Linear analysis using secants for materials with temperature dependent nonlinear elastic modulus and thermal expansion properties

Science.gov (United States)

Pepi, John W.

2017-08-01

Thermally induced stress is readily calculated for linear elastic material properties using Hooke's law in which, for situations where expansion is constrained, stress is proportional to the product of the material elastic modulus and its thermal strain. When material behavior is nonlinear, one needs to make use of nonlinear theory. However, we can avoid that complexity in some situations. For situations in which both elastic modulus and coefficient of thermal expansion vary with temperature, solutions can be formulated using secant properties. A theoretical approach is thus presented to calculate stresses for nonlinear, neo-Hookean, materials. This is important for high acuity optical systems undergoing large temperature extremes.

Unraveling complex nonlinear elastic behaviors in rocks using dynamic acousto-elasticity

Science.gov (United States)

Riviere, J.; Guyer, R.; Renaud, G.; TenCate, J. A.; Johnson, P. A.

2012-12-01

In comparison with standard nonlinear ultrasonic methods like frequency mixing or resonance based measurements that allow one to extract average, bulk variations of modulus and attenuation versus strain level, dynamic acousto-elasticity (DAE) allows to obtain the elastic behavior over the entire dynamic cycle, detailing the full nonlinear behavior under tension and compression, including hysteresis and memory effects. This method consists of exciting a sample in Bulk-mode resonance at strains of 10-7 to 10-5 and simultaneously probing with a sequence of high frequency, low amplitude pulses. Time of flight and amplitudes of these pulses, respectively related to nonlinear elastic and dissipative parameters, can be plotted versus vibration strain level. Despite complex nonlinear signatures obtained for most rocks, it can be shown that for low strain amplitude (Pasqualini et al., JGR 2007), but not with the extreme detail of elasticity provided by DAE. Previous quasi-static measurements made in Berea sandstone (Claytor et al, GRL 2009), show that the hysteretic behavior disappears when the protocol is performed at a very low strain-rate (static limit). Therefore, future work will aim at linking quasi-static and dynamic observations, i.e. the frequency or strain-rate dependence, in order to understand underlying physical phenomena.

Non-linear buckling of an FGM truncated conical shell surrounded by an elastic medium

International Nuclear Information System (INIS)

Sofiyev, A.H.; Kuruoglu, N.

2013-01-01

In this paper, the non-linear buckling of the truncated conical shell made of functionally graded materials (FGMs) surrounded by an elastic medium has been studied using the large deformation theory with von Karman–Donnell-type of kinematic non-linearity. A two-parameter foundation model (Pasternak-type) is used to describe the shell–foundation interaction. The FGM properties are assumed to vary continuously through the thickness direction. The fundamental relations, the modified Donnell type non-linear stability and compatibility equations of the FGM truncated conical shell resting on the Pasternak-type elastic foundation are derived. By using the Superposition and Galerkin methods, the non-linear stability equations for the FGM truncated conical shell is solved. Finally, influences of variations of Winkler foundation stiffness and shear subgrade modulus of the foundation, compositional profiles and shell characteristics on the dimensionless critical non-linear axial load are investigated. The present results are compared with the available data for a special case. -- Highlights: • Nonlinear buckling of FGM conical shell surrounded by elastic medium is studied. • Pasternak foundation model is used to describe the shell–foundation interaction. • Nonlinear basic equations are derived. • Problem is solved by using Superposition and Galerkin methods. • Influences of various parameters on the nonlinear critical load are investigated

Nonlinear theory of electroelastic and magnetoelastic interactions

CERN Document Server

Dorfmann, Luis

2014-01-01

This book provides a unified theory of nonlinear electro-magnetomechanical interactions of soft materials capable of large elastic deformations. The authors include an overview of the basic principles of the classical theory of electromagnetism from the fundamental notions of point charges and magnetic dipoles through to distributions of charge and current in a non-deformable continuum, time-dependent electromagnetic fields and Maxwell’s equations. They summarize the basic ingredients of continuum mechanics that are required to account for the deformability of material and present nonlinear constitutive frameworks for electroelastic and magnetoelastic interactions in a highly deformable material. The equations contained in the book are used to formulate and solve a variety of representative boundary-value problems for both nonlinear electroelasticity and magnetoelasticity.

Self-induced parametric amplification arising from nonlinear elastic coupling in a micromechanical resonating disk gyroscope.

Science.gov (United States)

Nitzan, Sarah H; Zega, Valentina; Li, Mo; Ahn, Chae H; Corigliano, Alberto; Kenny, Thomas W; Horsley, David A

2015-03-12

Parametric amplification, resulting from intentionally varying a parameter in a resonator at twice its resonant frequency, has been successfully employed to increase the sensitivity of many micro- and nano-scale sensors. Here, we introduce the concept of self-induced parametric amplification, which arises naturally from nonlinear elastic coupling between the degenerate vibration modes in a micromechanical disk-resonator, and is not externally applied. The device functions as a gyroscope wherein angular rotation is detected from Coriolis coupling of elastic vibration energy from a driven vibration mode into a second degenerate sensing mode. While nonlinear elasticity in silicon resonators is extremely weak, in this high quality-factor device, ppm-level nonlinear elastic effects result in an order-of-magnitude increase in the observed sensitivity to Coriolis force relative to linear theory. Perