oscillations of velocity, we prove rigorously that the gradient part of the weak solutions (velocity) of the degenerate quantum compressible Navier-Stokes equations converge to the strong solution of the incompressible Navier-Stokes equations. Our results improve considerably the ones obtained by Yang, Ju and Yang [25] where only the well-prepared initial data case is considered. While for the whole space case, thanks to the Strichartz's estimates of linear wave equations, we can obtain the convergence of the weak solutions of the degenerate quantum compressible Navier-Stokes equations to the strong solution of the incompressible Navier-Stokes/Euler equations with a linear damping term. Moreover, the convergence rates are also given.

Elasticity of stishovite at high pressure

Science.gov (United States)

Li, Baosheng; Rigden, Sally M.; Liebermann, Robert C.

1996-08-01

The elastic-wave velocities of stishovite, the rutile-structured polymorph of SiO 2, were measured to 3 GPa at room temperature in a piston cylinder apparatus using ultrasonic interferometry on polycrystalline samples. These polycrystalline samples (2-3 mm in length and diameter) were hot-pressed at 14 GPa and 1050°C in a 2000 ton uniaxial split-sphere apparatus (USSA-2000) using fused silica rods as starting material. They were characterized as low porosity (less than 1%), single phase, fine grained, free of cracks and preferred orientation, and acoustically isotropic by using density measurement, X-ray diffraction, scanning electron microscopy, and bench-top velocity measurements. On the basis of subsequent in situ X-ray diffraction study at high P and T on peak broadening on similar specimens, it is evident that the single crystal grains within these polycrystalline aggregates are well equilibrated and that these specimens are free of residual strain. P- and S-wave velocities measured at 1 atm are within 1.5% of the Hashin-Shtrikman bounds calculated from single-crystal elastic moduli. Measured pressure derivatives of the bulk and shear moduli, K' 0 = 5.3 ± 0.1 and G' 0 = 1.8 ± 0.1, are not unusual compared with values measured for other transition zone phases such as silicate spinel and majorite garnet. Isothermal compression curves calculated with the measured values of K0 and K' 0 agree well with experimental P-V data to 16 GPa. The experimental value of dG /dP is in excellent agreement with predictions based on elasticity systematics. Theoretical models are not yet able to replicate the measured values of K' 0 and G' 0.

Identification of elastic properties of composite plate

International Nuclear Information System (INIS)

Kovalovs, A; Rucevskis, S

2011-01-01

Composite laminates are used extensively in the aerospace industry, especially for the fabrication of high-performance structures. The determination of stiffness parameters for complex materials, such as fibre-reinforced composites, is much more complicated than for isotropic materials. A conventional way is testing the coupon specimens, which are manufactured by technology similar to that used for the real, large structures. When such a method is used, the question arises of whether the material properties obtained from the coupon tests are the same as those in the large structure. Therefore, the determination of actual material properties for composite laminates using non-destructive evaluation techniques has been widely investigated. A number of various non-destructive evaluation techniques have been proposed for determining the material properties of composite laminates. In the present study, attention is focused on the identification of the elastic properties of laminated plate using vibration test data. The problem associated with vibration testing is converting the measured modal frequencies to elastic constants. A standard method for solving this problem is the use of a numerical-experimental model and optimization techniques. The identification functional represents the gap between the numerical model response and the experimental one. This gap should be minimized, taking into account the side constraints on the design variables (elastic constants). The minimization problem is solved by using non-linear mathematical programming techniques and sensitivity analysis. The results obtained were verified by comparing the experimentally measured eigenfrequencies with the numerical ones obtained by FEM at the point of optima

Numerical methods for incompressible viscous flows with engineering applications

Science.gov (United States)

Rose, M. E.; Ash, R. L.

1988-01-01

A numerical scheme has been developed to solve the incompressible, 3-D Navier-Stokes equations using velocity-vorticity variables. This report summarizes the development of the numerical approximation schemes for the divergence and curl of the velocity vector fields and the development of compact schemes for handling boundary and initial boundary value problems.

A mathematical model for turbulent incompressible flows through mixing grids

International Nuclear Information System (INIS)

Allaire, G.

1989-01-01

A mathematical model is proposed for the computation of turbulent incompressible flows through mixing grids. This model is obtained as follows: in a three-dimentional-domain we represent a mixing grid by small identical wings of size ε 2 periodically distributed at the nodes of a plane regular mesh of size ε, and we consider incompressible Navier-Stokes equations with a no-slip condition on the wings. Using an appropriate homogenization process we pass to the limit when ε tends to zero and we obtain a Brinkman equation, i.e. a Navier-Stokes equation plus a zero-order term for the velocity, in a homogeneous domain without anymore wings. The interest of this model is that the spatial discretization is simpler in a homogeneous domain, and, moreover, the new term, which expresses the grid's mixing effect, can be evaluated with a local computation around a single wing

Investigation of structural, electronic and anisotropic elastic properties of Ru-doped WB{sub 2} compound by increased valence electron concentration

Energy Technology Data Exchange (ETDEWEB)

Surucu, Gokhan, E-mail: g_surucu@yahoo.com [Ahi Evran University, Department of Electric and Energy, 40100, Kirsehir (Turkey); Gazi University, Photonics Application and Research Center, 06500, Ankara (Turkey); Kaderoglu, Cagil [Ankara University, Department of Engineering Physics, 06100, Ankara (Turkey); Deligoz, Engin; Ozisik, Haci [Aksaray University, Department of Physics, 68100, Aksaray (Turkey)

2017-03-01

First principles density functional theory (DFT) calculations have been used to investigate the structural, anisotropic elastic and electronic properties of ruthenium doped tungsten-diboride ternary compounds (W{sub 1−x}Ru{sub x}B{sub 2}) for an increasing molar fraction of Ru atom from 0.1 to 0.9 by 0.1. Among the nine different compositions, W{sub 0.3}Ru{sub 0.7}B{sub 2} has been found as the most stable one due to the formation energy and band filling theory calculations. Moreover, the band structures and partial density of states (PDOS) have been computed for each x composition. After obtaining the elastic constants for all x compositions, the secondary results such as Bulk modulus, Young’s modulus, Poisson’s ratio, Shear modulus, and Vickers Hardness of polycrystalline aggregates have been derived and the relevant mechanical properties have been discussed. In addition, the elastic anisotropy has been visualized in detail by plotting the directional dependence of compressibility, Poisson ratio, Young’s and Shear moduli. - Highlights: • Effects of Ru substitution in WB{sub 2} using increased valence electron concentration. • Structural, electronic, mechanic and elastic properties for increasing Ru content. • Considered alloys are incompressible, brittle, stiffer and high hard materials.

Sensitivity analysis for elastic full-waveform inversion in VTI media

KAUST Repository

Kamath, Nishant

2014-08-05

Multiparameter full-waveform inversion (FWI) is generally nonunique, and the results are strongly influenced by the geometry of the experiment and the type of recorded data. Studying the sensitivity of different subsets of data to the model parameters may help in choosing an optimal acquisition design, inversion workflow, and parameterization. Here, we derive the Fréchet kernel for FWI of multicomponent data from a 2D VTI (tranversely isotropic with a vertical symmetry axis) medium. The kernel is obtained by linearizing the elastic wave equation using the Born approximation and employing the asymptotic Green\\'s function. The amplitude of the kernel (‘radiation pattern’) yields the angle-dependent energy scattered by a perturbation in a certain model parameter. The perturbations are described in terms of the P- and S-wave vertical velocities and the P-wave normal-moveout and horizontal velocities. The background medium is assumed to be homogeneous and isotropic, which allows us to obtain simple expressions for the radiation patterns corresonding to all four velocities. These patterns help explain the FWI results for multicomponent transmission data generated for Gaussian anomalies in the Thomsen parameters inserted into a homogeneous VTI medium.

Sensitivity analysis for elastic full-waveform inversion in VTI media

KAUST Repository

Kamath, Nishant; Tsvankin, Ilya

2014-01-01

Multiparameter full-waveform inversion (FWI) is generally nonunique, and the results are strongly influenced by the geometry of the experiment and the type of recorded data. Studying the sensitivity of different subsets of data to the model parameters may help in choosing an optimal acquisition design, inversion workflow, and parameterization. Here, we derive the Fréchet kernel for FWI of multicomponent data from a 2D VTI (tranversely isotropic with a vertical symmetry axis) medium. The kernel is obtained by linearizing the elastic wave equation using the Born approximation and employing the asymptotic Green's function. The amplitude of the kernel (‘radiation pattern’) yields the angle-dependent energy scattered by a perturbation in a certain model parameter. The perturbations are described in terms of the P- and S-wave vertical velocities and the P-wave normal-moveout and horizontal velocities. The background medium is assumed to be homogeneous and isotropic, which allows us to obtain simple expressions for the radiation patterns corresonding to all four velocities. These patterns help explain the FWI results for multicomponent transmission data generated for Gaussian anomalies in the Thomsen parameters inserted into a homogeneous VTI medium.

Finite deformation of incompressible fiber-reinforced elastomers: A computational micromechanics approach

Science.gov (United States)

Moraleda, Joaquín; Segurado, Javier; LLorca, Javier

2009-09-01

The in-plane finite deformation of incompressible fiber-reinforced elastomers was studied using computational micromechanics. Composite microstructure was made up of a random and homogeneous dispersion of aligned rigid fibers within a hyperelastic matrix. Different matrices (Neo-Hookean and Gent), fibers (monodisperse or polydisperse, circular or elliptical section) and reinforcement volume fractions (10-40%) were analyzed through the finite element simulation of a representative volume element of the microstructure. A successive remeshing strategy was employed when necessary to reach the large deformation regime in which the evolution of the microstructure influences the effective properties. The simulations provided for the first time "quasi-exact" results of the in-plane finite deformation for this class of composites, which were used to assess the accuracy of the available homogenization estimates for incompressible hyperelastic composites.

A Generalized Version of a Low Velocity Impact between a Rigid Sphere and a Transversely Isotropic Strain-Hardening Plate Supported by a Rigid Substrate Using the Concept of Noninteger Derivatives

Directory of Open Access Journals (Sweden)

Abdon Atangana

2013-01-01

Full Text Available A low velocity impact between a rigid sphere and transversely isotropic strain-hardening plate supported by a rigid substrate is generalized to the concept of noninteger derivatives order. A brief history of fractional derivatives order is presented. The fractional derivatives order adopted is in Caputo sense. The new equation is solved via the analytical technique, the Homotopy decomposition method (HDM. The technique is described and the numerical simulations are presented. Since it is very important to accurately predict the contact force and its time history, the three stages of the indentation process, including (1 the elastic indentation, (2 the plastic indentation, and (3 the elastic unloading stages, are investigated.

Preconditioned characteristic boundary conditions based on artificial compressibility method for solution of incompressible flows

Science.gov (United States)

Hejranfar, Kazem; Parseh, Kaveh

2017-09-01

The preconditioned characteristic boundary conditions based on the artificial compressibility (AC) method are implemented at artificial boundaries for the solution of two- and three-dimensional incompressible viscous flows in the generalized curvilinear coordinates. The compatibility equations and the corresponding characteristic variables (or the Riemann invariants) are mathematically derived and then applied as suitable boundary conditions in a high-order accurate incompressible flow solver. The spatial discretization of the resulting system of equations is carried out by the fourth-order compact finite-difference (FD) scheme. In the preconditioning applied here, the value of AC parameter in the flow field and also at the far-field boundary is automatically calculated based on the local flow conditions to enhance the robustness and performance of the solution algorithm. The code is fully parallelized using the Concurrency Runtime standard and Parallel Patterns Library (PPL) and its performance on a multi-core CPU is analyzed. The incompressible viscous flows around a 2-D circular cylinder, a 2-D NACA0012 airfoil and also a 3-D wavy cylinder are simulated and the accuracy and performance of the preconditioned characteristic boundary conditions applied at the far-field boundaries are evaluated in comparison to the simplified boundary conditions and the non-preconditioned characteristic boundary conditions. It is indicated that the preconditioned characteristic boundary conditions considerably improve the convergence rate of the solution of incompressible flows compared to the other boundary conditions and the computational costs are significantly decreased.

Directional anisotropy, finite size effect and elastic properties of hexagonal boron nitride

International Nuclear Information System (INIS)

Thomas, Siby; Ajith, K M; Valsakumar, M C

2016-01-01

Classical molecular dynamics simulations have been performed to analyze the elastic and mechanical properties of two-dimensional (2D) hexagonal boron nitride (h-BN) using a Tersoff-type interatomic empirical potential. We present a systematic study of h-BN for various system sizes. Young’s modulus and Poisson’s ratio are found to be anisotropic for finite sheets whereas they are isotropic for the infinite sheet. Both of them increase with system size in accordance with a power law. It is concluded from the computed values of elastic constants that h-BN sheets, finite or infinite, satisfy Born’s criterion for mechanical stability. Due to the the strong in-plane sp 2 bonds and the small mass of boron and nitrogen atoms, h-BN possesses high longitudinal and shear velocities. The variation of bending rigidity with system size is calculated using the Foppl–von Karman approach by coupling the in-plane bending and out-of-plane stretching modes of the 2D h-BN. (paper)

Unique encoding for streamline topologies of incompressible and inviscid flows in multiply connected domains

Energy Technology Data Exchange (ETDEWEB)

Sakajo, T [Department of Mathematics, Kyoto University, Kitashirakawa Oiwake-cho, Sakyo-ku, Kyoto 606-8502 (Japan); Sawamura, Y; Yokoyama, T, E-mail: sakajo@math.kyoto-u.ac.jp [JST CREST, Kawaguchi, Saitama 332-0012 (Japan)

2014-06-01

This study considers the flow of incompressible and inviscid fluid in two-dimensional multiply connected domains. For such flows, encoding algorithms to assign a unique sequence of words to any structurally stable streamline topology based on the theory presented by Yokoyama and Sakajo (2013 Proc. R. Soc. A 469 20120558) are proposed. As an application, we utilize the algorithms to characterize the evolution of an incompressible and viscid flow around a flat plate inclined to the uniform flow in terms of the change of the word representations for their instantaneous streamline topologies. (papers)

An Equal-Order DG Method for the Incompressible Navier-Stokes Equations

KAUST Repository

Cockburn, Bernardo; Kanschat, Guido; Schö tzau, Dominik

2008-01-01

We introduce and analyze a discontinuous Galerkin method for the incompressible Navier-Stokes equations that is based on finite element spaces of the same polynomial order for the approximation of the velocity and the pressure. Stability

Five-dimensional truncation of the plane incompressible navier-stokes equations

Energy Technology Data Exchange (ETDEWEB)

Boldrighini, C [Camerino Univ. (Italy). Istituto di Matematica; Franceschini, V [Modena Univ. (Italy). Istituto Matematico

1979-01-01

A five-modes truncation of the Navier-Stokes equations for a two dimensional incompressible fluid on a torus is considered. A computer analysis shows that for a certain range of the Reynolds number the system exhibits a stochastic behaviour, approached through an involved sequence of bifurcations.

Oberbeck-Bousinesq approximation for the motion of two incompressible fluids

Czech Academy of Sciences Publication Activity Database

Denisova, I.V.; Nečasová, Šárka

2009-01-01

Roč. 159, č. 4 (2009), s. 436-451 ISSN 1072-3374 R&D Projects: GA AV ČR IAA100190804; GA MŠk LC06052 Institutional research plan: CEZ:AV0Z10190503 Keywords : surface tension * Oberbeck -Bousinesq approximation * incompressible fluids Subject RIV: BA - General Mathematics

Finite element modelling of moisture related and visco-elastic deformations in inhomogeneous timber beams

DEFF Research Database (Denmark)

Ormarsson, Sigurdur; Dahlblom, Ola

2013-01-01

Wood is a hygro-mechanical, non-isotropic and inhomogeneous material concerning both modulus of elasticity (MOE) and shrinkage properties. In stress calculations associated with ordinary timber design, these matters are often not dealt with properly. The main reason for this is that stress...... and the longitudinal shrinkage coefficient vary considerably from pith to bark. The question is how much these variations affect the stress distribution in wooden structures exposed to variable moisture climate. The paper presents a finite element implementation of a beam element with the aim of studying how wooden...

Micro-CT based finite element models for elastic properties of glass-ceramic scaffolds.

Science.gov (United States)

Tagliabue, Stefano; Rossi, Erica; Baino, Francesco; Vitale-Brovarone, Chiara; Gastaldi, Dario; Vena, Pasquale

2017-01-01

In this study, the mechanical properties of porous glass-ceramic scaffolds are investigated by means of three-dimensional finite element models based on micro-computed tomography (micro-CT) scan data. In particular, the quantitative relationship between the morpho-architectural features of the obtained scaffolds, such as macroscopic porosity and strut thickness, and elastic properties, is sought. The macroscopic elastic properties of the scaffolds have been obtained through numerical homogenization approaches using the mechanical characteristics of the solid walls of the scaffolds (assessed through nanoindentation) as input parameters for the numerical simulations. Anisotropic mechanical properties of the produced scaffolds have also been investigated by defining a suitable anisotropy index. A comparison with morphological data obtained through the micro-CT scans is also presented. The proposed study shows that the produced glass-ceramic scaffolds exhibited a macroscopic porosity ranging between 29% and 97% which corresponds to an average stiffness ranging between 42.4GPa and 36MPa. A quantitative estimation of the isotropy of the macroscopic elastic properties has been performed showing that the samples with higher solid fractions were those closest to an isotropic material. Copyright © 2016 Elsevier Ltd. All rights reserved.

On three-dimensional incompressible Navier-Stokes fluid on cantor sets in spherical Cantor type co-ordinate system

Directory of Open Access Journals (Sweden)

Meng Zhi-Jun

2016-01-01

Full Text Available This paper addresses the systems of the incompressible Navier-Stokes equations on Cantor sets without the external force involving the fractal heat-conduction problem vial local fractional derivative. The spherical Cantor type co-ordinate method is used to transfer the incompressible Navier-Stokes equation from the Cantorian co-ordinate system into the spherical Cantor type co-ordinate system.

Development of Modified Incompressible Ideal Gas Model for Natural Draft Cooling Tower Flow Simulation

Science.gov (United States)

Hyhlík, Tomáš

2018-06-01

The article deals with the development of incompressible ideal gas like model, which can be used as a part of mathematical model describing natural draft wet-cooling tower flow, heat and mass transfer. It is shown, based on the results of a complex mathematical model of natural draft wet-cooling tower flow, that behaviour of pressure, temperature and density is very similar to the case of hydrostatics of moist air, where heat and mass transfer in the fill zone must be taken into account. The behaviour inside the cooling tower is documented using density, pressure and temperature distributions. The proposed equation for the density is based on the same idea like the incompressible ideal gas model, which is only dependent on temperature, specific humidity and in this case on elevation. It is shown that normalized density difference of the density based on proposed model and density based on the nonsimplified model is in the order of 10-4. The classical incompressible ideal gas model, Boussinesq model and generalised Boussinesq model are also tested. These models show deviation in percentages.

Development of Modified Incompressible Ideal Gas Model for Natural Draft Cooling Tower Flow Simulation

Directory of Open Access Journals (Sweden)

Hyhlík Tomáš

2018-01-01

Full Text Available The article deals with the development of incompressible ideal gas like model, which can be used as a part of mathematical model describing natural draft wet-cooling tower flow, heat and mass transfer. It is shown, based on the results of a complex mathematical model of natural draft wet-cooling tower flow, that behaviour of pressure, temperature and density is very similar to the case of hydrostatics of moist air, where heat and mass transfer in the fill zone must be taken into account. The behaviour inside the cooling tower is documented using density, pressure and temperature distributions. The proposed equation for the density is based on the same idea like the incompressible ideal gas model, which is only dependent on temperature, specific humidity and in this case on elevation. It is shown that normalized density difference of the density based on proposed model and density based on the nonsimplified model is in the order of 10-4. The classical incompressible ideal gas model, Boussinesq model and generalised Boussinesq model are also tested. These models show deviation in percentages.

Laminar motion of the incompressible fluids in self-acting thrust bearings with spiral grooves.

Science.gov (United States)

Velescu, Cornel; Popa, Nicolae Calin

2014-01-01

We analyze the laminar motion of incompressible fluids in self-acting thrust bearings with spiral grooves with inner or external pumping. The purpose of the study is to find some mathematical relations useful to approach the theoretical functionality of these bearings having magnetic controllable fluids as incompressible fluids, in the presence of a controllable magnetic field. This theoretical study approaches the permanent motion regime. To validate the theoretical results, we compare them to some experimental results presented in previous papers. The laminar motion of incompressible fluids in bearings is described by the fundamental equations of fluid dynamics. We developed and particularized these equations by taking into consideration the geometrical and functional characteristics of these hydrodynamic bearings. Through the integration of the differential equation, we determined the pressure and speed distributions in bearings with length in the "pumping" direction. These pressure and speed distributions offer important information, both quantitative (concerning the bearing performances) and qualitative (evidence of the viscous-inertial effects, the fluid compressibility, etc.), for the laminar and permanent motion regime.

Laminar Motion of the Incompressible Fluids in Self-Acting Thrust Bearings with Spiral Grooves

Directory of Open Access Journals (Sweden)

Cornel Velescu

2014-01-01

Full Text Available We analyze the laminar motion of incompressible fluids in self-acting thrust bearings with spiral grooves with inner or external pumping. The purpose of the study is to find some mathematical relations useful to approach the theoretical functionality of these bearings having magnetic controllable fluids as incompressible fluids, in the presence of a controllable magnetic field. This theoretical study approaches the permanent motion regime. To validate the theoretical results, we compare them to some experimental results presented in previous papers. The laminar motion of incompressible fluids in bearings is described by the fundamental equations of fluid dynamics. We developed and particularized these equations by taking into consideration the geometrical and functional characteristics of these hydrodynamic bearings. Through the integration of the differential equation, we determined the pressure and speed distributions in bearings with length in the “pumping” direction. These pressure and speed distributions offer important information, both quantitative (concerning the bearing performances and qualitative (evidence of the viscous-inertial effects, the fluid compressibility, etc., for the laminar and permanent motion regime.

Some axisymmetric equilibria for certain ideal and resistive magnetohydrodynamics with incompressible flows

Directory of Open Access Journals (Sweden)

S.M. Moawad

Full Text Available In this paper, the equilibrium properties of some ideal and resistive magnetohydrodynamics (MHD are investigated. The governing equations are taken in the steady state for parallel and non-parallel flow to magnetic filed. The governing equations are reduced to Bernoulli-Grad-Shafranov system. The problem of finding exact equilibria to the governing equations in the presence of incompressible mass flows is studied. Several nonlinear equilibria of the governing equations are obtained with aid of constructed constraints. The obtained results cover several previously configurations and include new considerations about the nonlinearity of magnetic flux stream variables. The possibility of applying the obtained results to magnetic confinement devices are discussed. Keywords: Magnetohydrodynamics, Axisymmetric plasma, Resistivity, Incompressible flows, Exact equilibria, Magnetic confinement devices

Simulating propagation of decomposed elastic waves using low-rank approximate mixed-domain integral operators for heterogeneous transversely isotropic media

KAUST Repository

Cheng, Jiubing; Wu, Zedong; Alkhalifah, Tariq Ali

2014-01-01

decomposition in anisotropic media is costly as the operators involved is dependent on the velocity, and thus not stationary. In this abstract, we propose an efficient approach to directly extrapolate the decomposed elastic waves using lowrank approximate mixed

Visualization and computer graphics on isotropically emissive volumetric displays.

Science.gov (United States)

Mora, Benjamin; Maciejewski, Ross; Chen, Min; Ebert, David S

2009-01-01

The availability of commodity volumetric displays provides ordinary users with a new means of visualizing 3D data. Many of these displays are in the class of isotropically emissive light devices, which are designed to directly illuminate voxels in a 3D frame buffer, producing X-ray-like visualizations. While this technology can offer intuitive insight into a 3D object, the visualizations are perceptually different from what a computer graphics or visualization system would render on a 2D screen. This paper formalizes rendering on isotropically emissive displays and introduces a novel technique that emulates traditional rendering effects on isotropically emissive volumetric displays, delivering results that are much closer to what is traditionally rendered on regular 2D screens. Such a technique can significantly broaden the capability and usage of isotropically emissive volumetric displays. Our method takes a 3D dataset or object as the input, creates an intermediate light field, and outputs a special 3D volume dataset called a lumi-volume. This lumi-volume encodes approximated rendering effects in a form suitable for display with accumulative integrals along unobtrusive rays. When a lumi-volume is fed directly into an isotropically emissive volumetric display, it creates a 3D visualization with surface shading effects that are familiar to the users. The key to this technique is an algorithm for creating a 3D lumi-volume from a 4D light field. In this paper, we discuss a number of technical issues, including transparency effects due to the dimension reduction and sampling rates for light fields and lumi-volumes. We show the effectiveness and usability of this technique with a selection of experimental results captured from an isotropically emissive volumetric display, and we demonstrate its potential capability and scalability with computer-simulated high-resolution results.

INHOMOGENEOUS NEARLY INCOMPRESSIBLE DESCRIPTION OF MAGNETOHYDRODYNAMIC TURBULENCE

International Nuclear Information System (INIS)

Hunana, P.; Zank, G. P.

2010-01-01

The nearly incompressible theory of magnetohydrodynamics (MHD) is formulated in the presence of a static large-scale inhomogeneous background. The theory is an inhomogeneous generalization of the homogeneous nearly incompressible MHD description of Zank and Matthaeus and a polytropic equation of state is assumed. The theory is primarily developed to describe solar wind turbulence where the assumption of a composition of two-dimensional (2D) and slab turbulence with the dominance of the 2D component has been used for some time. It was however unclear, if in the presence of a large-scale inhomogeneous background, the dominant component will also be mainly 2D and we consider three distinct MHD regimes for the plasma beta β > 1. For regimes appropriate to the solar wind (β 2 s δp is not valid for the leading-order O(M) density fluctuations, and therefore in observational studies, the density fluctuations should not be analyzed through the pressure fluctuations. The pseudosound relation is valid only for higher order O(M 2 ) density fluctuations, and then only for short-length scales and fast timescales. The spectrum of the leading-order density fluctuations should be modeled as k -5/3 in the inertial range, followed by a Bessel function solution K ν (k), where for stationary turbulence ν = 1, in the viscous-convective and diffusion range. Other implications for solar wind turbulence with an emphasis on the evolution of density fluctuations are also discussed.

Nested structures approach in designing an isotropic negative-index material for infrared

DEFF Research Database (Denmark)

Andryieuski, Andrei; Malureanu, Radu; Lavrinenko, Andrei

2009-01-01

We propose a new generic approach for designing isotropic metamaterial with nested cubic structures. As an example, a three-dimensional isotropic unit cell design "Split Cube in Cage" (SCiC) is shown to exhibit an effective negative refractive index on infrared wavelengths. We report on the refra......We propose a new generic approach for designing isotropic metamaterial with nested cubic structures. As an example, a three-dimensional isotropic unit cell design "Split Cube in Cage" (SCiC) is shown to exhibit an effective negative refractive index on infrared wavelengths. We report...

Elasticity in Elastics-An in-vitro study.

Science.gov (United States)

Kamisetty, Supradeep Kumar; Nimagadda, Chakrapani; Begam, Madhoom Ponnachi; Nalamotu, Raghuveer; Srivastav, Trilok; Gs, Shwetha

2014-04-01

Orthodontic tooth movement results from application of forces to teeth. Elastics in orthodontics have been used both intra-orally and extra- orally to a great effect. Their use, combined with good patient co-operation provides the clinician with the ability to correct both anteroposterior and vertical discrepancies. Force decay over a period of time is a major problem in the clinical usage of latex elastics and synthetic elastomers. This loss of force makes it difficult for the clinician to determine the actual force transmitted to the dentition. It's the intent of the clinician to maintain optimal force values over desired period of time. The majority of the orthodontic elastics on the market are latex elastics. Since the early 1990s, synthetic products have been offered in the market for latex-sensitive patients and are sold as nonlatex elastics. There is limited information on the risk that latex elastics may pose to patients. Some have estimated that 0.12-6% of the general population and 6.2% of dental professionals have hypersensitivity to latex protein. There are some reported cases of adverse reactions to latex in the orthodontic population but these are very limited to date. Although the risk is not yet clear, it would still be inadvisable to prescribe latex elastics to a patient with a known latex allergy. To compare the in-vitro performance of latex and non latex elastics. Samples of 0.25 inch, latex and non latex elastics (light, medium, heavy elastics) were obtained from three manufacturers (Forestadent, GAC, Glenroe) and a sample size of ten elastics per group was tested. The properties tested included cross sectional area, internal diameter, initial force generated by the elastics, breaking force and the force relaxation for the different types of elastics. Force relaxation testing involved stretching the elastics to three times marketed internal diameter (19.05 mm) and measuring force level at intervals over a period of 48 hours. The data were

The revised geometric measure of entanglement for isotropic state

International Nuclear Information System (INIS)

Cao Ya

2011-01-01

Based on the revised geometric measure of entanglement (RGME), we obtain the analytical expression of isotropic state and generalize to n-particle and d-dimension mixed state case. Meantime, we obtain the relation about isotropic state E-tilde sin 2 (ρ) ≤ E re (ρ). The results indicate RGME is an appropriate measure of entanglement. (authors)

Hardrock Elastic Physical Properties: Birch's Seismic Parameter Revisited

Science.gov (United States)

Wu, M.; Milkereit, B.

2014-12-01

Identifying rock composition and properties is imperative in a variety of fields including geotechnical engineering, mining, and petroleum exploration, in order to accurately make any petrophysical calculations. Density is, in particular, an important parameter that allows us to differentiate between lithologies and estimate or calculate other petrophysical properties. It is well established that compressional and shear wave velocities of common crystalline rocks increase with increasing densities (i.e. the Birch and Nafe-Drake relationships). Conventional empirical relations do not take into account S-wave velocity. Physical properties of Fe-oxides and massive sulfides, however, differ significantly from the empirical velocity-density relationships. Currently, acquiring in-situ density data is challenging and problematic, and therefore, developing an approximation for density based on seismic wave velocity and elastic moduli would be beneficial. With the goal of finding other possible or better relationships between density and the elastic moduli, a database of density, P-wave velocity, S-wave velocity, bulk modulus, shear modulus, Young's modulus, and Poisson's ratio was compiled based on a multitude of lab samples. The database is comprised of isotropic, non-porous metamorphic rock. Multi-parameter cross plots of the various elastic parameters have been analyzed in order to find a suitable parameter combination that reduces high density outliers. As expected, the P-wave velocity to S-wave velocity ratios show no correlation with density. However, Birch's seismic parameter, along with the bulk modulus, shows promise in providing a link between observed compressional and shear wave velocities and rock densities, including massive sulfides and Fe-oxides.

Incompressible LFR MHD. A fluid model for stability analysis of a fusion plasma

International Nuclear Information System (INIS)

Scheffel, J.; Faghihi, M.

1986-10-01

A fluid model including FLR effects, named Incompressible Finite Larmor Radius MagnetoHydroDynamics, is presented and derived in this paper. It is an extension of ordinary, incompressible MHD to include the Larmor radius effects due to ion gyroviscosity, Hall current and electron diamagnetism. It is intended to use the model for stability analysis, on the Alfven wave time scale, of a fusion plasma and it is consequently based on transport coefficients in the collisionless limit. It will be demonstrated that for a fairly dense and cool plasma, such as for the EXTRAP z-pinch, all three Larmor radius effects may become important, that for a JET-type plasma no FLR effect is pronounced, and that in a reactor plasma the Hall and electron diamagnetism term may play a role. For scaling lengths signigicantly smaller than the plasma radius the effect of the FLR terms becomes enhanced. To study the importance of the choice of equations of state for the model the m=1 and k 2 r 2 towards infinity instability in cylindrical geometry is given special attention for zero Larmor radius. The full stability criterion of the double adiabatic model, including pressure anisotropy, is presented for what we believe to be the first time. It is found that when perpendicular p > parallel p stability can be reached for very high plasma perpendicular β-values. We demonstrate that no less complicated energy conserving fluid model, which takes into account pressure anisotropy, other than the double adiabativ model can be obtained. Since pressure anisotropy generally only weakly affects stability, we can assume isotropy in the Incompressible FLR MHD model. Also, the energy equation is replaced by the incompressibility condition, making FLR terms appearing in the energy equation irrelevant. (authors)

The study of the elasticity of spider dragline silk with liquid crystal model

International Nuclear Information System (INIS)

Cui Linying; Liu Fei; Ouyang Zhongcan

2009-01-01

Spider dragline silk is an optimal biomaterial with a combination of high tensile strength and high elasticity, and it has long been suggested to belong to liquid crystalline materials. However, a satisfactory liquid crystal description for the mechanical properties of the dragline is still missing. To solve the long existing problem, we generalized the Maier-Saupe theory of nematics to construct a liquid crystal model of the deformation mechanism of the dragline silk. We show that the remarkable elasticity of the dragline can be understood as the isotropic-nematic phase transition of the chain network with the beginning of the transition corresponding to the yield point. The calculated curve fits well with the measurements and the yield point is obtained self-consistently within our framework. The present theory can also qualitatively account for the drop of stress in supercontracted spider silk. All these comprehensive agreements between theory and experiments strongly indicate the dragline to belong to liquid crystal materials.

Turbulence in nearly incompressible fluids: density spectrum, flows, correlations and implication to the interstellar medium

Directory of Open Access Journals (Sweden)

S. Dastgeer

2005-01-01

Full Text Available Interstellar scintillation and angular radio wave broadening measurements show that interstellar and solar wind (electron density fluctuations exhibit a Kolmogorov-like k-5/3 power spectrum extending over many decades in wavenumber space. The ubiquity of the Kolmogorov-like interstellar medium (ISM density spectrum led to an explanation based on coupling incompressible magnetohydrodynamic (MHD fluctuations to density fluctuations through a 'pseudosound' relation within the context of 'nearly incompressible' (NI hydrodynamics (HD and MHD models. The NI theory provides a fundamentally different explanation for the observed ISM density spectrum in that the density fluctuations can be a consequence of passive scalar convection due to background incompressible fluctuations. The theory further predicts generation of long-scale structures and various correlations between the density, temperature and the (magneto acoustic as well as convective pressure fluctuations in the compressible ISM fluids in different thermal regimes that are determined purely by the thermal fluctuation level. In this paper, we present the results of our two dimensional nonlinear fluid simulations, exploring various nonlinear aspects that lead to inertial range ISM turbulence within the context of a NI hydrodymanics model. In qualitative agreement with the NI predictions and the in-situ observations, we find that i the density fluctuations exhibit a Kolmogorov-like spectrum via a passive convection in the field of the background incompressible fluctuations, ii the compressible ISM fluctuations form long scale flows and structures, and iii the density and the temperature fluctuations are anti-correlated.

Comparative study of incompressible and isothermal compressible flow solvers for cavitating flow dynamics

Energy Technology Data Exchange (ETDEWEB)

Park, Sun Ho [Korea Maritime and Ocean University, Busan (Korea, Republic of); Rhee, Shin Hyung [Seoul National University, Seoul (Korea, Republic of)

2015-08-15

Incompressible flow solvers are generally used for numerical analysis of cavitating flows, but with limitations in handling compressibility effects on vapor phase. To study compressibility effects on vapor phase and cavity interface, pressure-based incompressible and isothermal compressible flow solvers based on a cell-centered finite volume method were developed using the OpenFOAM libraries. To validate the solvers, cavitating flow around a hemispherical head-form body was simulated and validated against the experimental data. The cavity shedding behavior, length of a re-entrant jet, drag history, and the Strouhal number were compared between the two solvers. The results confirmed that computations of the cavitating flow including compressibility effects improved the reproduction of cavitation dynamics.

Numerical Modeling and Experimental Study of Elastic-Plastic Behavior of Carbon Nanotubes Reinforced Nanocompsites of PA6/NBR Using a Microfinite Element Model

Directory of Open Access Journals (Sweden)

Mir Hamid Reza Ghoreishy

2014-12-01

Full Text Available A theoretical and experimental study was conducted on the mechanical behavior of nanocomposites based on PA6/NBR thermoplastic elastomer reinforced by single wall carbon nanotubes (SWNTs. The selected samples include 60 and 40% NBR with 0.5, 1.0 and 1.5% SWNT. The modeling methodology was based on the use of two-dimensional "representative volume elements" (RVE. The Abaqus/standard code was employed to carry out the non-linear finite element calculations. Plane stress elements were selected for discretization of the domain. Linear elastic and isotropic hardening elastic-plastic models were utilized to describe the mechanical behaviors of the carbon nanotubes and polymer matrix, respectively. The samples were simultaneously prepared using melt mixing method in a laboratory internal mixer. Different orientations including regular in both longitudinal and transverse directions and random were selected for the nanotubes in the matrix. Also, two structural forms including hollow and solid for the carbon nanotubes were chosen. The highest and lowest predicted moduli were obtained from models with regular orientation in longitudinal and transverse directions, respectively. On the other hand, comparison between the predicted elastic modulus and elastic-plastic behaviors of the samples with their corresponding experimental data revealed that the random orientation in conjunction with hollow structural form gives the best results. Moreover, the selected material model for the thermoplastic elastomer i.e., isotropic hardening can precisely describe the mechanical behavior in both tension and compression modes. It is also concluded that the main source of error in this modeling methodology can be attributed to the effects of interface between polymer and nanotubes and orientation in perpendicular directions.

Mathematical problems of the dynamics of incompressible fluid on a rotating sphere

CERN Document Server

Skiba, Yuri N

2017-01-01

This book presents selected mathematical problems involving the dynamics of a two-dimensional viscous and ideal incompressible fluid on a rotating sphere. In this case, the fluid motion is completely governed by the barotropic vorticity equation (BVE), and the viscosity term in the vorticity equation is taken in its general form, which contains the derivative of real degree of the spherical Laplace operator. This work builds a bridge between basic concepts and concrete outcomes by pursuing a rich combination of theoretical, analytical and numerical approaches, and is recommended for specialists developing mathematical methods for application to problems in physics, hydrodynamics, meteorology and geophysics, as well for upper undergraduate or graduate students in the areas of dynamics of incompressible fluid on a rotating sphere, theory of functions on a sphere, and flow stability.

Low-frequency wave propagation in an elastic plate loaded by a two-layer fluid

DEFF Research Database (Denmark)

Indeitsev, Dmitrij; Sorokin, Sergey

2012-01-01

concern is propagation of low-frequency waves in such a coupled waveguide. In the present paper, we assume that an inhomogeneous fluid may be modelled as two homogeneous, inviscid and incompressible layers with slightly different densities. The lighter layer of fresh water lies on top of the heavier layer......In several technical applications, for example, in the Arctic off-shore oil industry, it is necessary to predict waveguide properties of floating elastic plates in contact with a relatively thin layer of water, which has a non-uniform density distribution across its depth. The issue of particular...... formulation, such as depths of the layers, stiffness and inertia of the plate, are assessed in several frequency ranges. Dispersion diagrams obtained from approximate dispersion relations are compared with their exact counterparts....

Fast algorithms for evaluating the stress field of dislocation lines in anisotropic elastic media

Science.gov (United States)

Chen, C.; Aubry, S.; Oppelstrup, T.; Arsenlis, A.; Darve, E.

2018-06-01

In dislocation dynamics (DD) simulations, the most computationally intensive step is the evaluation of the elastic interaction forces among dislocation ensembles. Because the pair-wise interaction between dislocations is long-range, this force calculation step can be significantly accelerated by the fast multipole method (FMM). We implemented and compared four different methods in isotropic and anisotropic elastic media: one based on the Taylor series expansion (Taylor FMM), one based on the spherical harmonics expansion (Spherical FMM), one kernel-independent method based on the Chebyshev interpolation (Chebyshev FMM), and a new kernel-independent method that we call the Lagrange FMM. The Taylor FMM is an existing method, used in ParaDiS, one of the most popular DD simulation softwares. The Spherical FMM employs a more compact multipole representation than the Taylor FMM does and is thus more efficient. However, both the Taylor FMM and the Spherical FMM are difficult to derive in anisotropic elastic media because the interaction force is complex and has no closed analytical formula. The Chebyshev FMM requires only being able to evaluate the interaction between dislocations and thus can be applied easily in anisotropic elastic media. But it has a relatively large memory footprint, which limits its usage. The Lagrange FMM was designed to be a memory-efficient black-box method. Various numerical experiments are presented to demonstrate the convergence and the scalability of the four methods.

First-principles calculations of the electronic, vibrational, and elastic properties of the magnetic laminate Mn2GaC

International Nuclear Information System (INIS)

Thore, A.; Dahlqvist, M.; Alling, B.; Rosén, J.

2014-01-01

In this paper, we report the by first-principles predicted properties of the recently discovered magnetic MAX phase Mn 2 GaC. The electronic band structure and vibrational dispersion relation, as well as the electronic and vibrational density of states, have been calculated. The band structure close to the Fermi level indicates anisotropy with respect to electrical conductivity, while the distribution of the electronic and vibrational states for both Mn and Ga depend on the chosen relative orientation of the Mn spins across the Ga sheets in the Mn–Ga–Mn trilayers. In addition, the elastic properties have been calculated, and from the five elastic constants, the Voigt bulk modulus is determined to be 157 GPa, the Voigt shear modulus 93 GPa, and the Young's modulus 233 GPa. Furthermore, Mn 2 GaC is found relatively elastically isotropic, with a compression anisotropy factor of 0.97, and shear anisotropy factors of 0.9 and 1, respectively. The Poisson's ratio is 0.25. Evaluated elastic properties are compared to theoretical and experimental results for M 2 AC phases where M = Ti, V, Cr, Zr, Nb, Ta, and A = Al, S, Ge, In, Sn.

Structure, elastic stiffness, and hardness of Os 1- xRu xB 2 solid solution transition-metal diborides

KAUST Repository

Kanoun, Mohammed; Hermet, Patrick; Goumri-Said, Souraya

2012-01-01

On the basis of recent experiments, the solid solution transition-metal diborides were proposed to be new ultra-incompressible hard materials. We investigate using density functional theory based methods the structural and mechanical properties, electronic structure, and hardness of Os 1-xRu xB 2 solid solutions. A difference in chemical bonding occurs between OsB 2 and RuB 2 diborides, leading to significantly different elastic properties: a large bulk, shear moduli, and hardness for Os-rich diborides and relatively small bulk, shear moduli, and hardness for Ru-rich diborides. The electronic structure and bonding characterization are also analyzed as a function of Ru-dopant concentration in the OsB 2 lattice. © 2012 American Chemical Society.

Structure, elastic stiffness, and hardness of Os 1- xRu xB 2 solid solution transition-metal diborides

KAUST Repository

Kanoun, Mohammed

2012-05-31

On the basis of recent experiments, the solid solution transition-metal diborides were proposed to be new ultra-incompressible hard materials. We investigate using density functional theory based methods the structural and mechanical properties, electronic structure, and hardness of Os 1-xRu xB 2 solid solutions. A difference in chemical bonding occurs between OsB 2 and RuB 2 diborides, leading to significantly different elastic properties: a large bulk, shear moduli, and hardness for Os-rich diborides and relatively small bulk, shear moduli, and hardness for Ru-rich diborides. The electronic structure and bonding characterization are also analyzed as a function of Ru-dopant concentration in the OsB 2 lattice. © 2012 American Chemical Society.

Scalable BDDC Algorithms for Cardiac Electromechanical Coupling

KAUST Repository

Pavarino, L. F.

2017-03-17

The spread of electrical excitation in the cardiac muscle and the subsequent contraction-relaxation process is quantitatively described by the cardiac electromechanical coupling model. The electrical model consists of the Bidomain system, which is a degenerate parabolic system of two nonlinear partial differential equations (PDEs) of reaction-diffusion type, describing the evolution in space and time of the intra- and extracellular electric potentials. The PDEs are coupled through the reaction term with a stiff system of ordinary differential equations (ODEs), the membrane model, which describes the flow of the ionic currents through the cellular membrane and the dynamics of the associated gating variables. The mechanical model consists of the quasi-static finite elasticity system, modeling the cardiac tissue as a nearly-incompressible transversely isotropic hyperelastic material, and coupled with a system of ODEs accounting for the development of biochemically generated active force.

Scalable BDDC Algorithms for Cardiac Electromechanical Coupling

KAUST Repository

Pavarino, L. F.; Scacchi, S.; Verdi, C.; Zampieri, E.; Zampini, Stefano

2017-01-01

The spread of electrical excitation in the cardiac muscle and the subsequent contraction-relaxation process is quantitatively described by the cardiac electromechanical coupling model. The electrical model consists of the Bidomain system, which is a degenerate parabolic system of two nonlinear partial differential equations (PDEs) of reaction-diffusion type, describing the evolution in space and time of the intra- and extracellular electric potentials. The PDEs are coupled through the reaction term with a stiff system of ordinary differential equations (ODEs), the membrane model, which describes the flow of the ionic currents through the cellular membrane and the dynamics of the associated gating variables. The mechanical model consists of the quasi-static finite elasticity system, modeling the cardiac tissue as a nearly-incompressible transversely isotropic hyperelastic material, and coupled with a system of ODEs accounting for the development of biochemically generated active force.

Bringing to Light Hidden Elasticity in the Liquid State Using In-Situ Pretransitional Liquid Crystal Swarms.

Directory of Open Access Journals (Sweden)

Philipp Kahl

Full Text Available The present work reveals that at the sub-millimeter length-scale, molecules in the liquid state are not dynamically free but elastically correlated. It is possible to "visualize" these hidden elastic correlations by using the birefringent properties of pretransitional swarms persistent in liquids presenting a weak first order transition. The strategy consists in observing the optical response of the isotropic phase of mesogenic fluids to a weak (low energy mechanical excitation. We show that a synchronized optical response is observable at frequencies as low as 0.01Hz and at temperatures far away from any phase transition (up to at least 15°C above the transition. The observation of a synchronized optical signal at very low frequencies points out a collective response and supports the existence of long-range elastic (solid-like correlations existing at the sub-millimeter length-scale in agreement to weak solid-like responses already identified in various liquids including liquid water. This concept of elastically linked molecules differs deeply with the academic view of molecules moving freely in the liquid state and has profound consequences on the mechanisms governing collective effects as glass formation, gelation and transport, or synchronized processes in physiological media.

On a hierarchical construction of the anisotropic LTSN solution from the isotropic LTSN solution

International Nuclear Information System (INIS)

Foletto, Taline; Segatto, Cynthia F.; Bodmann, Bardo E.; Vilhena, Marco T.

2015-01-01

In this work, we present a recursive scheme targeting the hierarchical construction of anisotropic LTS N solution from the isotropic LTS N solution. The main idea relies in the decomposition of the associated LTS N anisotropic matrix as a sum of two matrices in which one matrix contains the isotropic and the other anisotropic part of the problem. The matrix containing the anisotropic part is considered as the source of the isotropic problem. The solution of this problem is made by the decomposition of the angular flux as a truncated series of intermediate functions and replace in the isotropic equation. After the replacement of these into the split isotropic equation, we construct a set of isotropic recursive problems, that are readily solved by the classic LTS N isotropic method. We apply this methodology to solve problems considering homogeneous and heterogeneous anisotropic regions. Numerical results are presented and compared with the classical LTS N anisotropic solution. (author)

Inviscid incompressible limits of the full Navier-Stokes-Fourier system

Czech Academy of Sciences Publication Activity Database

Feireisl, Eduard; Novotný, A.

2013-01-01

Roč. 321, č. 3 (2013), s. 605-628 ISSN 0010-3616 R&D Projects: GA ČR GA201/09/0917 Institutional support: RVO:67985840 Keywords : Navier-Stokes-Fourier system * inviscid limit * incompressible limit Subject RIV: BA - General Mathematics Impact factor: 1.901, year: 2013 http://link.springer.com/article/10.1007%2Fs00220-013-1691-4

Equilibrium states for a plane incompressible perfect fluid

Energy Technology Data Exchange (ETDEWEB)

Boldrighini, C; Frigio, S [Camerino Univ. (Italy). Istituto di Matematica

1980-01-01

We associate to the plane incompressible Euler equation with periodic conditions the corresponding Hopf equation, as an equation for measures on the space of solenoidal distributions. We define equilibrium states as the solutions of the stationary Hopf equation. We find a class of equilibrium states which corresponds to a class of infinitely divisible distributions, and investigate the properties of gaussian and poissonian states. Equilibrium dynamics for a class of poissonian states is constructed by means of the Onsager vortex equations.

Spatial Angular Compounding for Elastography without the Incompressibility Assumption

OpenAIRE

Rao, Min; Varghese, Tomy

2005-01-01

Spatial-angular compounding is a new technique that enables the reduction of noise artifacts in ultrasound elastography. Previous results using spatial angular compounding, however, were based on the use of the tissue incompressibility assumption. Compounded elastograms were obtained from a spatially-weighted average of local strain estimated from radiofrequency echo signals acquired at different insonification angles. In this paper, we present a new method for reducing the noise artifacts in...

Author Details

African Journals Online (AJOL)

) - Articles Propagation of shear waves in an irregular magnetoelastic monoclinic layer sandwiched between two isotropic half-spaces ... Propagation of S-waves in a non-homogeneous anisotropic incompressible and initially stressed medium

Acquisition Challenge: The Importance of Incompressibility in Comparing Learning Curve Models

Science.gov (United States)

2015-10-01

primary platform for analysis based on production history and availability of relevant airframe costs. F-15 airframe costs were acquired from two databases...assembly line at Ford or Toyota . Given this dynamic, assuming the real incompress- ibility factor is somewhere between 0.0 and 0.1 is not implausible

A finite-density calculation of the surface tension of isotropic-nematic interfaces

International Nuclear Information System (INIS)

Moore, B.G.; McMullen, W.E.

1992-01-01

The surface tension of the isotropic-nematic interface in a fluid of intermediate-sized hard particles is studied and calculated. The transition from isotropic to nematic is fixed to occur in a continuous fashion by varying the biaxiality of the model particles. A reversal in the preferred orientation of the bulk nematic relative to the isotropic-nematic interface suggests an oblique orientation of the bulk nematic. 32 refs., 8 figs

Some fundamental definitions of the elastic parameters for homogenous isotropic linear materials in road design and analysis

CSIR Research Space (South Africa)

De Beer, Morris

2008-07-01

Full Text Available - wave and ρ the material density. The elastic moduli P-wave modulus, M, is defined so that M = K + 4µ / 3 and M can then be determined by Equation 11, with a known speed Vp P MV 2 ρ = (11) It should however also... gas (such as air within compacted road materials), the adiabatic bulk modulus KS is approximately given by pKS κ= (4) Where: κ is the adiabatic index, (sometimes calledγ ); p is the pressure. In a fluid (such as moisture...

Comparison of three-dimensional isotropic and conventional MR arthrography with respect to the diagnosis of rotator cuff and labral lesions: Focus on isotropic fat-suppressed proton density and VIBE sequences

International Nuclear Information System (INIS)

Park, S.Y.; Lee, I.S.; Park, S.K.; Cheon, S.J.; Ahn, J.M.; Song, J.W.

2014-01-01

Aim: To compare the diagnostic accuracies of three-dimensional (3D) isotropic magnetic resonance arthrography (MRA) using fat-suppressed proton density (PD) or volume interpolated breath-hold examination (VIBE) sequences with that of conventional MRA for the diagnosis of rotator cuff and labral lesions. Materials and methods: Eighty-six patients who underwent arthroscopic surgery were included. 3D isotropic sequences were performed in the axial plane using fat-suppressed PD (group A) in 53 patients and using VIBE (group B) in 33 patients. Reformatted images were obtained corresponding to conventional images, and evaluated for the presence of labral and rotator cuff lesions using conventional and 3D isotropic sequences. The diagnostic performances of each sequence were determined using arthroscopic findings as the standard. Results: Good to excellent interobserver agreements were obtained for both 3D isotropic sequences for the evaluation of rotator cuff and labral lesions. Excellent agreement was found between two-dimensional (2D) and 3D isotropic MRA, except for supraspinatus tendon (SST) tears by both readers and for subscapularis tendon (SCT) tears by reader 2 in group B. 2D MRA and 3D isotropic sequences had high diagnostic performances for rotator and labral tears, and the difference between the two imaging methods was insignificant. Conclusions: The diagnostic performances of 3D isotropic VIBE and PD sequences were similar to those of 2D MRA

Elastic fields, dipole tensors, and interaction between self-interstitial atom defects in bcc transition metals

Science.gov (United States)

Dudarev, S. L.; Ma, Pui-Wai

2018-03-01

Density functional theory (DFT) calculations show that self-interstitial atom (SIA) defects in nonmagnetic body-centered-cubic (bcc) metals adopt strongly anisotropic configurations, elongated in the direction [S. Han et al., Phys. Rev. B 66, 220101 (2002), 10.1103/PhysRevB.66.220101; D. Nguyen-Manh et al., Phys. Rev. B 73, 020101 (2006), 10.1103/PhysRevB.73.020101; P. M. Derlet et al., Phys. Rev. B 76, 054107 (2007), 10.1103/PhysRevB.76.054107; S. L. Dudarev, Annu. Rev. Mater. Res. 43, 35 (2013), 10.1146/annurev-matsci-071312-121626]. Elastic distortions, associated with such anisotropic atomic structures, appear similar to distortions around small prismatic dislocation loops, although the extent of this similarity has never been quantified. We derive analytical formulas for the dipole tensors of SIA defects, which show that, in addition to the prismatic dislocation looplike character, the elastic field of a SIA defect also has a significant isotropic dilatation component. Using empirical potentials and DFT calculations, we parametrize dipole tensors of defects for all the nonmagnetic bcc transition metals. This enables a quantitative evaluation of the energy of elastic interaction between the defects, which also shows that in a periodic three-dimensional simple cubic arrangement of crowdions, long-range elastic interactions between a defect and all its images favor a orientation of the defect.

Isotropic Negative Thermal Expansion Metamaterials.

Science.gov (United States)

Wu, Lingling; Li, Bo; Zhou, Ji

2016-07-13

Negative thermal expansion materials are important and desirable in science and engineering applications. However, natural materials with isotropic negative thermal expansion are rare and usually unsatisfied in performance. Here, we propose a novel method to achieve two- and three-dimensional negative thermal expansion metamaterials via antichiral structures. The two-dimensional metamaterial is constructed with unit cells that combine bimaterial strips and antichiral structures, while the three-dimensional metamaterial is fabricated by a multimaterial 3D printing process. Both experimental and simulation results display isotropic negative thermal expansion property of the samples. The effective coefficient of negative thermal expansion of the proposed models is demonstrated to be dependent on the difference between the thermal expansion coefficient of the component materials, as well as on the circular node radius and the ligament length in the antichiral structures. The measured value of the linear negative thermal expansion coefficient of the three-dimensional sample is among the largest achieved in experiments to date. Our findings provide an easy and practical approach to obtaining materials with tunable negative thermal expansion on any scale.

Wind turbine rotor-tower interaction using an incompressible overset grid method

DEFF Research Database (Denmark)

Zahle, Frederik; Johansen, Jeppe; Sørensen, Niels N.

2007-01-01

In this paper 3D Navier-Stokes simulations of the flow over the NREL Phase VI turbine are presented. The computations are carried out using the structured grid, incompressible, finite volume flow solver EllipSys3D, which has been extended to include the use of overset grids. Computations are pres...

New criteria for isotropic and textured metals

Science.gov (United States)

Cazacu, Oana

2018-05-01

In this paper a isotropic criterion expressed in terms of both invariants of the stress deviator, J2 and J3 is proposed. This criterion involves a unique parameter, α, which depends only on the ratio between the yield stresses in uniaxial tension and pure shear. If this parameter is zero, the von Mises yield criterion is recovered; if a is positive the yield surface is interior to the von Mises yield surface whereas when a is negative, the new yield surface is exterior to it. Comparison with polycrystalline calculations using Taylor-Bishop-Hill model [1] for randomly oriented face-centered (FCC) polycrystalline metallic materials show that this new criterion captures well the numerical yield points. Furthermore, the criterion reproduces well yielding under combined tension-shear loadings for a variety of isotropic materials. An extension of this isotropic yield criterion such as to account for orthotropy in yielding is developed using the generalized invariants approach of Cazacu and Barlat [2]. This new orthotropic criterion is general and applicable to three-dimensional stress states. The procedure for the identification of the material parameters is outlined. Illustration of the predictive capabilities of the new orthotropic is demonstrated through comparison between the model predictions and data on aluminum sheet samples.

Numerical investigation of shape domain effect to its elasticity and surface energy using adaptive finite element method

Science.gov (United States)

Alfat, Sayahdin; Kimura, Masato; Firihu, Muhammad Zamrun; Rahmat

2018-05-01

In engineering area, investigation of shape effect in elastic materials was very important. It can lead changing elasticity and surface energy, and also increase of crack propagation in the material. A two-dimensional mathematical model was developed to investigation of elasticity and surface energy in elastic material by Adaptive Finite Element Method. Besides that, behavior of crack propagation has observed for every those materials. The government equations were based on a phase field approach in crack propagation model that developed by Takaishi-Kimura. This research has varied four shape domains where physical properties of materials were same (Young's modulus E = 70 GPa and Poisson's ratio ν = 0.334). Investigation assumptions were; (1) homogeneous and isotropic material, (2) there was not initial cracking at t = 0, (3) initial displacement was zero [u1, u2] = 0) at initial condition (t = 0), and (4) length of time simulation t = 5 with interval Δt = 0.005. Mode I/II or mixed mode crack propagation has been used for the numerical investigation. Results of this studies were very good and accurate to show changing energy and behavior of crack propagation. In the future time, this research can be developed to complex phenomena and domain. Furthermore, shape optimization can be investigation by the model.

Meshless Solution of Incompressible Flow Over Backward-Facing Step

Directory of Open Access Journals (Sweden)

Mužík Juraj

2016-05-01

Full Text Available Article presents the use of the meshless method for numerical simulation of incompressible fluid flow. The article presents the implementation of the meshless local Petrov-Galerkin method (MLPG, with Navier-Stokes equation formulated using the local weighted residual principle. The trial function construction process is the most important part of the meshless method implementation. In this article the radial basis functions (RBF are used for the process of the trial functions construction.

Directional statistics-based reflectance model for isotropic bidirectional reflectance distribution functions.

Science.gov (United States)

Nishino, Ko; Lombardi, Stephen

2011-01-01

We introduce a novel parametric bidirectional reflectance distribution function (BRDF) model that can accurately encode a wide variety of real-world isotropic BRDFs with a small number of parameters. The key observation we make is that a BRDF may be viewed as a statistical distribution on a unit hemisphere. We derive a novel directional statistics distribution, which we refer to as the hemispherical exponential power distribution, and model real-world isotropic BRDFs as mixtures of it. We derive a canonical probabilistic method for estimating the parameters, including the number of components, of this novel directional statistics BRDF model. We show that the model captures the full spectrum of real-world isotropic BRDFs with high accuracy, but a small footprint. We also demonstrate the advantages of the novel BRDF model by showing its use for reflection component separation and for exploring the space of isotropic BRDFs.

Ellipsoidal basis for isotropic oscillator

International Nuclear Information System (INIS)

Kallies, W.; Lukac, I.; Pogosyan, G.S.; Sisakyan, A.N.

1994-01-01

The solutions of the Schroedinger equation are derived for the isotropic oscillator potential in the ellipsoidal coordinate system. The explicit expression is obtained for the ellipsoidal integrals of motion through the components of the orbital moment and Demkov's tensor. The explicit form of the ellipsoidal basis is given for the lowest quantum numbers. 10 refs.; 1 tab. (author)

Coupled incompressible Smoothed Particle Hydrodynamics model for continuum-based modelling sediment transport

Science.gov (United States)

Pahar, Gourabananda; Dhar, Anirban

2017-04-01

A coupled solenoidal Incompressible Smoothed Particle Hydrodynamics (ISPH) model is presented for simulation of sediment displacement in erodible bed. The coupled framework consists of two separate incompressible modules: (a) granular module, (b) fluid module. The granular module considers a friction based rheology model to calculate deviatoric stress components from pressure. The module is validated for Bagnold flow profile and two standardized test cases of sediment avalanching. The fluid module resolves fluid flow inside and outside porous domain. An interaction force pair containing fluid pressure, viscous term and drag force acts as a bridge between two different flow modules. The coupled model is validated against three dambreak flow cases with different initial conditions of movable bed. The simulated results are in good agreement with experimental data. A demonstrative case considering effect of granular column failure under full/partial submergence highlights the capability of the coupled model for application in generalized scenario.

Numerical study of the stress-strain state of reinforced plate on an elastic foundation by the Bubnov-Galerkin method

Science.gov (United States)

Beskopylny, Alexey; Kadomtseva, Elena; Strelnikov, Grigory

2017-10-01

The stress-strain state of a rectangular slab resting on an elastic foundation is considered. The slab material is isotropic. The slab has stiffening ribs that directed parallel to both sides of the plate. Solving equations are obtained for determining the deflection for various mechanical and geometric characteristics of the stiffening ribs which are parallel to different sides of the plate, having different rigidity for bending and torsion. The calculation scheme assumes an orthotropic slab having different cylindrical stiffness in two mutually perpendicular directions parallel to the reinforcing ribs. An elastic foundation is adopted by Winkler model. To determine the deflection the Bubnov-Galerkin method is used. The deflection is taken in the form of an expansion in a series with unknown coefficients by special polynomials, which are a combination of Legendre polynomials.

Elastic contact mechanics: percolation of the contact area and fluid squeeze-out.

Science.gov (United States)

Persson, B N J; Prodanov, N; Krick, B A; Rodriguez, N; Mulakaluri, N; Sawyer, W G; Mangiagalli, P

2012-01-01

The dynamics of fluid flow at the interface between elastic solids with rough surfaces depends sensitively on the area of real contact, in particular close to the percolation threshold, where an irregular network of narrow flow channels prevails. In this paper, numerical simulation and experimental results for the contact between elastic solids with isotropic and anisotropic surface roughness are compared with the predictions of a theory based on the Persson contact mechanics theory and the Bruggeman effective medium theory. The theory predictions are in good agreement with the experimental and numerical simulation results and the (small) deviation can be understood as a finite-size effect. The fluid squeeze-out at the interface between elastic solids with randomly rough surfaces is studied. We present results for such high contact pressures that the area of real contact percolates, giving rise to sealed-off domains with pressurized fluid at the interface. The theoretical predictions are compared to experimental data for a simple model system (a rubber block squeezed against a flat glass plate), and for prefilled syringes, where the rubber plunger stopper is lubricated by a high-viscosity silicon oil to ensure functionality of the delivery device. For the latter system we compare the breakloose (or static) friction, as a function of the time of stationary contact, to the theory prediction.

Isotropic harmonic oscillator plus inverse quadratic potential in N-dimensional spaces

International Nuclear Information System (INIS)

Oyewumi, K.A.; Bangudu, E.A.

2003-01-01

Some aspects of the N-dimensional isotropic harmonic plus inverse quadratic potential were discussed. The hyperradial equation for isotropic harmonic oscillator plus inverse quadratic potential is solved by transformation into the confluent hypergeometric equation to obtain the normalized hyperradial solution. Together with the hyperangular solutions (hyperspherical harmonics), these form the complete energy eigenfunctions of the N-dimensional isotropic harmonic oscillator plus inverse quadratic potential and the energy eigenvalues are also obtained. These are dimensionally dependent. The dependence of radial solution on the dimensions or potential strength and the degeneracy of the energy levels are discussed. (author)

Validity of the isotropic thermal conductivity assumption in supercell lattice dynamics

Science.gov (United States)

Ma, Ruiyuan; Lukes, Jennifer R.

2018-02-01

Superlattices and nano phononic crystals have attracted significant attention due to their low thermal conductivities and their potential application as thermoelectric materials. A widely used expression to calculate thermal conductivity, presented by Klemens and expressed in terms of the relaxation time by Callaway and Holland, originates from the Boltzmann transport equation. In its most general form, this expression involves a direct summation of the heat current contributions from individual phonons of all wavevectors and polarizations in the first Brillouin zone. In common practice, the expression is simplified by making an isotropic assumption that converts the summation over wavevector to an integral over wavevector magnitude. The isotropic expression has been applied to superlattices and phononic crystals, but its validity for different supercell sizes has not been studied. In this work, the isotropic and direct summation methods are used to calculate the thermal conductivities of bulk Si, and Si/Ge quantum dot superlattices. The results show that the differences between the two methods increase substantially with the supercell size. These differences arise because the vibrational modes neglected in the isotropic assumption provide an increasingly important contribution to the thermal conductivity for larger supercells. To avoid the significant errors that can result from the isotropic assumption, direct summation is recommended for thermal conductivity calculations in superstructures.

NASA-VOF3D, 3-D Transient, Free Surface, Incompressible Fluid Dynamic

International Nuclear Information System (INIS)

Torrey, M.D.

1992-01-01

1 - Description of program or function: NASA-VOF3D is a three- dimensional, transient, free surface, incompressible fluid dynamics program. It is specifically designed to calculate confined flows in a low gravity environment in which surface physics must be accurately treated. It allows multiple free surfaces with surface tension and wall adhesion and includes a partial cell treatment that allows curved boundaries and internal obstacles. Variable mesh spacing is permitted in all three coordinate directions. Boundary conditions available are rigid free-slip wall, rigid no-slip, wall, continuative, periodic, and specified pressure outflow boundary. 2 - Method of solution: NASA-VOF3D simulates incompressible flows with free surfaces using the volume-of-fluid (VOF) algorithm. This technique is based on the use of donor-acceptor differencing to track the free surface across an Eulerian grid. The free surfaces are treated by introducing a function defined to be unity at any point occupied by the fluid and zero elsewhere. The complete Navier- Stokes equations for an incompressible fluid are solved by finite differences with surface tension effects included. Wall adhesion may be included or neglected as a user option. The pressures (and velocities) are advanced in time throughout the computing mesh by either a conjugate residual method or the successive over-relaxation (SOR) method. The conjugate residual method is vectorized for the Cray and uses a scaled coefficient matrix. 3 - Restrictions on the complexity of the problem: NASA-VOF3D is restricted to cylindrical coordinate representation of the geometry. A three-dimensional wall-adhesion procedure is available only for straight-walled containers

Identification of multiple cracks in 2D elasticity by means of the reciprocity principle and cluster analysis

Science.gov (United States)

Shifrin, Efim I.; Kaptsov, Alexander V.

2018-01-01

An inverse 2D elastostatic problem is considered. It is assumed that an isotropic, linear elastic body can contain a finite number of rectilinear, well-separated cracks. The surfaces of the cracks are assumed to be free of the loads. A method is developed for reconstruction the cracks by means of the applied loads and displacements on the boundary of the body, obtained in a single static test. The method is based on the reciprocity principle, elements of the theory of distributions, and cluster analysis. Numerical examples are considered.

3D geometrically isotropic metamaterial for telecom wavelengths

DEFF Research Database (Denmark)

Malureanu, Radu; Andryieuski, Andrei; Lavrinenko, Andrei

2009-01-01

of the unit cell is not infinitely small, certain geometrical constraints have to be fulfilled to obtain an isotropic response of the material [3]. These conditions and the metal behaviour close to the plasma frequency increase the design complexity. Our unit cell is composed of two main parts. The first part...... is obtained in a certain bandwidth. The proposed unit cell has the cubic point group of symmetry and being repeatedly placed in space can effectively reveal isotropic optical properties. We use the CST commercial software to characterise the “cube-in-cage” structure. Reflection and transmission spectra...

Elasticity for geotechnicians a modern exposition of Kelvin, Boussinesq, Flamant, Cerruti, Melan, and Mindlin problems

CERN Document Server

Podio-Guidugli, Paolo

2014-01-01

This book deals in a modern manner with a family of named problems from an old and mature subject, classical elasticity. These problems are formulated over either a half or the whole of a linearly elastic and isotropic two- or three-dimensional space, subject to loads concentrated at points or lines. The discussion of each problem begins with a careful examination of the prevailing symmetries, and proceeds with inverting the canonical order, in that it moves from a search for balanced stress fields to the associated strain and displacement fields. The book, although slim, is  fairly well self-contained; the only prerequisite is a reasonable familiarity with linear algebra (in particular, manipulation of vectors and tensors) and with the usual differential operators of mathematical physics (gradient, divergence, curl, and Laplacian); the few nonstandard notions are introduced with care. Support material for all parts of the book is found in the final Appendix.

Surface incompressibility from semiclassical relativistic mean field calculations

International Nuclear Information System (INIS)

Patra, S.K.; Centelles, M.; Vinas, X.; Estal, M. del

2002-01-01

By using the scaling method and the Thomas-Fermi and extended Thomas-Fermi approaches to relativistic mean field theory the surface contribution to the leptodermous expansion of the finite nuclei incompressibility K A has been self-consistently computed. The validity of the simplest expansion, which contains volume, volume-symmetry, surface, and Coulomb terms, is examined by comparing it with self-consistent results of K A for some currently used nonlinear σ-ω parameter sets. A numerical estimate of higher-order contributions to the leptodermous expansion, namely, the curvature and surface-symmetry terms, is made

Discrete exterior calculus discretization of incompressible Navier–Stokes equations over surface simplicial meshes

KAUST Repository

Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi

2016-01-01

A conservative discretization of incompressible Navier–Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a

Incompressible limit of compressible Navier-Stokes equations

International Nuclear Information System (INIS)

Bessaih, H.

1994-01-01

In this paper we study the system which describes the motion of compressible viscous fluid in a bounded domain Ω of R 3 . When we introduce a parameter λ, that is the inverse of the Mach number, we prove, under small initial data and external force (for barotropic flows), that the solution of Navier-Stokes equations is the incompressible limit of the solution of compressible Navier-Stokes equations, as the Mach number becomes small. For this, we show the existence of a solution verifying estimates independent of λ. Compactness argument allow us to pass to the limit on λ in the nonlinear terms. (author). 17 refs

Dynamic elastic-plastic response of a 2-DOF mass-spring system.

Energy Technology Data Exchange (ETDEWEB)

Corona, Edmundo [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2018-02-01

The objective of the work presented here arose from abnormal, drop scenarios and specifically the question of how the accelerations and accumulation of plastic strains of internal components could be a ected by the material properties of the external structure. In some scenarios, the impact loads can induce cyclic motion of the internal components. Therefore, a second objective was to explore di erences that could be expected when simulations are conducted using isotropic hardening vs. kinematic hardening plasticity models. The simplest model that can be used to investigate the objectives above is a two-degree-offreedom mass/spring model where the springs exhibit elastic-plastic behavior. The purpose of this memo is to develop such model and present a few results that address the objectives.

A general shakedown theorem for elastic/plastic bodies with work hardening

International Nuclear Information System (INIS)

Ponter, A.R.S.

1975-01-01

In recent years the design of metallic structures under variable loading has been assisted by the application of Melan's lower bound theorem for the shakedown on an elastic/perfectly plastic structure. The design codes for both portal frames and pressure vessels have taken account of such calculations. The theory of shakedown suffers from two defects, geometry changes are ignored and the material behaviour is described by a perfectly plastic constitutive relationship which includes neither work hardening nor the Bauschinger effect. This paper is concerned with the latter problem. A very general lower bound shakedown theorem is derived for an arbitrary time-independent material in terms of functional properties of the constitutive relationship. The theorem is then applied to perfect, isotropic and kinematic hardening plasticity. (Auth.)

INCOMPRESSIBLE LAMINAR BOUNDARY LAYER CONTROL BY BLOWING AND SUCTION

OpenAIRE

AZZEDINE NAHOUI; LAKHDAR BAHI

2013-01-01

A two-dimensional incompressible laminar boundary layer and its control using blowing and suction over a flat plate and around the NACA 0012 and 661012 profiles, is studied numerically. The study is based on the Prandtl boundary layer model using the finite differences method and the Crank-Nicolson scheme. The velocity distribution, the boundary layer thickness and the friction coefficient, are determined and presented with and without control. The application of the control technique, has de...

In-Plane free Vibration Analysis of an Annular Disk with Point Elastic Support

Directory of Open Access Journals (Sweden)

S. Bashmal

2011-01-01

Full Text Available In-plane free vibrations of an elastic and isotropic annular disk with elastic constraints at the inner and outer boundaries, which are applied either along the entire periphery of the disk or at a point are investigated. The boundary characteristic orthogonal polynomials are employed in the Rayleigh-Ritz method to obtain the frequency parameters and the associated mode shapes. Boundary characteristic orthogonal polynomials are generated for the free boundary conditions of the disk while artificial springs are used to account for different boundary conditions. The frequency parameters for different boundary conditions of the outer edge are evaluated and compared with those available in the published studies and computed from a finite element model. The computed mode shapes are presented for a disk clamped at the inner edge and point supported at the outer edge to illustrate the free in-plane vibration behavior of the disk. Results show that addition of point clamped support causes some of the higher modes to split into two different frequencies with different mode shapes.

Measurement of tissue-radiation dosage using a thermal steady-state elastic shear wave.

Science.gov (United States)

Chang, Sheng-Yi; Hsieh, Tung-Sheng; Chen, Wei-Ru; Chen, Jin-Chung; Chou, Chien

2017-08-01

A biodosimeter based on thermal-induced elastic shear wave (TIESW) in silicone acellular porcine dermis (SAPD) at thermal steady state has been proposed and demonstrated. A square slab SAPD treated with ionizing radiation was tested. The SAPD becomes a continuous homogeneous and isotropic viscoelastic medium due to the generation of randomly coiled collagen fibers formed from their bundle-like structure in the dermis. A harmonic TIESW then propagates on the surface of the SAPD as measured by a nanometer-scaled strain-stress response under thermal equilibrium conditions at room temperature. TIESW oscillation frequency was noninvasively measured in real time by monitoring the transverse displacement of the TIESW on the SAPD surface. Because the elastic shear modulus is highly sensitive to absorbed doses of ionizing radiation, this proposed biodosimeter can become a highly sensitive and noninvasive method for quantitatively determining tissue-absorbed dosage in terms of TIESW’s oscillation frequency. Detection sensitivity at 1 cGy and dynamic ranges covering 1 to 40 cGy and 80 to 500 cGy were demonstrated.

Nonlinear sausage-wave propagation in a magnetic slab in an incompressible fluid

International Nuclear Information System (INIS)

Ruderman, M.S.

1993-01-01

Long nonlinear sausage-wave propagation in a magnetic slab in an incompressible plasma is considered. The governing equation is derived with the aid of the reductive perturbation method. The solutions of this equation in the form of periodic waves of permanent shape are found numerically. (Author)

A matrix-free, implicit, incompressible fractional-step algorithm for fluid–structure interaction applications

CSIR Research Space (South Africa)

Oxtoby, Oliver F

2012-05-01

Full Text Available In this paper we detail a fast, fully-coupled, partitioned fluid–structure interaction (FSI) scheme. For the incompressible fluid, new fractional-step algorithms are proposed which make possible the fully implicit, but matrixfree, parallel solution...

A combined application of boundary-element and Runge-Kutta methods in three-dimensional elasticity and poroelasticity

Directory of Open Access Journals (Sweden)

Igumnov Leonid

2015-01-01

Full Text Available The report presents the development of the time-boundary element methodology and a description of the related software based on a stepped method of numerical inversion of the integral Laplace transform in combination with a family of Runge-Kutta methods for analyzing 3-D mixed initial boundary-value problems of the dynamics of inhomogeneous elastic and poro-elastic bodies. The results of the numerical investigation are presented. The investigation methodology is based on direct-approach boundary integral equations of 3-D isotropic linear theories of elasticity and poroelasticity in Laplace transforms. Poroelastic media are described using Biot models with four and five base functions. With the help of the boundary-element method, solutions in time are obtained, using the stepped method of numerically inverting Laplace transform on the nodes of Runge-Kutta methods. The boundary-element method is used in combination with the collocation method, local element-by-element approximation based on the matched interpolation model. The results of analyzing wave problems of the effect of a non-stationary force on elastic and poroelastic finite bodies, a poroelastic half-space (also with a fictitious boundary and a layered half-space weakened by a cavity, and a half-space with a trench are presented. Excitation of a slow wave in a poroelastic medium is studied, using the stepped BEM-scheme on the nodes of Runge-Kutta methods.

Testing the mutually enhanced magicity effect in nuclear incompressibility via the giant monopole resonance in the {sup 204,206,208}Pb isotopes

Energy Technology Data Exchange (ETDEWEB)

Patel, D. [Department of Physics, University of Notre Dame, Notre Dame, IN 46556 (United States); Joint Institute for Nuclear Astrophysics, University of Notre Dame, Notre Dame, IN 46556 (United States); Garg, U., E-mail: garg@nd.edu [Department of Physics, University of Notre Dame, Notre Dame, IN 46556 (United States); Joint Institute for Nuclear Astrophysics, University of Notre Dame, Notre Dame, IN 46556 (United States); Fujiwara, M. [Research Center for Nuclear Physics, Osaka University, Osaka 567-0047 (Japan); Adachi, T. [Kernfysisch Versneller Instituut, University of Groningen, 9747 AA Groningen (Netherlands); Akimune, H. [Department of Physics, Konan University, Kobe 568-8501 (Japan); Berg, G.P.A. [Department of Physics, University of Notre Dame, Notre Dame, IN 46556 (United States); Joint Institute for Nuclear Astrophysics, University of Notre Dame, Notre Dame, IN 46556 (United States); Harakeh, M.N. [Kernfysisch Versneller Instituut, University of Groningen, 9747 AA Groningen (Netherlands); GANIL, CEA/DSM-CNRS/IN2P3, 14076 Cean (France); Itoh, M. [Cyclotron and Radioisotope Center, Tohoku University, Sendai 980-8578 (Japan); Iwamoto, C. [Department of Physics, Konan University, Kobe 568-8501 (Japan); Long, A.; Matta, J.T. [Department of Physics, University of Notre Dame, Notre Dame, IN 46556 (United States); Joint Institute for Nuclear Astrophysics, University of Notre Dame, Notre Dame, IN 46556 (United States); Murakami, T. [Division of Physics and Astronomy, Kyoto University, Kyoto 606-8502 (Japan); Okamoto, A. [Department of Physics, Konan University, Kobe 568-8501 (Japan); Sault, K. [Department of Physics, University of Notre Dame, Notre Dame, IN 46556 (United States); Talwar, R. [Department of Physics, University of Notre Dame, Notre Dame, IN 46556 (United States); Joint Institute for Nuclear Astrophysics, University of Notre Dame, Notre Dame, IN 46556 (United States); Uchida, M. [Department of Physics, Tokyo Institute of Technology, Tokyo 152-8850 (Japan); and others

2013-10-07

Using inelastic α-scattering at extremely forward angles, including 0°, the strength distributions of the isoscalar giant monopole resonance (ISGMR) have been measured in the {sup 204,206,208}Pb isotopes in order to examine the proposed mutually enhanced magicity (MEM) effect on the nuclear incompressibility. The MEM effect had been suggested as a likely explanation of the “softness” of nuclear incompressibility observed in the ISGMR measurements in the Sn and Cd isotopes. Our experimental results rule out any manifestation of the MEM effect in nuclear incompressibility and leave the question of the softness of the open-shell nuclei unresolved still.

Three dimensional simulation of compressible and incompressible flows through the finite element method

International Nuclear Information System (INIS)

Costa, Gustavo Koury

2004-11-01

Although incompressible fluid flows can be regarded as a particular case of a general problem, numerical methods and the mathematical formulation aimed to solve compressible and incompressible flows have their own peculiarities, in such a way, that it is generally not possible to attain both regimes with a single approach. In this work, we start from a typically compressible formulation, slightly modified to make use of pressure variables and, through augmenting the stabilising parameters, we end up with a simplified model which is able to deal with a wide range of flow regimes, from supersonic to low speed gas flows. The resulting methodology is flexible enough to allow for the simulation of liquid flows as well. Examples using conservative and pressure variables are shown and the results are compared to those published in the literature, in order to validate the method. (author)

Viscoelastic Model for Lung Parenchyma for Multi-Scale Modeling of Respiratory System Phase I: Hypo-Elastic Model for CFD Implementation

Energy Technology Data Exchange (ETDEWEB)

Freed, Alan D.; Einstein, Daniel R.

2011-04-14

An isotropic constitutive model for the parenchyma of lung has been derived from the theory of hypo-elasticity. The intent is to use it to represent the mechanical response of this soft tissue in sophisticated, computational, fluid-dynamic models of the lung. This demands that the continuum model be accurate, yet simple and effcient. An objective algorithm for its numeric integration is provided. The response of the model is determined for several boundary-value problems whose experiments are used for material characterization. The effective elastic, bulk, and shear moduli, and Poisson’s ratio, as tangent functions, are also derived. The model is characterized against published experimental data for lung. A bridge between this continuum model and a dodecahedral model of alveolar geometry is investigated, with preliminary findings being reported.

Single-cell mechanics--An experimental-computational method for quantifying the membrane-cytoskeleton elasticity of cells.

Science.gov (United States)

Tartibi, M; Liu, Y X; Liu, G-Y; Komvopoulos, K

2015-11-01

The membrane-cytoskeleton system plays a major role in cell adhesion, growth, migration, and differentiation. F-actin filaments, cross-linkers, binding proteins that bundle F-actin filaments to form the actin cytoskeleton, and integrins that connect the actin cytoskeleton network to the cell plasma membrane and extracellular matrix are major cytoskeleton constituents. Thus, the cell cytoskeleton is a complex composite that can assume different shapes. Atomic force microscopy (AFM)-based techniques have been used to measure cytoskeleton material properties without much attention to cell shape. A recently developed surface chemical patterning method for long-term single-cell culture was used to seed individual cells on circular patterns. A continuum-based cell model, which uses as input the force-displacement response obtained with a modified AFM setup and relates the membrane-cytoskeleton elastic behavior to the cell geometry, while treating all other subcellular components suspended in the cytoplasmic liquid (gel) as an incompressible fluid, is presented and validated by experimental results. The developed analytical-experimental methodology establishes a framework for quantifying the membrane-cytoskeleton elasticity of live cells. This capability may have immense implications in cell biology, particularly in studies seeking to establish correlations between membrane-cytoskeleton elasticity and cell disease, mortality, differentiation, and migration, and provide insight into cell infiltration through nonwoven fibrous scaffolds. The present method can be further extended to analyze membrane-cytoskeleton viscoelasticity, examine the role of other subcellular components (e.g., nucleus envelope) in cell elasticity, and elucidate the effects of mechanical stimuli on cell differentiation and motility. This is the first study to decouple the membrane-cytoskeleton elasticity from cell stiffness and introduce an effective approach for measuring the elastic modulus. The

A meshless scheme for incompressible fluid flow using a velocity-pressure correction method

KAUST Repository

Bourantas, Georgios; Loukopoulos, Vassilios C.

2013-01-01

A meshless point collocation method is proposed for the numerical solution of the steady state, incompressible Navier-Stokes (NS) equations in their primitive u-v-p formulation. The flow equations are solved in their strong form using either a

Some recent advances in 3D crack and contact analysis of elastic solids with transverse isotropy and multifield coupling

Science.gov (United States)

Chen, Wei-Qiu

2015-10-01

Significant progress has been made in mixed boundary-value problems associated with three-dimensional (3D) crack and contact analyses of advanced materials featuring more complexities compared to the conventional isotropic elastic materials. These include material anisotropy and multifield coupling, two typical characteristics of most current multifunctional materials. In this paper we try to present a state-of-the-art description of 3D exact/analytical solutions derived for crack and contact problems of elastic solids with both transverse isotropy and multifield coupling in the latest decade by the potential theory method in the spirit of V. I. Fabrikant, whose ingenious breakthrough brings new vigor and vitality to the old research subject of classical potential theory. We are particularly interested in crack and contact problems with certain nonlinear features. Emphasis is also placed on the coupling between the temperature field (or the like) and other physical fields (e.g., elastic, electric, and magnetic fields). We further highlight the practical significance of 3D contact solutions, in particular in applications related to modern scanning probe microscopes.

Shape sensitivity analysis of time-dependent flows of incompressible non-Newtonian fluids

Czech Academy of Sciences Publication Activity Database

Sokolowski, J.; Stebel, Jan

2011-01-01

Roč. 40, č. 4 (2011), s. 1077-1097 ISSN 0324-8569 R&D Projects: GA ČR GA201/09/0917 Institutional research plan: CEZ:AV0Z10190503 Keywords : shape optimization * shape gradient * incompressible viscous fluid Subject RIV: BA - General Mathematics Impact factor: 0.300, year: 2010

Concerning the Effect of a Viscoelastic Foundation on the Dynamic Stability of a Pipeline System Conveying an Incompressible Fluid

Directory of Open Access Journals (Sweden)

Vincent Olunloyo

2016-12-01

Full Text Available In this paper, we present an analytical method for solving a well-posed boundary value problem of mathematical physics governing the vibration characteristics of an internal flow propelled fluid-structure interaction where the pipeline segment is idealized as an elastic hollow beam conveying an incompressible fluid on a viscoelastic foundation. The effect of Coriolis and damping forces on the overall dynamic response of the system is investigated. In actuality, for a pipe segment supported at both ends and subject to a free motion, these two forces generate conjugate complex frequencies for all flow velocities. On employing integral transforms and complex variable functions, a closed form analytical expression is derived for the overall dynamic response. It is demonstrated that a concise mathematical expression for the natural frequency associated with any mode of vibration can be deduced from the algebraic product of the complex frequency pairs. By a way of comparative analysis for damping decrement physics reminiscent with laminated structures, mathematical expressions are derived to illustrate viscoelastic damping effects on dynamic stability for any flow velocity. The integrity of the analytical solution is verified and validated by confirming theresults in literature in appropriate asymptotic limits.

Incomplete augmented Lagrangian preconditioner for steady incompressible Navier-Stokes equations.

Science.gov (United States)

Tan, Ning-Bo; Huang, Ting-Zhu; Hu, Ze-Jun

2013-01-01

An incomplete augmented Lagrangian preconditioner, for the steady incompressible Navier-Stokes equations discretized by stable finite elements, is proposed. The eigenvalues of the preconditioned matrix are analyzed. Numerical experiments show that the incomplete augmented Lagrangian-based preconditioner proposed is very robust and performs quite well by the Picard linearization or the Newton linearization over a wide range of values of the viscosity on both uniform and stretched grids.

Origin of shear thickening in semidilute wormlike micellar solutions and evidence of elastic turbulence

International Nuclear Information System (INIS)

Marín-Santibáñez, Benjamín M.; Pérez-González, José; Rodríguez-González, Francisco

2014-01-01

The origin of shear thickening in an equimolar semidilute wormlike micellar solution of cetylpyridinium chloride and sodium salicylate was investigated in this work by using Couette rheometry, flow visualization, and capillary Rheo-particle image velocimetry. The use of the combined methods allowed the discovery of gradient shear banding flow occurring from a critical shear stress and consisting of two main bands, one isotropic (transparent) of high viscosity and one structured (turbid) of low viscosity. Mechanical rheometry indicated macroscopic shear thinning behavior in the shear banding regime. However, local velocimetry showed that the turbid band increased its viscosity along with the shear stress, even though barely reached the value of the viscosity of the isotropic phase. This shear band is the precursor of shear induced structures that subsequently give rise to the average increase in viscosity or apparent shear thickening of the solution. Further increase in the shear stress promoted the growing of the turbid band across the flow region and led to destabilization of the shear banding flow independently of the type of rheometer used, as well as to vorticity banding in Couette flow. At last, vorticity banding disappeared and the flow developed elastic turbulence with chaotic dynamics

Global Well-Posedness of the Incompressible Magnetohydrodynamics

Science.gov (United States)

Cai, Yuan; Lei, Zhen

2018-06-01

This paper studies the Cauchy problem of the incompressible magnetohydro dynamic systems with or without viscosity ν. Under the assumption that the initial velocity field and the displacement of the initialmagnetic field froma non-zero constant are sufficiently small in certain weighted Sobolev spaces, the Cauchy problem is shown to be globally well-posed for all ν ≧ 0 and all spaces with dimension n ≧ 2. Such a result holds true uniformly in nonnegative viscosity parameters. The proof is based on the inherent strong null structure of the systems introduced by Lei (Commun Pure Appl Math 69(11):2072-2106, 2016) and the ghost weight technique introduced by Alinhac (Invent Math 145(3):597-618, 2001).

CONVEC: a computer program for transient incompressible fluid flow based on quadratic finite elements. Part 1: theoretical aspects

International Nuclear Information System (INIS)

Laval, H.

1981-01-01

This report describes the theoretical and numerical aspects of the finite element computer code CONVEC designed for the transient analysis of two-dimensional plane or three-dimensional axisymmetric incompressible flows including the effects of heat transfer. The governing equations for the above class of problems are the time-dependent incompressible Navier-Stokes equations and the thermal energy equation. The general class of flow problems analysed by CONVEC is discussed and the equations for the initial-boundary value problem are represented. A brief description of the finite element method and the weighted residual formulation is presented. The numerical solution of the incompressible equations is achieved by using a fractional step method. The mass lumping process associated with an explicit time integration scheme is described. The time integration is analysed and the stability conditions are derived. Numerical applications are presented. Standard problems of natural and forced convection are solved and the solutions obtained are compared with other numerical solutions published in the literature

First-order system least squares for the pure traction problem in planar linear elasticity

Energy Technology Data Exchange (ETDEWEB)

Cai, Z.; Manteuffel, T.; McCormick, S.; Parter, S.

1996-12-31

This talk will develop two first-order system least squares (FOSLS) approaches for the solution of the pure traction problem in planar linear elasticity. Both are two-stage algorithms that first solve for the gradients of displacement, then for the displacement itself. One approach, which uses L{sup 2} norms to define the FOSLS functional, is shown under certain H{sup 2} regularity assumptions to admit optimal H{sup 1}-like performance for standard finite element discretization and standard multigrid solution methods that is uniform in the Poisson ratio for all variables. The second approach, which is based on H{sup -1} norms, is shown under general assumptions to admit optimal uniform performance for displacement flux in an L{sup 2} norm and for displacement in an H{sup 1} norm. These methods do not degrade as other methods generally do when the material properties approach the incompressible limit.

Isotropic blackbody cosmic microwave background radiation as evidence for a homogeneous universe.

Science.gov (United States)

Clifton, Timothy; Clarkson, Chris; Bull, Philip

2012-08-03

The question of whether the Universe is spatially homogeneous and isotropic on the largest scales is of fundamental importance to cosmology but has not yet been answered decisively. Surprisingly, neither an isotropic primary cosmic microwave background (CMB) nor combined observations of luminosity distances and galaxy number counts are sufficient to establish such a result. The inclusion of the Sunyaev-Zel'dovich effect in CMB observations, however, dramatically improves this situation. We show that even a solitary observer who sees an isotropic blackbody CMB can conclude that the Universe is homogeneous and isotropic in their causal past when the Sunyaev-Zel'dovich effect is present. Critically, however, the CMB must either be viewed for an extended period of time, or CMB photons that have scattered more than once must be detected. This result provides a theoretical underpinning for testing the cosmological principle with observations of the CMB alone.

Suitable weak solutions: from compressible viscous to incompressible inviscid fluid flows

Czech Academy of Sciences Publication Activity Database

Feireisl, Eduard; Novotný, A.; Petzeltová, Hana

2013-01-01

Roč. 356, č. 2 (2013), s. 683-702 ISSN 0025-5831 R&D Projects: GA ČR GA201/09/0917 Institutional research plan: CEZ:AV0Z10190503 Keywords : relative entropy * incompressible limit * inviscid limit Subject RIV: BA - General Mathematics Impact factor: 1.201, year: 2013 http://link.springer.com/article/10.1007%2Fs00208-012-0862-5

Numerical Study on Several Stabilized Finite Element Methods for the Steady Incompressible Flow Problem with Damping

Directory of Open Access Journals (Sweden)

Jilian Wu

2013-01-01

Full Text Available We discuss several stabilized finite element methods, which are penalty, regular, multiscale enrichment, and local Gauss integration method, for the steady incompressible flow problem with damping based on the lowest equal-order finite element space pair. Then we give the numerical comparisons between them in three numerical examples which show that the local Gauss integration method has good stability, efficiency, and accuracy properties and it is better than the others for the steady incompressible flow problem with damping on the whole. However, to our surprise, the regular method spends less CPU-time and has better accuracy properties by using Crout solver.

Initial magnetic susceptibility of the diluted magnetopolymer elastic composites

International Nuclear Information System (INIS)

Borin, D.Yu.; Odenbach, S.

2017-01-01

In this work diluted magnetopolymer elastic composites based on magnetic microparticles are experimentally studied. Considered samples have varied concentration of the magnetic powder and different structural anisotropy. Experimental data on magnetic properties are accomplished by microstructural observations performed using X-Ray tomography. Influence of the particles amount and structuring effects on the initial magnetic susceptibility of the composites as well as the applicability of the Maxwell-Garnett approximation, which is widely used in considerations of magnetopolymer elastic composites, are evaluated. It is demonstrated that the approximation works well for diluted samples containing randomly distributed magnetic particles and for the diluted samples with chain-like structures oriented perpendicular to an externally applied field, while it fails to predict the susceptibility of the samples with structures oriented parallel to the field. Moreover, it is shown, that variation of the chains morphology does not significantly change the composite initial magnetic susceptibility. - Highlights: • The Maxwell-Garnet prediction works well for the diluted isotropic composites. • The Maxwell-Garnet prediction can be used for composites with structures oriented perpendicular to an applied field. • Chains oriented parallel to an applied field significantly increase the composite initial magnetic susceptibility. • The number and thickness of chains is not of the highest importance for the diluted composites. • The crucial reason of the observed effect is expected to be the demagnetisation factor of the chains.

The isotropic Universe

International Nuclear Information System (INIS)

Raine, D.J.

1981-01-01

This introduction to contemporary ideas in cosmology differs from other books on the 'expanding Universe' in its emphasis on physical cosmology and on the physical basis of the general theory of relativity. It is considered that the remarkable degree of isotropy, rather than the expansion, can be regarded as the central observational feature of the Universe. The various theories and ideas in 'big-bang' cosmology are discussed, providing an insight into current problems. Chapter headings are: quality of matter; expanding Universe; quality of radiation; quantity of matter; general theory of relativity; cosmological models; cosmological tests; matter and radiation; limits of isotropy; why is the Universe isotropic; singularities; evolution of structure. (U.K.)

Nonlinear normal vibration modes in the dynamics of nonlinear elastic systems

International Nuclear Information System (INIS)

Mikhlin, Yu V; Perepelkin, N V; Klimenko, A A; Harutyunyan, E

2012-01-01

Nonlinear normal modes (NNMs) are a generalization of the linear normal vibrations. By the Kauderer-Rosenberg concept in the regime of the NNM all position coordinates are single-values functions of some selected position coordinate. By the Shaw-Pierre concept, the NNM is such a regime when all generalized coordinates and velocities are univalent functions of a couple of dominant (active) phase variables. The NNMs approach is used in some applied problems. In particular, the Kauderer-Rosenberg NNMs are analyzed in the dynamics of some pendulum systems. The NNMs of forced vibrations are investigated in a rotor system with an isotropic-elastic shaft. A combination of the Shaw-Pierre NNMs and the Rauscher method is used to construct the forced NNMs and the frequency responses in the rotor dynamics.

An Isotropic Light Sensor for Measurements of Visible Actinic Flux in Clouds

NARCIS (Netherlands)

Hage, J.C.H. van der; Roode, S.R. de

1999-01-01

A low-cost isotropic light sensor is described consisting of a spherical diffuser connected to a single photodiode by a light conductor. The directional response to light is isotropic to a high degree. The small, lightweight, and rugged construction makes this instrument suitable not only for

Calculated isotropic Raman spectra from interacting H2-rare-gas pairs

International Nuclear Information System (INIS)

Gustafsson, M; Głaz, W; Bancewicz, T; Godet, J-L; Maroulis, G; Haskapoulos, A

2014-01-01

We report on a theoretical study of the H 2 -He and H 2 -Ar pair trace-polarizability and the corresponding isotropic Raman spectra. The conventional quantum mechanical approach for calculations of interaction-induced spectra, which is based on an isotropic interaction potential, is employed. This is compared with a close-coupling approach, which allows for inclusion of the full, anisotropic potential. It is established that the anisotropy of the potential plays a minor role for these spectra. The computed isotropic collision-induced Raman intensity, which is due to dissimilar pairs in H 2 -He and H 2 -Ar gas mixtures, is comparable to the intensities due to similar pairs (H 2 -H 2 , He-He, and Ar-Ar), which have been studied previously

Nonlinear elastic inclusions in isotropic solids

KAUST Repository

Yavari, A.; Goriely, A.

2013-01-01

We introduce a geometric framework to calculate the residual stress fields and deformations of nonlinear solids with inclusions and eigenstrains. Inclusions are regions in a body with different reference configurations from the body itself and can

Mechanical and electronic properties of monolayer and bilayer phosphorene under uniaxial and isotropic strains.

Science.gov (United States)

Hu, Ting; Han, Yang; Dong, Jinming

2014-11-14

The mechanical and electronic properties of both the monolayer and bilayer phosphorenes under either isotropic or uniaxial strain have been systematically investigated using first-principles calculations. It is interesting to find that: 1) Under a large enough isotropic tensile strain, the monolayer phosphorene would lose its pucker structure and transform into a flat hexagonal plane, while two inner sublayers of the bilayer phosphorene could be bonded due to its interlayer distance contraction. 2) Under the uniaxial tensile strain along a zigzag direction, the pucker distance of each layer in the bilayer phosphorene can exhibit a specific negative Poisson's ratio. 3) The electronic properties of both the monolayer and bilayer phosphorenes are sensitive to the magnitude and direction of the applied strains. Their band gaps decrease more rapidly under isotropic compressive strain than under uniaxial strain. Also, their direct-indirect band gap transitions happen at the larger isotropic tensile strains compared with that under uniaxial strain. 4) Under the isotropic compressive strain, the bilayer phosphorene exhibits a transition from a direct-gap semiconductor to a metal. In contrast, the monolayer phosphorene initially has the direct-indirect transition and then transitions to a metal. However, under isotropic tensile strain, both the bilayer and monolayer phosphorene show the direct-indirect transition and, finally, the transition to a metal. Our numerical results may open new potential applications of phosphorene in nanoelectronics and nanomechanical devices by external isotropic strain or uniaxial strain along different directions.

Isotropic quantum walks on lattices and the Weyl equation

Science.gov (United States)

D'Ariano, Giacomo Mauro; Erba, Marco; Perinotti, Paolo

2017-12-01

We present a thorough classification of the isotropic quantum walks on lattices of dimension d =1 ,2 ,3 with a coin system of dimension s =2 . For d =3 there exist two isotropic walks, namely, the Weyl quantum walks presented in the work of D'Ariano and Perinotti [G. M. D'Ariano and P. Perinotti, Phys. Rev. A 90, 062106 (2014), 10.1103/PhysRevA.90.062106], resulting in the derivation of the Weyl equation from informational principles. The present analysis, via a crucial use of isotropy, is significantly shorter and avoids a superfluous technical assumption, making the result completely general.

Flow-induced elastic anisotropy of metallic glasses

International Nuclear Information System (INIS)

Sun, Y.H.; Concustell, A.; Carpenter, M.A.; Qiao, J.C.; Rayment, A.W.; Greer, A.L.

2016-01-01

As-cast bulk metallic glasses are isotropic, but anisotropy can be induced by thermomechanical treatments. For example, the diffraction halo in the structure function S(Q) observed in transmission becomes elliptical (rather than circular) after creep in uniaxial tension or compression. Published studies associate this with frozen-in anelastic strain and bond-orientational anisotropy. Results so far are inconsistent on whether viscoplastic flow of metallic glasses can induce anisotropy. Preliminary diffraction data suggest that the anisotropy, if any, is very low, while measurements of the elastic properties suggest that there is induced anisotropy, opposite in sign to that due to anelastic strain. We study three bulk metallic glasses, Ce 65 Al 10 Cu 20 Co 5 , La 55 Ni 10 Al 35 , and Pd 40 Ni 30 Cu 10 P 20 . By using resonant ultrasound spectroscopy to determine the full elasticity tensor, the effects of relaxation and rejuvenation can be reliably separated from uniaxial anisotropy (of either sign). The effects of viscoplastic flow in tension are reported for the first time. We find that viscoplastic flow of bulk metallic glasses, particularly in tension, can induce significant anisotropy that is distinct from that associated with frozen-in anelastic strain. The conditions for inducing such anisotropy are explored in terms of the Weissenberg number (ratio of relaxation times for primary relaxation and for shear strain rate). There is a clear need for further work to characterize the structural origins of flow-induced anisotropy and to explore the prospects for improved mechanical and other properties through induced anisotropy.

Incompressible Navier-Stokes equation from Einstein-Maxwell and Gauss-Bonnet-Maxwell theories

International Nuclear Information System (INIS)

Niu Chao; Tian Yu; Wu Xiaoning; Ling Yi

2012-01-01

The dual fluid description for a general cutoff surface at radius r=r c outside the horizon in the charged AdS black brane bulk space-time is investigated, first in the Einstein-Maxwell theory. Under the non-relativistic long-wavelength expansion with parameter ε, the coupled Einstein-Maxwell equations are solved up to O(ε 2 ). The incompressible Navier-Stokes equation with external force density is obtained as the constraint equation at the cutoff surface. For non-extremal black brane, the viscosity of the dual fluid is determined by the regularity of the metric fluctuation at the horizon, whose ratio to entropy density η/s is independent of both the cutoff r c and the black brane charge. Then, we extend our discussion to the Gauss-Bonnet-Maxwell case, where the incompressible Navier-Stokes equation with external force density is also obtained at a general cutoff surface. In this case, it turns out that the ratio η/s is independent of the cutoff r c but dependent on the charge density of the black brane.

Structure-Preserving Variational Multiscale Modeling of Turbulent Incompressible Flow with Subgrid Vortices

Science.gov (United States)

Evans, John; Coley, Christopher; Aronson, Ryan; Nelson, Corey

2017-11-01

In this talk, a large eddy simulation methodology for turbulent incompressible flow will be presented which combines the best features of divergence-conforming discretizations and the residual-based variational multiscale approach to large eddy simulation. In this method, the resolved motion is represented using a divergence-conforming discretization, that is, a discretization that preserves the incompressibility constraint in a pointwise manner, and the unresolved fluid motion is explicitly modeled by subgrid vortices that lie within individual grid cells. The evolution of the subgrid vortices is governed by dynamical model equations driven by the residual of the resolved motion. Consequently, the subgrid vortices appropriately vanish for laminar flow and fully resolved turbulent flow. As the resolved velocity field and subgrid vortices are both divergence-free, the methodology conserves mass in a pointwise sense and admits discrete balance laws for energy, enstrophy, and helicity. Numerical results demonstrate the methodology yields improved results versus state-of-the-art eddy viscosity models in the context of transitional, wall-bounded, and rotational flow when a divergence-conforming B-spline discretization is utilized to represent the resolved motion.

An efficient immersed boundary-lattice Boltzmann method for the hydrodynamic interaction of elastic filaments

Science.gov (United States)

Tian, Fang-Bao; Luo, Haoxiang; Zhu, Luoding; Liao, James C.; Lu, Xi-Yun

2012-01-01

We have introduced a modified penalty approach into the flow-structure interaction solver that combines an immersed boundary method (IBM) and a multi-block lattice Boltzmann method (LBM) to model an incompressible flow and elastic boundaries with finite mass. The effect of the solid structure is handled by the IBM in which the stress exerted by the structure on the fluid is spread onto the collocated grid points near the boundary. The fluid motion is obtained by solving the discrete lattice Boltzmann equation. The inertial force of the thin solid structure is incorporated by connecting this structure through virtual springs to a ghost structure with the equivalent mass. This treatment ameliorates the numerical instability issue encountered in this type of problems. Thanks to the superior efficiency of the IBM and LBM, the overall method is extremely fast for a class of flow-structure interaction problems where details of flow patterns need to be resolved. Numerical examples, including those involving multiple solid bodies, are presented to verify the method and illustrate its efficiency. As an application of the present method, an elastic filament flapping in the Kármán gait and the entrainment regions near a cylinder is studied to model fish swimming in these regions. Significant drag reduction is found for the filament, and the result is consistent with the metabolic cost measured experimentally for the live fish. PMID:23564971

An efficient immersed boundary-lattice Boltzmann method for the hydrodynamic interaction of elastic filaments

Science.gov (United States)

Tian, Fang-Bao; Luo, Haoxiang; Zhu, Luoding; Liao, James C.; Lu, Xi-Yun

2011-08-01

We have introduced a modified penalty approach into the flow-structure interaction solver that combines an immersed boundary method (IBM) and a multi-block lattice Boltzmann method (LBM) to model an incompressible flow and elastic boundaries with finite mass. The effect of the solid structure is handled by the IBM in which the stress exerted by the structure on the fluid is spread onto the collocated grid points near the boundary. The fluid motion is obtained by solving the discrete lattice Boltzmann equation. The inertial force of the thin solid structure is incorporated by connecting this structure through virtual springs to a ghost structure with the equivalent mass. This treatment ameliorates the numerical instability issue encountered in this type of problems. Thanks to the superior efficiency of the IBM and LBM, the overall method is extremely fast for a class of flow-structure interaction problems where details of flow patterns need to be resolved. Numerical examples, including those involving multiple solid bodies, are presented to verify the method and illustrate its efficiency. As an application of the present method, an elastic filament flapping in the Kármán gait and the entrainment regions near a cylinder is studied to model fish swimming in these regions. Significant drag reduction is found for the filament, and the result is consistent with the metabolic cost measured experimentally for the live fish.

Mathematical aspects of finite element methods for incompressible viscous flows

Science.gov (United States)

Gunzburger, M. D.

1986-01-01

Mathematical aspects of finite element methods are surveyed for incompressible viscous flows, concentrating on the steady primitive variable formulation. The discretization of a weak formulation of the Navier-Stokes equations are addressed, then the stability condition is considered, the satisfaction of which insures the stability of the approximation. Specific choices of finite element spaces for the velocity and pressure are then discussed. Finally, the connection between different weak formulations and a variety of boundary conditions is explored.

The propagation of nonlinear rayleigh waves in layered elastic half-space

International Nuclear Information System (INIS)

Ahmetolan, S.

2004-01-01

In this work, the propagation of small but finite amplitude generalized Rayleigh waves in an elastic half-space covered by a different elastic layer of uniform and finite thickness is considered. The constituent materials are assumed to be homogeneous, isotropic, compressible hyperelastic. Excluding the harmonic resonance phenomena, it is shown that the nonlinear self modulation of generalized Rayleigh waves is governed asymptotically by a nonlinear Schrodinger (NLS) equation. The stability of the solutions and the existence of solitary wave-type solutions a NLS are strongly depend on the sign of the product of the coefficients of the nonlinear and dipersion terms of the equation.Therefore the analysis continues with the examination of dependence of these coefficients on the nonlinear material parameters. Three different models have been considered which are nonlinear layer-nonlinear half space, linear layer-nonlinear half space and nonlinear layer-linear half space. The behavior of the coefficients of the NLS equation was also analyzed the limit as h(thickness of the layer) goes to zero and k(the wave number) is constant. Then conclusions are drawn about the effect of nonlinear material parameters on the wave modulation. In the numerical investigations both hypothetical and real material models are used

Structural, elastic and thermodynamic properties under pressure and temperature effects of MgIn{sub 2}S{sub 4} and CdIn{sub 2}S{sub 4}

Energy Technology Data Exchange (ETDEWEB)

Bouhemadou, A., E-mail: a_bouhemadou@yahoo.fr [Laboratory for Developing New Materials and their Characterization, Department of Physics, Faculty of Science, University of Setif, 19000 Setif (Algeria); Haddadi, K. [Laboratory for Developing New Materials and their Characterization, Department of Physics, Faculty of Science, University of Setif, 19000 Setif (Algeria); Khenata, R. [Laboratoire de Physique Quantique et de Modelisation Mathematique (LPQ3M), Departement de Technologie, Universite de Mascara, 29000 Mascara (Algeria); Rached, D. [Department of Physics, Faculty of Science, University of Sidi-Bel-Abbes, 22000 (Algeria); Bin-Omran, S. [Department of Physics and Astronomy, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451 (Saudi Arabia)

2012-06-15

A density functional-based method is used to investigate the structural, elastic and thermodynamic properties of the cubic spinel semiconductors MgIn{sub 2}S{sub 4} and CdIn{sub 2}S{sub 4} at different pressures and temperatures. Computed ground structural parameters are in good agreement with the available experimental data. Single-crystal elastic parameters are calculated for pressure up to 10 GPa and temperature up to 1200 K. The obtained elastic constants values satisfy the requirement of mechanical stability, indicating that MgIn{sub 2}S{sub 4} and CdIn{sub 2}S{sub 4} compounds could be stable in the investigated pressure range. Isotropic elastic parameters for ideal polycrystalline MgIn{sub 2}S{sub 4} and CdIn{sub 2}S{sub 4} aggregates are computed in the framework of the Voigt-Reuss-Hill approximation. Pressure and thermal effects on some macroscopic properties such as lattice constant, volume expansion coefficient and heat capacities are predicted using the quasi-harmonic Debye model in which the lattice vibrations are taken into account.

Design methodology of single-feed compact near-isotropic antenna design

KAUST Repository

Su, Zhen

2017-06-07

The abundance of mobile wireless devices is giving rise to a new paradigm known as Internet of Things. In this paradigm, wireless devices will be everywhere and communicating with each other. Since they will be oriented randomly in the environment, they should be able to communicate equally in all directions in order to have stable communication link. Hence, compact near isotropic antennas are required, which can enable orientation insensitive communication. In this paper, we propose a simple design methodology to design a compact near-isotropic wire antenna based on equal vector potentials. As a proof of concept, a quarter wavelength monopole antennas has been designed that is wrapped on a 3D-printed box keeping the vector potentials in three orthogonal different directions equal. By optimizing the dimension of the antenna arms, a nearly isotropic radiation pattern is thus achieved. The results show that the antenna has a maximum gain of 2.2dBi at 900 MHz with gain derivation of 9.4dB.

Elastic orthorhombic anisotropic parameter inversion: An analysis of parameterization

KAUST Repository

Oh, Juwon

2016-09-15

The resolution of a multiparameter full-waveform inversion (FWI) is highly influenced by the parameterization used in the inversion algorithm, as well as the data quality and the sensitivity of the data to the elastic parameters because the scattering patterns of the partial derivative wavefields (PDWs) vary with parameterization. For this reason, it is important to identify an optimal parameterization for elastic orthorhombic FWI by analyzing the radiation patterns of the PDWs for many reasonable model parameterizations. We have promoted a parameterization that allows for the separation of the anisotropic properties in the radiation patterns. The central parameter of this parameterization is the horizontal P-wave velocity, with an isotropic scattering potential, influencing the data at all scales and directions. This parameterization decouples the influence of the scattering potential given by the P-wave velocity perturbation fromthe polar changes described by two dimensionless parameter perturbations and from the azimuthal variation given by three additional dimensionless parameters perturbations. In addition, the scattering potentials of the P-wave velocity perturbation are also decoupled from the elastic influences given by one S-wave velocity and two additional dimensionless parameter perturbations. The vertical S-wave velocity is chosen with the best resolution obtained from S-wave reflections and converted waves, little influence on P-waves in conventional surface seismic acquisition. The influence of the density on observed data can be absorbed by one anisotropic parameter that has a similar radiation pattern. The additional seven dimensionless parameters describe the polar and azimuth variations in the P- and S-waves that we may acquire, with some of the parameters having distinct influences on the recorded data on the earth\\'s surface. These characteristics of the new parameterization offer the potential for a multistage inversion from high symmetry

Elastic orthorhombic anisotropic parameter inversion: An analysis of parameterization

KAUST Repository

Oh, Juwon; Alkhalifah, Tariq Ali

2016-01-01

The resolution of a multiparameter full-waveform inversion (FWI) is highly influenced by the parameterization used in the inversion algorithm, as well as the data quality and the sensitivity of the data to the elastic parameters because the scattering patterns of the partial derivative wavefields (PDWs) vary with parameterization. For this reason, it is important to identify an optimal parameterization for elastic orthorhombic FWI by analyzing the radiation patterns of the PDWs for many reasonable model parameterizations. We have promoted a parameterization that allows for the separation of the anisotropic properties in the radiation patterns. The central parameter of this parameterization is the horizontal P-wave velocity, with an isotropic scattering potential, influencing the data at all scales and directions. This parameterization decouples the influence of the scattering potential given by the P-wave velocity perturbation fromthe polar changes described by two dimensionless parameter perturbations and from the azimuthal variation given by three additional dimensionless parameters perturbations. In addition, the scattering potentials of the P-wave velocity perturbation are also decoupled from the elastic influences given by one S-wave velocity and two additional dimensionless parameter perturbations. The vertical S-wave velocity is chosen with the best resolution obtained from S-wave reflections and converted waves, little influence on P-waves in conventional surface seismic acquisition. The influence of the density on observed data can be absorbed by one anisotropic parameter that has a similar radiation pattern. The additional seven dimensionless parameters describe the polar and azimuth variations in the P- and S-waves that we may acquire, with some of the parameters having distinct influences on the recorded data on the earth's surface. These characteristics of the new parameterization offer the potential for a multistage inversion from high symmetry

The suite of analytical benchmarks for neutral particle transport in infinite isotropically scattering media

International Nuclear Information System (INIS)

Kornreich, D.E.; Ganapol, B.D.

1997-01-01

The linear Boltzmann equation for the transport of neutral particles is investigated with the objective of generating benchmark-quality evaluations of solutions for homogeneous infinite media. In all cases, the problems are stationary, of one energy group, and the scattering is isotropic. The solutions are generally obtained through the use of Fourier transform methods with the numerical inversions constructed from standard numerical techniques such as Gauss-Legendre quadrature, summation of infinite series, and convergence acceleration. Consideration of the suite of benchmarks in infinite homogeneous media begins with the standard one-dimensional problems: an isotropic point source, an isotropic planar source, and an isotropic infinite line source. The physical and mathematical relationships between these source configurations are investigated. The progression of complexity then leads to multidimensional problems with source configurations that also emit particles isotropically: the finite line source, the disk source, and the rectangular source. The scalar flux from the finite isotropic line and disk sources will have a two-dimensional spatial variation, whereas a finite rectangular source will have a three-dimensional variation in the scalar flux. Next, sources emitting particles anisotropically are considered. The most basic such source is the point beam giving rise to the Green's function, which is physically the most fundamental transport problem, yet may be constructed from the isotropic point source solution. Finally, the anisotropic plane and anisotropically emitting infinite line sources are considered. Thus, a firm theoretical and numerical base is established for the most fundamental neutral particle benchmarks in infinite homogeneous media

Taylor Instability of Incompressible Liquids

Science.gov (United States)

Fermi, E.; von Neumann, J.

1955-11-01

A discussion is presented in simplified form of the problem of the growth of an initial ripple on the surface of an incompressible liquid in the presence of an acceleration, g, directed from the outside into the liquid. The model is that of a heavy liquid occupying at t = 0 the half space above the plane z = 0, and a rectangular wave profile is assumed. The theory is found to represent correctly one feature of experimental results, namely the fact that the half wave of the heavy liquid into the vacuum becomes rapidly narrower while the half wave pushing into the heavy liquid becomes more and more blunt. The theory fails to account for the experimental results according to which the front of the wave pushing into the heavy liquid moves with constant velocity. The case of instability at the boundary of 2 fluids of different densities is also explored. Similar results are obtained except that the acceleration of the heavy liquid into the light liquid is reduced.

Incompressible boundary-layer stability analysis of LFC experimental data for sub-critical Mach numbers. M.S. Thesis

Science.gov (United States)

Berry, S. A.

1986-01-01

An incompressible boundary-layer stability analysis of Laminar Flow Control (LFC) experimental data was completed and the results are presented. This analysis was undertaken for three reasons: to study laminar boundary-layer stability on a modern swept LFC airfoil; to calculate incompressible design limits of linear stability theory as applied to a modern airfoil at high subsonic speeds; and to verify the use of linear stability theory as a design tool. The experimental data were taken from the slotted LFC experiment recently completed in the NASA Langley 8-Foot Transonic Pressure Tunnel. Linear stability theory was applied and the results were compared with transition data to arrive at correlated n-factors. Results of the analysis showed that for the configuration and cases studied, Tollmien-Schlichting (TS) amplification was the dominating disturbance influencing transition. For these cases, incompressible linear stability theory correlated with an n-factor for TS waves of approximately 10 at transition. The n-factor method correlated rather consistently to this value despite a number of non-ideal conditions which indicates the method is useful as a design tool for advanced laminar flow airfoils.

High order spectral difference lattice Boltzmann method for incompressible hydrodynamics

Science.gov (United States)

Li, Weidong

2017-09-01

This work presents a lattice Boltzmann equation (LBE) based high order spectral difference method for incompressible flows. In the present method, the spectral difference (SD) method is adopted to discretize the convection and collision term of the LBE to obtain high order (≥3) accuracy. Because the SD scheme represents the solution as cell local polynomials and the solution polynomials have good tensor-product property, the present spectral difference lattice Boltzmann method (SD-LBM) can be implemented on arbitrary unstructured quadrilateral meshes for effective and efficient treatment of complex geometries. Thanks to only first oder PDEs involved in the LBE, no special techniques, such as hybridizable discontinuous Galerkin method (HDG), local discontinuous Galerkin method (LDG) and so on, are needed to discrete diffusion term, and thus, it simplifies the algorithm and implementation of the high order spectral difference method for simulating viscous flows. The proposed SD-LBM is validated with four incompressible flow benchmarks in two-dimensions: (a) the Poiseuille flow driven by a constant body force; (b) the lid-driven cavity flow without singularity at the two top corners-Burggraf flow; and (c) the unsteady Taylor-Green vortex flow; (d) the Blasius boundary-layer flow past a flat plate. Computational results are compared with analytical solutions of these cases and convergence studies of these cases are also given. The designed accuracy of the proposed SD-LBM is clearly verified.

Superfluid H3e in globally isotropic random media

Science.gov (United States)

Ikeda, Ryusuke; Aoyama, Kazushi

2009-02-01

Recent theoretical and experimental studies of superfluid H3e in aerogels with a global anisotropy created, e.g., by an external stress have definitely shown that the A -like phase with an equal-spin pairing in such aerogel samples is in the Anderson-Brinkman-Morel (ABM) (or axial) pairing state. In this paper, the A -like phase of superfluid H3e in globally isotropic aerogel is studied in detail by assuming a weakly disordered system in which singular topological defects are absent. Through calculation of the free energy, a disordered ABM state is found to be the best candidate of the pairing state of the globally isotropic A -like phase. Further, it is found through a one-loop renormalization-group calculation that the coreless continuous vortices (or vortex-Skyrmions) are irrelevant to the long-distance behavior of disorder-induced textures, and that the superfluidity is maintained in spite of lack of the conventional superfluid long-range order. Therefore, the globally isotropic A -like phase at weak disorder is, like in the case with a globally stretched anisotropy, a glass phase with the ABM pairing and shows superfluidity.

The Isotropic Radio Background and Annihilating Dark Matter

Energy Technology Data Exchange (ETDEWEB)

Hooper, Dan [Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States); Belikov, Alexander V. [Institut d' Astrophysique (France); Jeltema, Tesla E. [Univ. of California, Santa Cruz, CA (United States); Linden, Tim [Univ. of California, Santa Cruz, CA (United States); Profumo, Stefano [Univ. of California, Santa Cruz, CA (United States); Slatyer, Tracy R. [Princeton Univ., Princeton, NJ (United States)

2012-11-01

Observations by ARCADE-2 and other telescopes sensitive to low frequency radiation have revealed the presence of an isotropic radio background with a hard spectral index. The intensity of this observed background is found to exceed the flux predicted from astrophysical sources by a factor of approximately 5-6. In this article, we consider the possibility that annihilating dark matter particles provide the primary contribution to the observed isotropic radio background through the emission of synchrotron radiation from electron and positron annihilation products. For reasonable estimates of the magnetic fields present in clusters and galaxies, we find that dark matter could potentially account for the observed radio excess, but only if it annihilates mostly to electrons and/or muons, and only if it possesses a mass in the range of approximately 5-50 GeV. For such models, the annihilation cross section required to normalize the synchrotron signal to the observed excess is sigma v ~ (0.4-30) x 10^-26 cm^3/s, similar to the value predicted for a simple thermal relic (sigma v ~ 3 x 10^-26 cm^3/s). We find that in any scenario in which dark matter annihilations are responsible for the observed excess radio emission, a significant fraction of the isotropic gamma ray background observed by Fermi must result from dark matter as well.

Boundary treatment for fourth-order staggered mesh discretizations of the incompressible Navier-Stokes equations

NARCIS (Netherlands)

Sanderse, B.; Verstappen, R.W.C.P.; Koren, B.

2014-01-01

A discretization method for the incompressible Navier–Stokes equations conserving the secondary quantities kinetic energy and vorticity was introduced, besides the primary quantities mass and momentum. This method was extended to fourth order accuracy. In this paper we propose a new consistent

Solutions to three-dimensional Navier-Stokes equations for incompressible fluids

Directory of Open Access Journals (Sweden)

Jorma Jormakka

2010-07-01

Full Text Available This article gives explicit solutions to the space-periodic Navier-Stokes problem with non-periodic pressure. These type of solutions are not unique and by using such solutions one can construct a periodic, smooth, divergence-free initial vector field allowing a space-periodic and time-bounded external force such that there exists a smooth solution to the 3-dimensional Navier-Stokes equations for incompressible fluid with those initial conditions, but the solution cannot be continued to the whole space.

Efficient anisotropic wavefield extrapolation using effective isotropic models

KAUST Repository

Alkhalifah, Tariq Ali; Ma, X.; Waheed, Umair bin; Zuberi, Mohammad

2013-01-01

Isotropic wavefield extrapolation is more efficient than anisotropic extrapolation, and this is especially true when the anisotropy of the medium is tilted (from the vertical). We use the kinematics of the wavefield, appropriately represented

Acoustic reflection log in transversely isotropic formations

Science.gov (United States)

Ronquillo Jarillo, G.; Markova, I.; Markov, M.

2018-01-01

We have calculated the waveforms of sonic reflection logging for a fluid-filled borehole located in a transversely isotropic rock. Calculations have been performed for an acoustic impulse source with the characteristic frequency of tens of kilohertz that is considerably less than the frequencies of acoustic borehole imaging tools. It is assumed that the borehole axis coincides with the axis of symmetry of the transversely isotropic rock. It was shown that the reflected wave was excited most efficiently at resonant frequencies. These frequencies are close to the frequencies of oscillations of a fluid column located in an absolutely rigid hollow cylinder. We have shown that the acoustic reverberation is controlled by the acoustic impedance of the rock Z = Vphρs for fixed parameters of the borehole fluid, where Vph is the velocity of horizontally propagating P-wave; ρs is the rock density. The methods of waveform processing to determine the parameters characterizing the reflected wave have been discussed.

On the Coupling of Incompressible Stokes or Navier–Stokes and Darcy Flows Through Porous Media

KAUST Repository

Girault, V.; Kanschat, G.; Riviè re, B.

2012-01-01

In this chapter, we present the theoretical analysis of coupled incompressible Navier-Stokes (or Stokes) flows and Darcy flows with the Beavers-Joseph-Saffman interface condition. We discuss alternative interface and porous media models. We review

New constitutive equations to describe infinitesimal elastic-plastic deformations

International Nuclear Information System (INIS)

Boecke, B.; Link, F.; Schneider, G.; Bruhns, O.T.

1983-01-01

A set of constitutive equations is presented to describe infinitesimal elastic-plastic deformations of austenitic steel in the range up to 600 deg C. This model can describe the hardening behaviour in the case of mechanical loading and hardening, and softening behaviour in the case of thermal loading. The loading path can be either monotonic or cyclic. For this purpose, the well-known isotropic hardening model is continually transferred into the kinematic model according to Prager, whereby suitable internal variables are chosen. The occurring process-dependent material functions are to be determined by uniaxial experiments. The hardening function g and the translation function c are determined by means of a linearized stress-strain behaviour in the plastic range, whereby a coupling condition must be taken into account. As a linear hardening process is considered to be too unrealistic, nonlinearity is achieved by introducing a small function w, the determination procedure of which is given. (author)

Mathematical models of incompressible fluids as singular limits of complete fluid systems

Czech Academy of Sciences Publication Activity Database

Feireisl, Eduard

2010-01-01

Roč. 78, č. 2 (2010), s. 523-560 ISSN 1424-9286 R&D Projects: GA ČR GA201/08/0315 Institutional research plan: CEZ:AV0Z10190503 Keywords : scale analysis * Navier-Stokes-Fourier system * incompressible limit Subject RIV: BA - General Mathematics Impact factor: 0.933, year: 2010 http://link.springer.com/article/10.1007%2Fs00032-010-0128-1

Segment-scale, force-level theory of mesoscopic dynamic localization and entropic elasticity in entangled chain polymer liquids

Science.gov (United States)

Dell, Zachary E.; Schweizer, Kenneth S.

2017-04-01

We develop a segment-scale, force-based theory for the breakdown of the unentangled Rouse model and subsequent emergence of isotropic mesoscopic localization and entropic elasticity in chain polymer liquids in the absence of ergodicity-restoring anisotropic reptation or activated hopping motion. The theory is formulated in terms of a conformational N-dynamic-order-parameter generalized Langevin equation approach. It is implemented using a universal field-theoretic Gaussian thread model of polymer structure and closed at the level of the chain dynamic second moment matrix. The physical idea is that the isotropic Rouse model fails due to the dynamical emergence, with increasing chain length, of time-persistent intermolecular contacts determined by the combined influence of local uncrossability, long range polymer connectivity, and a self-consistent treatment of chain motion and the dynamic forces that hinder it. For long chain melts, the mesoscopic localization length (identified as the tube diameter) and emergent entropic elasticity predictions are in near quantitative agreement with experiment. Moreover, the onset chain length scales with the semi-dilute crossover concentration with a realistic numerical prefactor. Distinctive novel predictions are made for various off-diagonal correlation functions that quantify the full spatial structure of the dynamically localized polymer conformation. As the local excluded volume constraint and/or intrachain bonding spring are softened to allow chain crossability, the tube diameter is predicted to swell until it reaches the radius-of-gyration at which point mesoscopic localization vanishes in a discontinuous manner. A dynamic phase diagram for such a delocalization transition is constructed, which is qualitatively consistent with simulations and the classical concept of a critical entanglement degree of polymerization.

Variable-viscosity thermal hemodynamic slip flow conveying nanoparticles through a permeable-walled composite stenosed artery

Science.gov (United States)

Akbar, Noreen Sher; Tripathi, Dharmendra; Bég, O. Anwar

2017-07-01

This paper presents a mathematical model for simulating viscous, incompressible, steady-state blood flow containing copper nanoparticles and coupled heat transfer through a composite stenosed artery with permeable walls. Wall slip hydrodynamic and also thermal buoyancy effects are included. The artery is simulated as an isotropic elastic tube, following Joshi et al. (2009), and a variable viscosity formulation is employed for the flowing blood. The equations governing the transport phenomena are non-dimensionalized and the resulting boundary value problem is solved analytically in the steady state subject to physically appropriate boundary conditions. Numerical computations are conducted to quantify the effects of relevant hemodynamic, thermophysical and nanoscale parameters emerging in the model on velocity and temperature profiles, wall shear stress, impedance resistance and also streamline distributions. The model may be applicable to drug fate transport modeling with nanoparticle agents and also to the optimized design of nanoscale medical devices for diagnosing stenotic diseases in circulatory systems.

Effect of heat treatment upon the mechanical and poro-mechanical behaviour of cement-based materials: hydraulic properties and morphological changes

International Nuclear Information System (INIS)

Chen, Xiao-Ting

2009-01-01

This work investigates the effects of morphological changes of a cement-based material subjected to heat treatment (up to 400 C). For a model W/C=0.5 mortar, we have characterized experimentally hydraulic behaviour (gas permeability), mechanical behaviour (in uniaxial compression, hydrostatic compression with or without deviatoric stress) and poro-mechanical behaviour (incompressibility moduli Kb, Ks and Biot's coefficient b) after a heating/cooling cycle. We have also developed an original experiment aimed at quantifying the accessible pore space volume under hydrostatic compression. The creation of occluded porosity under high confinement is confirmed, which justifies the observed decrease of solid matrix rigidity Ks under high confinement. A gas retention phenomenon was identified under simultaneous thermal and hydrostatic loadings for mortar, and industrial concretes (provided by CERIB and ANDRA). A predictive thermo-elasto-plastic model with isotropic damage and a micro-mechanical approach, which represents micro-cracking, are coupled in order to analyze or predict the evolution of mechanical and poro-elastic properties after heat cycling. (author)

Edge instability in incompressible planar active fluids

Science.gov (United States)

Nesbitt, David; Pruessner, Gunnar; Lee, Chiu Fan

2017-12-01

Interfacial instability is highly relevant to many important biological processes. A key example arises in wound healing experiments, which observe that an epithelial layer with an initially straight edge does not heal uniformly. We consider the phenomenon in the context of active fluids. Improving upon the approximation used by Zimmermann, Basan, and Levine [Eur. Phys. J.: Spec. Top. 223, 1259 (2014), 10.1140/epjst/e2014-02189-7], we perform a linear stability analysis on a two-dimensional incompressible hydrodynamic model of an active fluid with an open interface. We categorize the stability of the model and find that for experimentally relevant parameters, fingering instability is always absent in this minimal model. Our results point to the crucial role of density variation in the fingering instability in tissue regeneration.

Computational Elastic Knots

KAUST Repository

Zhao, Xin

2013-05-01

Elastic rods have been studied intensively since the 18th century. Even now the theory of elastic rods is still developing and enjoying popularity in computer graphics and physical-based simulation. Elastic rods also draw attention from architects. Architectural structures, NODUS, were constructed by elastic rods as a new method of form-finding. We study discrete models of elastic rods and NODUS structures. We also develop computational tools to find the equilibria of elastic rods and the shape of NODUS. Applications of elastic rods in forming torus knot and closing Bishop frame are included in this thesis.

Discrete Exterior Calculus Discretization of Incompressible Navier-Stokes Equations

KAUST Repository

Mohamed, Mamdouh S.

2017-05-23

A conservative discretization of incompressible Navier-Stokes equations over surface simplicial meshes is developed using discrete exterior calculus (DEC). Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy otherwise. The mimetic character of many of the DEC operators provides exact conservation of both mass and vorticity, in addition to superior kinetic energy conservation. The employment of barycentric Hodge star allows the discretization to admit arbitrary simplicial meshes. The discretization scheme is presented along with various numerical test cases demonstrating its main characteristics.

Analysis of the multi-component pseudo-pure-mode qP-wave inversion in vertical transverse isotropic (VTI) media

KAUST Repository

Djebbi, Ramzi

2014-08-05

Multi-parameter inversion in anisotropic media suffers from the inherent trade-off between the anisotropic parameters, even under the acoustic assumption. Multi-component data, often acquired nowadays in ocean bottom acquisition and land data, provide additional information capable of resolving anisotropic parameters under the acoustic approximation assumption. Based on Born scattering approximation, we develop formulas capable of characterizing the radiation patterns for the acoustic pseudo-pure mode P-waves. Though commonly reserved for the elastic fields, we use displacement fields to constrain the acoustic vertical transverse isotropic (VTI) representation of the medium. Using the asymptotic Green\\'s functions and a horizontal reflector we derive the radiation patterns for perturbations in the anisotropic media. The radiation pattern for the anellipticity parameter η is identically zero for the horizontal displacement. This allows us to dedicate this component to invert for velocity and δ. Computing the traveltime sensitivity kernels based on the unwrapped phase confirms the radiation patterns observations, and provide the model wavenumber behavior of the update.

Autonomic Vertical Elasticity of Docker Containers with ElasticDocker

OpenAIRE

Al-Dhuraibi , Yahya; Paraiso , Fawaz; Djarallah , Nabil; Merle , Philippe

2017-01-01

International audience; Elasticity is the key feature of cloud computing to scale computing resources according to application workloads timely. In the literature as well as in industrial products, much attention was given to the elasticity of virtual machines, but much less to the elasticity of containers. However, containers are the new trend for packaging and deploying microservices-based applications. Moreover, most of approaches focus on horizontal elasticity, fewer works address vertica...

Isotropic transmission of magnon spin information without a magnetic field.

Science.gov (United States)

Haldar, Arabinda; Tian, Chang; Adeyeye, Adekunle Olusola

2017-07-01

Spin-wave devices (SWD), which use collective excitations of electronic spins as a carrier of information, are rapidly emerging as potential candidates for post-semiconductor non-charge-based technology. Isotropic in-plane propagating coherent spin waves (magnons), which require magnetization to be out of plane, is desirable in an SWD. However, because of lack of availability of low-damping perpendicular magnetic material, a usually well-known in-plane ferrimagnet yttrium iron garnet (YIG) is used with a large out-of-plane bias magnetic field, which tends to hinder the benefits of isotropic spin waves. We experimentally demonstrate an SWD that eliminates the requirement of external magnetic field to obtain perpendicular magnetization in an otherwise in-plane ferromagnet, Ni 80 Fe 20 or permalloy (Py), a typical choice for spin-wave microconduits. Perpendicular anisotropy in Py, as established by magnetic hysteresis measurements, was induced by the exchange-coupled Co/Pd multilayer. Isotropic propagation of magnon spin information has been experimentally shown in microconduits with three channels patterned at arbitrary angles.

Differential geometric structures of stream functions: incompressible two-dimensional flow and curvatures

International Nuclear Information System (INIS)

Yamasaki, K; Iwayama, T; Yajima, T

2011-01-01

The Okubo-Weiss field, frequently used for partitioning incompressible two-dimensional (2D) fluids into coherent and incoherent regions, corresponds to the Gaussian curvature of the stream function. Therefore, we consider the differential geometric structures of stream functions and calculate the Gaussian curvatures of some basic flows. We find the following. (I) The vorticity corresponds to the mean curvature of the stream function. Thus, the stream-function surface for an irrotational flow and that for a parallel shear flow correspond to the minimal surface and a developable surface, respectively. (II) The relationship between the coherency and the magnitude of the vorticity is interpreted by the curvatures. (III) Using the Gaussian curvature, stability of single and double point vortex streets is analyzed. The results of this analysis are compared with the well-known linear stability analysis. (IV) Conformal mapping in fluid mechanics is the physical expression of the geometric fact that the sign of the Gaussian curvature does not change in conformal mapping. These findings suggest that the curvatures of stream functions are useful for understanding the geometric structure of an incompressible 2D flow.

Incompressible Modes Excited by Supersonic Shear in Boundary Layers: Acoustic CFS Instability

Energy Technology Data Exchange (ETDEWEB)

Belyaev, Mikhail A., E-mail: mbelyaev@berkeley.edu [Astronomy Department, University of California, Berkeley, CA 94720 (United States)

2017-02-01

We present an instability for exciting incompressible modes (e.g., gravity or Rossby modes) at the surface of a star accreting through a boundary layer. The instability excites a stellar mode by sourcing an acoustic wave in the disk at the boundary layer, which carries a flux of energy and angular momentum with the opposite sign as the energy and angular momentum density of the stellar mode. We call this instability the acoustic Chandrasekhar–Friedman–Schutz (CFS) instability, because of the direct analogy to the CFS instability for exciting modes on a rotating star by emission of energy in the form of gravitational waves. However, the acoustic CFS instability differs from its gravitational wave counterpart in that the fluid medium in which the acoustic wave propagates (i.e., the accretion disk) typically rotates faster than the star in which the incompressible mode is sourced. For this reason, the instability can operate even for a non-rotating star in the presence of an accretion disk. We discuss applications of our results to high-frequency quasi-periodic oscillations in accreting black hole and neutron star systems and dwarf nova oscillations in cataclysmic variables.

Scanning anisotropy parameters in horizontal transversely isotropic media

KAUST Repository

Masmoudi, Nabil; Stovas, Alexey; Alkhalifah, Tariq Ali

2016-01-01

in reservoir characterisation, specifically in terms of fracture delineation. We propose a travel-time-based approach to estimate the anellipticity parameter η and the symmetry axis azimuth ϕ of a horizontal transversely isotropic medium, given an inhomogeneous

Iterative and multigrid methods in the finite element solution of incompressible and turbulent fluid flow

Science.gov (United States)

Lavery, N.; Taylor, C.

1999-07-01

Multigrid and iterative methods are used to reduce the solution time of the matrix equations which arise from the finite element (FE) discretisation of the time-independent equations of motion of the incompressible fluid in turbulent motion. Incompressible flow is solved by using the method of reduce interpolation for the pressure to satisfy the Brezzi-Babuska condition. The k-l model is used to complete the turbulence closure problem. The non-symmetric iterative matrix methods examined are the methods of least squares conjugate gradient (LSCG), biconjugate gradient (BCG), conjugate gradient squared (CGS), and the biconjugate gradient squared stabilised (BCGSTAB). The multigrid algorithm applied is based on the FAS algorithm of Brandt, and uses two and three levels of grids with a V-cycling schedule. These methods are all compared to the non-symmetric frontal solver. Copyright

Isotropic Optical Mouse Placement for Mobile Robot Velocity Estimation

Directory of Open Access Journals (Sweden)

Sungbok Kim

2014-06-01

Full Text Available This paper presents the isotropic placement of multiple optical mice for the velocity estimation of a mobile robot. It is assumed that there can be positional restriction on the installation of optical mice at the bottom of a mobile robot. First, the velocity kinematics of a mobile robot with an array of optical mice is obtained and the resulting Jacobian matrix is analysed symbolically. Second, the isotropic, anisotropic and singular optical mouse placements are identified, along with the corresponding characteristic lengths. Third, the least squares mobile robot velocity estimation from the noisy optical mouse velocity measurements is discussed. Finally, simulation results for several different placements of three optical mice are given.

Investigation into the temperature dependence of isotropic- nematic phase transition of Gay- Berne liquid crystals

Directory of Open Access Journals (Sweden)

A Avazpour

2014-12-01

Full Text Available Density functional approach was used to study the isotropic- nematic (I-N transition and calculate the values of freezing parameters of the Gay- Berne liquid crystal model. New direct and pair correlation functions of a molecular fluid with Gay- Berne pair potential were used. These new functions were used in density functional theory as input to calculate the isotropic- nematic transition densities for elongation at various reduced temperatures. It was observed that the isotropic- nematic transition densities increase as the temperature increases. It was found that the new direct correlation function is suitable to study the isotropic- nematic transition of Gay- Berne liquids. Comparison to other works showed qualitative agreement

Elastic properties

International Nuclear Information System (INIS)

Ledbetter, H.M.

1983-01-01

This chapter investigates the following five aspects of engineering-material solid-state elastic constants: general properties, interrelationships, relationships to other physical properties, changes during cooling from ambient to near-zero temperature, and near-zero-temperature behavior. Topics considered include compressibility, bulk modulus, Young's modulus, shear modulus, Poisson's ratio, Hooke's law, elastic-constant measuring methods, thermodynamic potentials, higher-order energy terms, specific heat, thermal expansivity, magnetic materials, structural phase transitions, polymers, composites, textured aggregates, and other-phenomena correlations. Some of the conclusions concerning polycrystalline elastic properties and their temperature dependence are: elastic constants are physical, not mechanical, properties which relate thermodynamically to other physical properties such as specific heat and thermal expansivity; elastic constants at low temperatures are nearly temperature independent, as required by the third law of thermodynamics; and elastic constants can be used to study directional properties of materials, such as textured aggregates and composites

Birds, magnets, soap, and sandblasting: surprising connections in the theory of incompressible flocks

Science.gov (United States)

Toner, John

In this talk I'll describe the hydrodynamic theory of the motion of incompressible flocks: that is, collections of self-propelled entities (birds\\x9D) that are packed so tightly together that their density cannot change as they move. In two dimensions, this problem can be mapped onto an equilibrium magnet with a peculiar constraint. This problem, in turn, can be shown to be equivalent to a 2d smectic (soap\\x9D), with the flow lines of the flock playing the role of the smectic layers. Finally, this smectic problem can be mapped onto the 1+1 dimensional KPZ equation, which describes the growth or corrosion (sandblasting\\x9D) of a one dimensional interface. The scaling properties of this last system, which have been known exactly for a long time, can thereby be used to determine those of incompressible 2d flocks. One important implication of the resulting scaling laws is that such flocks can exhibit long-ranged order in two dimensions, unlike their equilibrium counterparts.

A Two-Phase Flow Solver for Incompressible Viscous Fluids, Using a Pure Streamfunction Formulation and the Volume of Fluid Technique

DEFF Research Database (Denmark)

Comminal, Raphaël; Spangenberg, Jon; Hattel, Jesper Henri

Accurate multi-phase flow solvers at low Reynolds number are of particular interest for the simulation of interface instabilities in the co-processing of multilayered material. We present a two-phase flow solver for incompressible viscous fluids which uses the streamfunction as the primary variable...... of the flow. Contrary to fractional step methods, the streamfunction formulation eliminates the pressure unknowns, and automatically fulfills the incompressibility constraint by construction. As a result, the method circumvents the loss of temporal accuracy at low Reynolds numbers. The interface is tracked...

A Two-Phase Flow Solver for Incompressible Viscous Fluids, Using a Pure Streamfunction Formulation and the Volume of Fluid Technique

DEFF Research Database (Denmark)

Comminal, Raphaël; Spangenberg, Jon; Hattel, Jesper Henri

2014-01-01

Accurate multi-phase flow solvers at low Reynolds number are of particular interest for the simulation of interface instabilities in the co-processing of multilayered material. We present a two-phase flow solver for incompressible viscous fluids which uses the streamfunction as the primary variable...... of the flow. Contrary to fractional step methods, the streamfunction formulation eliminates the pressure unknowns, and automatically fulfills the incompressibility constraint by construction. As a result, the method circumvents the loss of temporal accuracy at low Reynolds numbers. The interface is tracked...

Scalar properties of transversely isotropic tuff from images of orthogonal cross sections

International Nuclear Information System (INIS)

Berge, P.A.; Berryman, J.G.; Blair, S.C.; Pena, C.

1997-01-01

Image processing methods have been used very effectively to estimate physical properties of isotropic porous earth materials such as sandstones. Anisotropic materials can also be analyzed in order to estimate their physical properties, but additional care and a larger number of well-chosen images of cross sections are required to obtain correct results. Although low-symmetry anisotropic media present difficulties for two-dimensional image processing methods, geologic materials are often transversely isotropic. Scalar properties of porous materials such as porosity and specific surface area can be determined with only minor changes in the analysis when the medium is transversely isotropic rather than isotropic. For example, in a rock that is transitively isotropic due to thin layers or beds, the overall porosity may be obtained by analyzing images of cross sections taken orthogonal to the bedding planes, whereas cross sections lying within the bedding planes will determine only the local porosity of the bed itself. It is known for translationally invariant anisotropic media that the overall specific surface area can be obtained from radial averages of the two-point correlation function in the full three-dimensional volume. Layered materials are not translationally invariant in the direction of the layering, but we show nevertheless how averages of cross sections may be used to obtain the specific surface area for a transversely isotropic rock. We report values of specific surface area obtained for thin sections of Topopah Spring Tuff from Yucca Mountain, Nevada. This formation is being evaluated as a potential host rock for geologic disposal of nuclear waste. Although the present work has made use of thin sections of tuff for the images, the same methods of analysis could also be used to simplify quantitative analysis of three-dimensional volumes of pore structure data obtained by means of x-ray microtomography or other methods, using only a few representative cross

DESTRUCTION CRITERION IN MODEL OF NON-LINEAR ELASTIC PLASTIC MEDIUM

Directory of Open Access Journals (Sweden)

O. L. Shved

2014-01-01

Full Text Available The paper considers a destruction criterion in a specific phenomenological model of elastic plastic medium which significantly differs from the known criteria. In case of vector interpretation of rank-2 symmetric tensors yield surface in the Cauchy stress space is formed by closed piecewise concave surfaces of its deviator sections with due account of experimental data. Section surface is determined by normal vector which is selected from two private vectors of criterial “deviator” operator. Such selection is not always possible in the case of anisotropy growth. It is expected that destruction can only start when a process point in the stress space is located in the current deviator section of the yield surface. It occurs when a critical point appears in the section, and a private value of an operator becomes N-fold in the point that determines the private vector corresponding to the normal vector. Unique and reasonable selection of the normal vector becomes impossible in the critical point and an yield criteria loses its significance in the point.When the destruction initiation is determined there is a possibility of a special case due to the proposed conic form of the yield surface. The deviator section degenerates into the point at the yield surface peak. Criterion formulation at the surface peak lies in the fact that there is no physically correct solution while using a state equation in regard to elastic distortion measures with a fixed tensor of elastic turn. Such usage of the equation is always possible for the rest points of the yield surface and it is considered as an obligatory condition for determination of the deviator section. A critical point is generally absent at any deviator section of the yield surface for isotropic material. A limiting value of the mean stress has been calculated at uniform tension.

Pointwise decay of stationary rotational viscous incompressible flows with nonzero velocity at infinity

Czech Academy of Sciences Publication Activity Database

Deuring, P.; Kračmar, S.; Nečasová, Šárka

2013-01-01

Roč. 255, č. 7 (2013), s. 1576-1606 ISSN 0022-0396 R&D Projects: GA ČR(CZ) GAP201/11/1304 Institutional support: RVO:67985840 Keywords : stationary incompressible Navier-Stokes system * rotating body * fundamental solution Subject RIV: BA - General Mathematics Impact factor: 1.570, year: 2013 http://www.sciencedirect.com/science/article/pii/S0022039613002106

Topography-specific isotropic tunneling in nanoparticle monolayer with sub-nm scale crevices.

Science.gov (United States)

Wang, Guisheng; Jiao, Weihong; Yi, Lizhi; Zhang, Yuejiao; Wu, Ke; Zhang, Chao; Lv, Xianglong; Qian, Lihua; Li, Jianfeng; Yuan, Songliu; Chen, Liang

2016-10-07

Material used in flexible devices may experience anisotropic strain with identical magnitude, outputting coherent signals that tend to have a serious impact on device reliability. In this work, the surface topography of the nanoparticles (NPs) is proposed to be a parameter to control the performance of strain gauge based on tunneling behavior. In contrast to anisotropic tunneling in a monolayer of spherical NPs, electron tunneling in a monolayer of urchin-like NPs actually exhibits a nearly isotropic response to strain with different loading orientations. Isotropic tunneling of the urchin-like NPs is caused by the interlocked pikes of these urchin-like NPs in a random manner during external mechanical stimulus. Topography-dependent isotropic tunneling in two dimensions reported here opens a new opportunity to create highly reliable electronics with superior performance.

A Weakly Nonlinear Model for Kelvin–Helmholtz Instability in Incompressible Fluids

International Nuclear Information System (INIS)

Li-Feng, Wang; Wen-Hua, Ye; Zheng-Feng, Fan; Chuang, Xue; Ying-Jun, Li

2009-01-01

A weakly nonlinear model is proposed for the Kelvin–Helmholtz instability in two-dimensional incompressible fluids by expanding the perturbation velocity potential to third order. The third-order harmonic generation effects of single-mode perturbation are analyzed, as well as the nonlinear correction to the exponential growth of the fundamental modulation. The weakly nonlinear results are supported by numerical simulations. Density and resonance effects exist in the development of mode coupling. (fundamental areas of phenomenology (including applications))

A fast immersed boundary method for external incompressible viscous flows using lattice Green's functions

Science.gov (United States)

Liska, Sebastian; Colonius, Tim

2017-02-01

A new parallel, computationally efficient immersed boundary method for solving three-dimensional, viscous, incompressible flows on unbounded domains is presented. Immersed surfaces with prescribed motions are generated using the interpolation and regularization operators obtained from the discrete delta function approach of the original (Peskin's) immersed boundary method. Unlike Peskin's method, boundary forces are regarded as Lagrange multipliers that are used to satisfy the no-slip condition. The incompressible Navier-Stokes equations are discretized on an unbounded staggered Cartesian grid and are solved in a finite number of operations using lattice Green's function techniques. These techniques are used to automatically enforce the natural free-space boundary conditions and to implement a novel block-wise adaptive grid that significantly reduces the run-time cost of solutions by limiting operations to grid cells in the immediate vicinity and near-wake region of the immersed surface. These techniques also enable the construction of practical discrete viscous integrating factors that are used in combination with specialized half-explicit Runge-Kutta schemes to accurately and efficiently solve the differential algebraic equations describing the discrete momentum equation, incompressibility constraint, and no-slip constraint. Linear systems of equations resulting from the time integration scheme are efficiently solved using an approximation-free nested projection technique. The algebraic properties of the discrete operators are used to reduce projection steps to simple discrete elliptic problems, e.g. discrete Poisson problems, that are compatible with recent parallel fast multipole methods for difference equations. Numerical experiments on low-aspect-ratio flat plates and spheres at Reynolds numbers up to 3700 are used to verify the accuracy and physical fidelity of the formulation.

Helically symmetric equilibria with pressure anisotropy and incompressible plasma flow

Science.gov (United States)

Evangelias, A.; Kuiroukidis, A.; Throumoulopoulos, G. N.

2018-02-01

We derive a generalized Grad-Shafranov equation governing helically symmetric equilibria with pressure anisotropy and incompressible flow of arbitrary direction. Through the most general linearizing ansatz for the various free surface functions involved therein, we construct equilibrium solutions and study their properties. It turns out that pressure anisotropy can act either paramegnetically or diamagnetically, the parallel flow has a paramagnetic effect, while the non-parallel component of the flow associated with the electric field has a diamagnetic one. Also, pressure anisotropy and flow affect noticeably the helical current density.

The scattering potential of partial derivative wavefields in 3-D elastic orthorhombic media: an inversion prospective

KAUST Repository

Oh, Ju-Won

2016-07-04

Multiparameter full waveform inversion (FWI) applied to an elastic orthorhombic model description of the subsurface requires in theory a nine-parameter representation of each pixel of the model. Even with optimal acquisition on the Earth surface that includes large offsets, full azimuth, and multicomponent sensors, the potential for trade-off between the elastic orthorhombic parameters are large. The first step to understanding such trade-off is analysing the scattering potential of each parameter, and specifically, its scattering radiation patterns. We investigate such radiation patterns for diffraction and for scattering from a horizontal reflector considering a background isotropic model. The radiation patterns show considerable potential for trade-off between the parameters and the potentially limited resolution in their recovery. The radiation patterns of C11, C22, and C33 are well separated so that we expect to recover these parameters with limited trade-offs. However, the resolution of their recovery represented by recovered range of model wavenumbers varies between these parameters. We can only invert for the short wavelength components (reflection) of C33 while we can mainly invert for the long wavelength components (transmission) of the elastic coefficients C11 and C22 if we have large enough offsets. The elastic coefficients C13, C23, and C12 suffer from strong trade-offs with C55, C44, and C66, respectively. The trade-offs between C13 and C55, as well as C23 and C44, can be partially mitigated if we acquire P–SV and SV–SV waves. However, to reduce the trade-offs between C12 and C66, we require credible SH–SH waves. The analytical radiation patterns of the elastic constants are supported by numerical gradients of these parameters.

Isotropic Broadband E-Field Probe

Directory of Open Access Journals (Sweden)

Béla Szentpáli

2008-01-01

Full Text Available An E-field probe has been developed for EMC immunity tests performed in closed space. The leads are flexible resistive transmission lines. Their influence on the field distribution is negligible. The probe has an isotropic reception from 100 MHz to 18 GHz; the sensitivity is in the 3 V/m–10 V/m range. The device is an accessory of the EMC test chamber. The readout of the field magnitude is carried out by personal computer, which fulfils also the required corrections of the raw data.

Elastic interactions between hydrogen atoms in metals. II. Elastic interaction energies

International Nuclear Information System (INIS)

Shirley, A.I.; Hall, C.K.

1986-01-01

The fully harmonic lattice approximation derived in a previous paper is used to calculate the elastic interaction energies in the niobium-hydrogen system. The permanent-direct, permanent-indirect, induced-direct, and induced-indirect forces calculated previously each give rise to a corresponding elastic interaction between hydrogen atoms. The latter three interactions have three- and four-body terms in addition to the usual two-body terms. These quantities are calculated and compared with the corresponding two-body permanent elastic interactions obtained in the harmonic-approximation treatment of Horner and Wagner. The results show that the total induced elastic energy is approximately (1/3) the size of the total permanent elastic energy and opposite to it in sign. The total elastic energy due to three-body interactions is approximately (1/4) the size of the total two-body elastic energy, while the total four-body elastic energy is approximately 5% of the total two-body energy. These additional elastic energies are expected to have a profound effect on the thermodynamic and phase-change behavior of a metal hydride

Emergent dynamics of Cucker-Smale particles under the effects of random communication and incompressible fluids

Science.gov (United States)

Ha, Seung-Yeal; Xiao, Qinghua; Zhang, Xiongtao

2018-04-01

We study the dynamics of infinitely many Cucker-Smale (C-S) flocking particles under the interplay of random communication and incompressible fluids. For the dynamics of an ensemble of flocking particles, we use the kinetic Cucker-Smale-Fokker-Planck (CS-FP) equation with a degenerate diffusion, whereas for the fluid component, we use the incompressible Navier-Stokes (N-S) equations. These two subsystems are coupled via the drag force. For this coupled model, we present the global existence of weak and strong solutions in Rd (d = 2 , 3). Under the extra regularity assumptions of the initial data, the unique solvability of strong solutions is also established in R2. In a large coupling regime and periodic spatial domain T2 : =R2 /Z2, we show that the velocities of C-S particles and fluids are asymptotically aligned to two constant velocities which may be different.

Formal solution of the Navier-Stokes initial- and boundary-value problem for incompressible fluids

International Nuclear Information System (INIS)

Alankus, T.

1984-01-01

A general formal solution of the integral equivalent of Navier-Stokes equation for incompressible viscous fluids is presented through a linear operator acting on the functionals of solenoidal vector fields. This solution operator is completely determined by the Green functions of Laplace and diffusion equations corresponding to the flow region

Analytical and numerical analyses for a penny-shaped crack embedded in an infinite transversely isotropic multi-ferroic composite medium: semi-permeable electro-magnetic boundary condition

Science.gov (United States)

Zheng, R.-F.; Wu, T.-H.; Li, X.-Y.; Chen, W.-Q.

2018-06-01

The problem of a penny-shaped crack embedded in an infinite space of transversely isotropic multi-ferroic composite medium is investigated. The crack is assumed to be subjected to uniformly distributed mechanical, electric and magnetic loads applied symmetrically on the upper and lower crack surfaces. The semi-permeable (limited-permeable) electro-magnetic boundary condition is adopted. By virtue of the generalized method of potential theory and the general solutions, the boundary integro-differential equations governing the mode I crack problem, which are of nonlinear nature, are established and solved analytically. Exact and complete coupling magneto-electro-elastic field is obtained in terms of elementary functions. Important parameters in fracture mechanics on the crack plane, e.g., the generalized crack surface displacements, the distributions of generalized stresses at the crack tip, the generalized stress intensity factors and the energy release rate, are explicitly presented. To validate the present solutions, a numerical code by virtue of finite element method is established for 3D crack problems in the framework of magneto-electro-elasticity. To evaluate conveniently the effect of the medium inside the crack, several empirical formulae are developed, based on the numerical results.

INCOMPRESSIBLE LAMINAR BOUNDARY LAYER CONTROL BY BLOWING AND SUCTION

Directory of Open Access Journals (Sweden)

AZZEDINE NAHOUI

2013-12-01

Full Text Available A two-dimensional incompressible laminar boundary layer and its control using blowing and suction over a flat plate and around the NACA 0012 and 661012 profiles, is studied numerically. The study is based on the Prandtl boundary layer model using the finite differences method and the Crank-Nicolson scheme. The velocity distribution, the boundary layer thickness and the friction coefficient, are determined and presented with and without control. The application of the control technique, has demonstrated its positive effect on the transition point and the friction coefficient. Both control procedures are compared for different lengths, speeds and angles of blowing and suction.

Computing dispersion curves of elastic/viscoelastic transversely-isotropic bone plates coupled with soft tissue and marrow using semi-analytical finite element (SAFE) method.

Science.gov (United States)

Nguyen, Vu-Hieu; Tran, Tho N H T; Sacchi, Mauricio D; Naili, Salah; Le, Lawrence H

2017-08-01

We present a semi-analytical finite element (SAFE) scheme for accurately computing the velocity dispersion and attenuation in a trilayered system consisting of a transversely-isotropic (TI) cortical bone plate sandwiched between the soft tissue and marrow layers. The soft tissue and marrow are mimicked by two fluid layers of finite thickness. A Kelvin-Voigt model accounts for the absorption of all three biological domains. The simulated dispersion curves are validated by the results from the commercial software DISPERSE and published literature. Finally, the algorithm is applied to a viscoelastic trilayered TI bone model to interpret the guided modes of an ex-vivo experimental data set from a bone phantom. Copyright © 2017 Elsevier Ltd. All rights reserved.

Seismic wave propagation in non-homogeneous elastic media by boundary elements

CERN Document Server

Manolis, George D; Rangelov, Tsviatko V; Wuttke, Frank

2017-01-01

This book focuses on the mathematical potential and computational efficiency of the Boundary Element Method (BEM) for modeling seismic wave propagation in either continuous or discrete inhomogeneous elastic/viscoelastic, isotropic/anisotropic media containing multiple cavities, cracks, inclusions and surface topography. BEM models may take into account the entire seismic wave path from the seismic source through the geological deposits all the way up to the local site under consideration. The general presentation of the theoretical basis of elastodynamics for inhomogeneous and heterogeneous continua in the first part is followed by the analytical derivation of fundamental solutions and Green's functions for the governing field equations by the usage of Fourier and Radon transforms. The numerical implementation of the BEM is for antiplane in the second part as well as for plane strain boundary value problems in the third part. Verification studies and parametric analysis appear throughout the book, as do both ...

Topology optimization using the improved element-free Galerkin method for elasticity*

International Nuclear Information System (INIS)

Wu Yi; Ma Yong-Qi; Feng Wei; Cheng Yu-Min

2017-01-01

The improved element-free Galerkin (IEFG) method of elasticity is used to solve the topology optimization problems. In this method, the improved moving least-squares approximation is used to form the shape function. In a topology optimization process, the entire structure volume is considered as the constraint. From the solid isotropic microstructures with penalization, we select relative node density as a design variable. Then we choose the minimization of compliance to be an objective function, and compute its sensitivity with the adjoint method. The IEFG method in this paper can overcome the disadvantages of the singular matrices that sometimes appear in conventional element-free Galerkin (EFG) method. The central processing unit (CPU) time of each example is given to show that the IEFG method is more efficient than the EFG method under the same precision, and the advantage that the IEFG method does not form singular matrices is also shown. (paper)

Uncertainty principles for inverse source problems for electromagnetic and elastic waves

Science.gov (United States)

Griesmaier, Roland; Sylvester, John

2018-06-01

In isotropic homogeneous media, far fields of time-harmonic electromagnetic waves radiated by compactly supported volume currents, and elastic waves radiated by compactly supported body force densities can be modelled in very similar fashions. Both are projected restricted Fourier transforms of vector-valued source terms. In this work we generalize two types of uncertainty principles recently developed for far fields of scalar-valued time-harmonic waves in Griesmaier and Sylvester (2017 SIAM J. Appl. Math. 77 154–80) to this vector-valued setting. These uncertainty principles yield stability criteria and algorithms for splitting far fields radiated by collections of well-separated sources into the far fields radiated by individual source components, and for the restoration of missing data segments. We discuss proper regularization strategies for these inverse problems, provide stability estimates based on the new uncertainty principles, and comment on reconstruction schemes. A numerical example illustrates our theoretical findings.

Isotropic gates and large gamma detector arrays versus angular distributions

International Nuclear Information System (INIS)

Iacob, V.E.; Duchene, G.

1997-01-01

Angular information extracted from in-beam γ ray measurements are of great importance for γ ray multipolarity and nuclear spin assignments. In our days large Ge detector arrays became available allowing the measurements of extremely weak γ rays in almost 4π sr solid angle (e.g., EUROGAM detector array). Given the high detector efficiency it is common for the mean suppressed coincidence multiplicity to reach values as high as 4 to 6. Thus, it is possible to gate on particular γ rays in order to enhance the relative statistics of a definite reaction channel and/or a definite decaying path in the level scheme of the selected residual nucleus. As compared to angular correlations, the conditioned angular distribution spectra exhibit larger statistics because in the latter the gate-setting γ ray may be observed by all the detectors in the array, relaxing somehow the geometrical restrictions of the angular correlations. Since the in-beam γ ray emission is anisotropic one could inquire that gate setting as mentioned above, based on anisotropic γ ray which would perturb the angular distributions in the unfolded events. As our work proved, there is no reason to worry about this if the energy gate runs over the whole solid angle in an ideal 4π sr detector, i.e., if the gate is isotropic. In real quasi 4π sr detector arrays the corresponding quasi isotropic gate preserves the angular properties of the unfolded data, too. However extraction of precise angular distribution coefficient especially a 4 , requires the consideration of the deviation of the quasi isotropic gate relative to the (ideal) isotropic gate

Towards Isotropic Vortex Pinning in YBCO Films with Double-doping BHO-Y2O3 and BZO-Y2O3 Artificial Pining Centers

Science.gov (United States)

Gautam, Bibek; Sebastian, Mary Ann; Chen, Shihong; Haugan, Timothy; Chen, Yanbin; Xing, Zhongwen; Prestigiacomo, Joseph; Osofsky, Mike; Wu, Judy

2017-12-01

Strong and isotropic vortex pinning landscape is demanded for high field applications of YaBa2Cu3O7-x (YBCO) epitaxial thin films. Double-doping (DD) of artificial pinning centers (APCs) of mixed morphologies has been identified as a viable approach for this purpose. This work presents a comparative study on the transport critical current density J c (H, θ) of 3.0 vol.%Y2O3+2.0 (or 6.0) vol.% BaZrO3 (BZO DD) and 3.0 vol.%Y2O3+ 2.0 (or 6.0) vol.% BaHfO3 (BHO DD) films. Based on the elastic strain model, BaHfO3 (BHO) nanorods have lower rigidity than their BaZrO3 (BZO) counterparts, which means their c-axis alignment is more susceptible to the local strain generated by the secondary dopant of Y2O3. Considering the increasing strain field with higher BZO (or BHO doping), the higher susceptibility may result in a large portion of the BHO APCs moving away from perfect c-axis alignment and enhancing isotropic pinning with respect to the H orientation. This is confirmed since the BHO DD films illustrate a less pronounced J c peak at H//c-axis and hence more isotropic J c(θ) than their BZO DD counterparts. At 9.0 T, the variation of the J c across the entire θ range (0-90 degree) is less than 18% for the BHO DD film, in contrast to about 100% for the 2.0 vol.% BZO DD counterpart. At the higher BHO concentration of 6.0 vol.%, this higher tunability of the Y2O3 leads to increased ab-plane aligned BHO APCs and hence enhanced J c at H//ab-plane.

Depth migration in transversely isotropic media with explicit operators

Energy Technology Data Exchange (ETDEWEB)

Uzcategui, Omar [Colorado School of Mines, Golden, CO (United States)

1994-12-01

The author presents and analyzes three approaches to calculating explicit two-dimensional (2D) depth-extrapolation filters for all propagation modes (P, SV, and SH) in transversely isotropic media with vertical and tilted axis of symmetry. These extrapolation filters are used to do 2D poststack depth migration, and also, just as for isotropic media, these 2D filters are used in the McClellan transformation to do poststack 3D depth migration. Furthermore, the same explicit filters can also be used to do depth-extrapolation of prestack data. The explicit filters are derived by generalizations of three different approaches: the modified Taylor series, least-squares, and minimax methods initially developed for isotropic media. The examples here show that the least-squares and minimax methods produce filters with accurate extrapolation (measured in the ability to position steep reflectors) for a wider range of propagation angles than that obtained using the modified Taylor series method. However, for low propagation angles, the modified Taylor series method has smaller amplitude and phase errors than those produced by the least-squares and minimax methods. These results suggest that to get accurate amplitude estimation, modified Taylor series filters would be somewhat preferred in areas with low dips. In areas with larger dips, the least-squares and minimax methods would give a distinctly better delineation of the subsurface structures.

Elastic Evaluation of Poly(Lactic Acid) Electrospun Membranes Using the Pulsed Photoacoustic Technique

Science.gov (United States)

Navarrete, M.; Vera-Graziano, R.; Maciel-Cerda, A.; Sánchez-Arévalo, F. M.; Godínez, F. A.

2017-08-01

Fibrous membranes manufactured by electrospinning possess unique features such as a high porosity and large specific surface area, making them suitable for applications in tissue engineering. However, the determination of their mechanical behavior under different loading conditions remains one of the most difficult technical problems for researchers to overcome. While the tensile properties of this kind of membrane are commonly reported in the literature, few explorations of their properties in other directions have been reported. In this paper, the pulsed photoacoustic technique is employed to obtain the elastic constants of electrospun non-woven membranes, specifically in two directions ( L, T). The electrospun samples are hybrid fiber membranes of poly(lactic acid) and hydroxyapatite (HA) nanoparticles at different concentrations. It is found that the concentration of HA nanoparticles determines the mechanical response of the membrane, where the nanoparticles act either as a reinforcement or as a mesh defect. The elastic constants (EL, ET, GL, GT, vL, ν T) are obtained through velocity waves related to the stress-strain equations, using samples with two different geometries and considering the electrospinning mats as a transversely isotropic material. These values are compared to those acquired using macro-tensile testing equipment according to the ASTM D1708 standard.

Second order elasticity at hypersonic frequencies of reactive polyurethanes as seen by generalized Cauchy relations

International Nuclear Information System (INIS)

Philipp, M; Vergnat, C; Mueller, U; Sanctuary, R; Baller, J; Krueger, J K; Possart, W; Alnot, P

2009-01-01

The non-equilibrium process of polymerization of reactive polymers can be accompanied by transition phenomena like gelation or the chemical glass transition. The sensitivity of the mechanical properties at hypersonic frequencies-including the generalized Cauchy relation-to these transition phenomena is studied for three different polyurethanes using Brillouin spectroscopy. As for epoxies, the generalized Cauchy relation surprisingly holds true for the non-equilibrium polymerization process and for the temperature dependence of polyurethanes. Neither the sol-gel transition nor the chemical and thermal glass transitions are visible in the representation of the generalized Cauchy relation. Taking into account the new results and combining them with general considerations about the elastic properties of the isotropic state, an improved physical foundation of the generalized Cauchy relation is proposed.

Second order elasticity at hypersonic frequencies of reactive polyurethanes as seen by generalized Cauchy relations

Energy Technology Data Exchange (ETDEWEB)

Philipp, M; Vergnat, C; Mueller, U; Sanctuary, R; Baller, J; Krueger, J K [Laboratoire de Physique des Materiaux, Universite du Luxembourg, 162A, avenue de la Faiencerie, L-1511 Luxembourg (Luxembourg); Possart, W [Fachbereich Werkstoffwissenschaften, Universitaet des Saarlandes, D-66123 Saarbruecken (Germany); Alnot, P [LPMI, Universite Nancy (France)], E-mail: martine.philipp@uni.lu

2009-01-21

The non-equilibrium process of polymerization of reactive polymers can be accompanied by transition phenomena like gelation or the chemical glass transition. The sensitivity of the mechanical properties at hypersonic frequencies-including the generalized Cauchy relation-to these transition phenomena is studied for three different polyurethanes using Brillouin spectroscopy. As for epoxies, the generalized Cauchy relation surprisingly holds true for the non-equilibrium polymerization process and for the temperature dependence of polyurethanes. Neither the sol-gel transition nor the chemical and thermal glass transitions are visible in the representation of the generalized Cauchy relation. Taking into account the new results and combining them with general considerations about the elastic properties of the isotropic state, an improved physical foundation of the generalized Cauchy relation is proposed.

Second order elasticity at hypersonic frequencies of reactive polyurethanes as seen by generalized Cauchy relations.

Science.gov (United States)

Philipp, M; Vergnat, C; Müller, U; Sanctuary, R; Baller, J; Possart, W; Alnot, P; Krüger, J K

2009-01-21

The non-equilibrium process of polymerization of reactive polymers can be accompanied by transition phenomena like gelation or the chemical glass transition. The sensitivity of the mechanical properties at hypersonic frequencies-including the generalized Cauchy relation-to these transition phenomena is studied for three different polyurethanes using Brillouin spectroscopy. As for epoxies, the generalized Cauchy relation surprisingly holds true for the non-equilibrium polymerization process and for the temperature dependence of polyurethanes. Neither the sol-gel transition nor the chemical and thermal glass transitions are visible in the representation of the generalized Cauchy relation. Taking into account the new results and combining them with general considerations about the elastic properties of the isotropic state, an improved physical foundation of the generalized Cauchy relation is proposed.

Elastic strain relaxation in interfacial dislocation patterns: II. From long- and short-range interactions to local reactions

Science.gov (United States)

Vattré, A.

2017-08-01

The long- and short-range interactions as well as planar reactions between two infinitely periodic sets of crossing dislocations are investigated using anisotropic elasticity theory in face- (fcc) and body- (bcc) centered cubic materials. Two preliminary cases are proposed to examine the substantial changes in the elastic stress states and the corresponding strain energies due to a slight rearrangement in the internal dislocation geometries and characters. In general, significant differences and discrepancies resulting from the considered cubic crystal structure and the approximation of isotropic elasticity are exhibited. In a third scenario, special attention is paid to connecting specific internal dislocation structures from the previous cases with non-equilibrium configurations predicted by the quantized Frank-Bilby equation for the (111) fcc and (110) bcc twist grain boundaries. The present solutions lead to the formation of energetically favorable dislocation junctions with non-randomly strain-relaxed configurations of lower energy. In particular, the local dislocation interactions and reactions form equilibrium hexagonal-shaped patterns with planar three-fold dislocation nodes without producing spurious far-field stresses.Numerical application results are presented from a selection of cubic metals including aluminum, copper, tantalum, and niobium. In contrast to the fcc materials, asymmetric dislocation nodes occur in the anisotropic bcc cases, within which the minimum-energy paths for predicting the fully strain-relaxed dislocation patterns depend on the Zener anisotropic factor with respect to unity. The associated changes in the dislocation structures as well as the removal of the elastic strain energy upon relaxations are quantified and also discussed.

Characterization of nuclear graphite elastic properties using laser ultrasonic methods

Science.gov (United States)

Zeng, Fan W.; Han, Karen; Olasov, Lauren R.; Gallego, Nidia C.; Contescu, Cristian I.; Spicer, James B.

2015-05-01

Laser ultrasonic methods have been used to characterize the elastic behaviors of commercially-available and legacy nuclear graphites. Since ultrasonic techniques are sensitive to various aspects of graphite microstructure including preferred grain orientation, microcrack orientation and porosity, laser ultrasonics is a candidate technique for monitoring graphite degradation and structural integrity in environments expected in high-temperature, gas-cooled nuclear reactors. Aspects of materials texture can be assessed by studying ultrasonic wavespeeds as a function of propagation direction and polarization. Shear wave birefringence measurements, in particular, can be used to evaluate elastic anisotropy. In this work, laser ultrasonic measurements of graphite moduli have been made to provide insight into the relationship between the microstructures and the macroscopic stiffnesses of these materials. In particular, laser ultrasonic measurements have been made using laser line sources to produce shear waves with specific polarizations. By varying the line orientation relative to the sample, shear wave birefringence measurements have been recorded. Results from shear wave birefringence measurements show that an isostatically molded graphite, such as PCIB, behaves isotropically, while an extruded graphite, such as H-451, displays significant ultrasonic texture. Graphites have complicated microstructures that depend on the manufacturing processes used, and ultrasonic texture in these materials could originate from grain orientation and preferred microcrack alignment. Effects on material isotropy due to service related microstructural changes are possible and the ultimate aim of this work is to determine the degree to which these changes can be assessed nondestructively using laser ultrasonics measurements.

Incompressible Turbulent Flow Simulation Using the κ-ɛ Model and Upwind Schemes

Directory of Open Access Journals (Sweden)

V. G. Ferreira

2007-01-01

Full Text Available In the computation of turbulent flows via turbulence modeling, the treatment of the convective terms is a key issue. In the present work, we present a numerical technique for simulating two-dimensional incompressible turbulent flows. In particular, the performance of the high Reynolds κ-ɛ model and a new high-order upwind scheme (adaptative QUICKEST by Kaibara et al. (2005 is assessed for 2D confined and free-surface incompressible turbulent flows. The model equations are solved with the fractional-step projection method in primitive variables. Solutions are obtained by using an adaptation of the front tracking GENSMAC (Tomé and McKee (1994 methodology for calculating fluid flows at high Reynolds numbers. The calculations are performed by using the 2D version of the Freeflow simulation system (Castello et al. (2000. A specific way of implementing wall functions is also tested and assessed. The numerical procedure is tested by solving three fluid flow problems, namely, turbulent flow over a backward-facing step, turbulent boundary layer over a flat plate under zero-pressure gradients, and a turbulent free jet impinging onto a flat surface. The numerical method is then applied to solve the flow of a horizontal jet penetrating a quiescent fluid from an entry port beneath the free surface.

Estimation of transversely isotropic material properties from magnetic resonance elastography using the optimised virtual fields method.

Science.gov (United States)

Miller, Renee; Kolipaka, Arunark; Nash, Martyn P; Young, Alistair A

2018-03-12

Magnetic resonance elastography (MRE) has been used to estimate isotropic myocardial stiffness. However, anisotropic stiffness estimates may give insight into structural changes that occur in the myocardium as a result of pathologies such as diastolic heart failure. The virtual fields method (VFM) has been proposed for estimating material stiffness from image data. This study applied the optimised VFM to identify transversely isotropic material properties from both simulated harmonic displacements in a left ventricular (LV) model with a fibre field measured from histology as well as isotropic phantom MRE data. Two material model formulations were implemented, estimating either 3 or 5 material properties. The 3-parameter formulation writes the transversely isotropic constitutive relation in a way that dissociates the bulk modulus from other parameters. Accurate identification of transversely isotropic material properties in the LV model was shown to be dependent on the loading condition applied, amount of Gaussian noise in the signal, and frequency of excitation. Parameter sensitivity values showed that shear moduli are less sensitive to noise than the other parameters. This preliminary investigation showed the feasibility and limitations of using the VFM to identify transversely isotropic material properties from MRE images of a phantom as well as simulated harmonic displacements in an LV geometry. Copyright © 2018 John Wiley & Sons, Ltd.

A discontinuous Galerkin finite element discretization of the Euler equations for compressible and incompressible fluids

NARCIS (Netherlands)

Pesch, L.; van der Vegt, Jacobus J.W.

2008-01-01

Using the generalized variable formulation of the Euler equations of fluid dynamics, we develop a numerical method that is capable of simulating the flow of fluids with widely differing thermodynamic behavior: ideal and real gases can be treated with the same method as an incompressible fluid. The

Development of Multigrid Methods for diffusion, Advection, and the incompressible Navier-Stokes Equations

Energy Technology Data Exchange (ETDEWEB)

Gjesdal, Thor

1997-12-31

This thesis discusses the development and application of efficient numerical methods for the simulation of fluid flows, in particular the flow of incompressible fluids. The emphasis is on practical aspects of algorithm development and on application of the methods either to linear scalar model equations or to the non-linear incompressible Navier-Stokes equations. The first part deals with cell centred multigrid methods and linear correction scheme and presents papers on (1) generalization of the method to arbitrary sized grids for diffusion problems, (2) low order method for advection-diffusion problems, (3) attempt to extend the basic method to advection-diffusion problems, (4) Fourier smoothing analysis of multicolour relaxation schemes, and (5) analysis of high-order discretizations for advection terms. The second part discusses a multigrid based on pressure correction methods, non-linear full approximation scheme, and papers on (1) systematic comparison of the performance of different pressure correction smoothers and some other algorithmic variants, low to moderate Reynolds numbers, and (2) systematic study of implementation strategies for high order advection schemes, high-Re flow. An appendix contains Fortran 90 data structures for multigrid development. 160 refs., 26 figs., 22 tabs.

Parallel iterative solution of the incompressible Navier-Stokes equations with application to rotating wings

Czech Academy of Sciences Publication Activity Database

Šístek, Jakub; Cirak, F.

2015-01-01

Roč. 122, 20 November (2015), s. 165-183 ISSN 0045-7930 R&D Projects: GA ČR GA14-02067S Institutional support: RVO:67985840 Keywords : Navier-Stokes * incompressible flow * Krylov subspace methods Subject RIV: BA - General Mathematics Impact factor: 1.891, year: 2015 http://www.sciencedirect.com/science/article/pii/S0045793015003023

A 3D printed dual GSM band near isotropic on-package antenna

KAUST Repository

Zhen, Su

2017-10-25

In this paper, we propose an on-package dual band monopole antenna with near-isotropic radiation pattern for GSM mobile applications. The proposed antenna is well matched for both GSM 900 and 1800 bands and provides decent gain for both the bands (1.67 and 3.27 dBi at 900 MHz and 1800 MHz respectively). The antenna is printed with silver ink on a 3D printed polymer based package. The package houses the GSM electronics and the battery. By optimizing the antenna arms width and length, a near-isotropic radiation pattern is achieved. Unlike the published isotropic antennas which are either single band or large in size, the proposed antenna covers both GSM bands with required bandwidth and is only half wavelength long. The design is low cost and highly suitable for various GSM applications such as localization, in additional to conventional communication applications.

Multimode Coupling Theory for Kelvin–Helmholtz Instability in Incompressible Fluid

International Nuclear Information System (INIS)

Li-Feng, Wang; Ying-Jun, Li; Wen-Hua, Ye; Zheng-Feng, Fan

2009-01-01

A weakly nonlinear model is proposed for multimode Kelvin–Helmholtz instability. The second-order mode coupling formula for Kelvin–Helmholtz instability in two-dimensional incompressible fluid is presented by expanding the perturbation velocity potential to second order. It is found that there is an important resonance in the course of the sum frequency mode coupling but the difference frequency mode coupling does not have. This resonance makes the sum frequency mode coupling process relatively complex. The sum frequency mode coupling is strongly dependent on time especially when the density of the two fluids is adjacent and the difference frequency mode coupling is not

Étalement d'une goutte stratifiée incompressible

Science.gov (United States)

de Gennes, Pierre-Gilles; Cazabat, Anne-Marie

L'étalement de films ultraminces de liquides simples sur une surface lisse horizontale conduit souvent à des gouttes à gradins d'une épaisseur moléculaire ([1]-[3]). Nous construisons ici un modèle pour la dynamique de l'étalement, en supposant que : (a) chaque gradin est un liquide bidimensionnel incompressible; (b) les molécules de la n-ième couche sont soumises à un potentiel (Wn) qui exprime leurs interactions à longue portée avec le solide; (c) on a un écoulement parallèle de cisaillement, et un écoulement normal de perméation. La perméation intervient seulement dans un certain « ruban » de largeur ξ sur le bord de chaque gradin. Dans le cas usuel, où le rayon du n-ième gradin Rn est trs supérieur à ξ, la dissipation est dominée par le cisaillement, et on arrive à des lois simples pour la vitesse de dilatation (ou de contraction) dotR_n. Very thin films of simple liquids often spread with well defined steps of molecular thickness ([1]-[3]). We construct a model for the dynamics of spreading assuming that: (a) each layer is an incompressible, 2 dimensional fluid; (b) the molecules in the (nth) layer experience a long range potential (e.g. Van der Waals) from the solid; (c) two types of flow occur: shear between layers and permeation normal to the layers. We find that permeation is important only in an annulus of small size ξ near each step. Between steps, the viscous effects in simple shear dominate, and this leads to simple laws for the dilation (or contraction) of the various layers.

Geometrically nonlinear dynamic analysis of doubly curved isotropic shells resting on elastic foundation by a combination of harmonic differential quadrature-finite difference methods

International Nuclear Information System (INIS)

Civalek, Oemer

2005-01-01

The nonlinear dynamic response of doubly curved shallow shells resting on Winkler-Pasternak elastic foundation has been studied for step and sinusoidal loadings. Dynamic analogues of Von Karman-Donnel type shell equations are used. Clamped immovable and simply supported immovable boundary conditions are considered. The governing nonlinear partial differential equations of the shell are discretized in space and time domains using the harmonic differential quadrature (HDQ) and finite differences (FD) methods, respectively. The accuracy of the proposed HDQ-FD coupled methodology is demonstrated by numerical examples. The shear parameter G of the Pasternak foundation and the stiffness parameter K of the Winkler foundation have been found to have a significant influence on the dynamic response of the shell. It is concluded from the present study that the HDQ-FD methodolgy is a simple, efficient, and accurate method for the nonlinear analysis of doubly curved shallow shells resting on two-parameter elastic foundation

Experimental study on the thermo-mechanical behaviour of stiff clay under non-isotropic stress state

International Nuclear Information System (INIS)

Tang, Anh Minh; Cui, Yu-Jun; Li, Xiang-Ling

2012-01-01

Document available in extended abstract form only. Stiff clay is usually considered as possible host-rock for geological radioactive waste disposal due to its low permeability and its self-sealing capacity. Boom Clay, for instance, is one of the clays currently considered by the Belgian radioactive waste management agency Ondraf/Niras as a potential host for a geological repository. In order to analyse the performance of this material, it is important to understand its behaviour under the coupled thermo-hydro-mechanical solicitations. In laboratory, several studies have been performed to study the volume change of clay under coupled thermomechanical loading. The results show that heating under drained conditions can induce thermal dilation at low confining stress and thermal contraction at high confining stress. On the other hand, compression tests performed at constant temperature show that the compressibility parameters of soil can be modified by temperature change. These features are now well considered in constitutive laws based on the framework of elasto-plasticity. Under undrained conditions, heating can increase pore-water pressure and this behaviour can be simulated using the theoretical thermo-poro-elastic framework. The temperature effect on the soil behaviour under triaxial compression is also often considered. It is commonly accepted that heating decreases the shear strength of clay but this softening can be hidden by the thermal contraction that occurs during heating which can induce at the same time soil hardening. In spite of these existing works, laboratory tests considering the thermo-mechanical loading path that the soil can be subjected to are still rare. Actually, in the case of geological radioactive waste disposal, after the installation of waste canisters, the soil is expected to be heated under non-isotropic stress state. Most of the existing laboratory works show heating tests in odometer cell or triaxial cell under isotropic stress

Strong solutions for an incompressible Navier-Stokes/Allen-Cahn system with different densities

Science.gov (United States)

Li, Yinghua; Huang, Mingxia

2018-06-01

In this paper, we investigate a coupled Navier-Stokes/Allen-Cahn system describing a diffuse interface model for two-phase flow of viscous incompressible fluids with different densities in a bounded domain Ω \\subset R^N(N=2,3). We prove the existence and uniqueness of local strong solutions to the initial boundary value problem when the initial density function ρ _0 has a positive lower bound.

Temperature-dependent study of isotropic-nematic transition for a Gay-Berne fluid using density-functional theory

International Nuclear Information System (INIS)

Singh, Ram Chandra

2007-01-01

We have used the density-functional theory to study the effect of varying temperature on the isotropic-nematic transition of a fluid of molecules interacting via the Gay-Berne intermolecular potential. The nematic phase is found to be stable with respect to isotropic phase in the temperature range 0.80≤T*≤1.25. Pair correlation functions needed as input information in density-functional theory is calculated using the Percus-Yevick integral equation theory. We find that the density-functional theory is good for studying the isotropic-nematic transition in molecular fluids if the values of the pair-correlation functions in the isotropic phase are known accurately. We have also compared our results with computer simulation results wherever they are available

Parallel iterative solution of the incompressible Navier-Stokes equations with application to rotating wings

Czech Academy of Sciences Publication Activity Database

Šístek, Jakub; Cirak, F.

2015-01-01

Roč. 122, 20 November (2015), s. 165-183 ISSN 0045-7930 R&D Projects: GA ČR GA14-02067S Institutional support: RVO:67985840 Keywords : Navier-Stokes * incompressible flow * Krylov subspace method s Subject RIV: BA - General Mathematics Impact factor: 1.891, year: 2015 http://www. science direct.com/ science /article/pii/S0045793015003023

Landmark-based elastic registration using approximating thin-plate splines.

Science.gov (United States)

Rohr, K; Stiehl, H S; Sprengel, R; Buzug, T M; Weese, J; Kuhn, M H

2001-06-01

We consider elastic image registration based on a set of corresponding anatomical point landmarks and approximating thin-plate splines. This approach is an extension of the original interpolating thin-plate spline approach and allows to take into account landmark localization errors. The extension is important for clinical applications since landmark extraction is always prone to error. Our approach is based on a minimizing functional and can cope with isotropic as well as anisotropic landmark errors. In particular, in the latter case it is possible to include different types of landmarks, e.g., unique point landmarks as well as arbitrary edge points. Also, the scheme is general with respect to the image dimension and the order of smoothness of the underlying functional. Optimal affine transformations as well as interpolating thin-plate splines are special cases of this scheme. To localize landmarks we use a semi-automatic approach which is based on three-dimensional (3-D) differential operators. Experimental results are presented for two-dimensional as well as 3-D tomographic images of the human brain.

Bell inequalities stronger than the Clauser-Horne-Shimony-Holt inequality for three-level isotropic states

International Nuclear Information System (INIS)

Ito, Tsuyoshi; Imai, Hiroshi; Avis, David

2006-01-01

We show that some two-party Bell inequalities with two-valued observables are stronger than the CHSH inequality for 3x3 isotropic states in the sense that they are violated by some isotropic states in the 3x3 system that do not violate the CHSH inequality. These Bell inequalities are obtained by applying triangular elimination to the list of known facet inequalities of the cut polytope on nine points. This gives a partial solution to an open problem posed by Collins and Gisin. The results of numerical optimization suggest that they are candidates for being stronger than the I 3322 Bell inequality for 3x3 isotropic states. On the other hand, we found no Bell inequalities stronger than the CHSH inequality for 2x2 isotropic states. In addition, we illustrate an inclusion relation among some Bell inequalities derived by triangular elimination

Blocky inversion of multichannel elastic impedance for elastic parameters

Science.gov (United States)

Mozayan, Davoud Karami; Gholami, Ali; Siahkoohi, Hamid Reza

2018-04-01

Petrophysical description of reservoirs requires proper knowledge of elastic parameters like P- and S-wave velocities (Vp and Vs) and density (ρ), which can be retrieved from pre-stack seismic data using the concept of elastic impedance (EI). We propose an inversion algorithm which recovers elastic parameters from pre-stack seismic data in two sequential steps. In the first step, using the multichannel blind seismic inversion method (exploited recently for recovering acoustic impedance from post-stack seismic data), high-resolution blocky EI models are obtained directly from partial angle-stacks. Using an efficient total-variation (TV) regularization, each angle-stack is inverted independently in a multichannel form without prior knowledge of the corresponding wavelet. The second step involves inversion of the resulting EI models for elastic parameters. Mathematically, under some assumptions, the EI's are linearly described by the elastic parameters in the logarithm domain. Thus a linear weighted least squares inversion is employed to perform this step. Accuracy of the concept of elastic impedance in predicting reflection coefficients at low and high angles of incidence is compared with that of exact Zoeppritz elastic impedance and the role of low frequency content in the problem is discussed. The performance of the proposed inversion method is tested using synthetic 2D data sets obtained from the Marmousi model and also 2D field data sets. The results confirm the efficiency and accuracy of the proposed method for inversion of pre-stack seismic data.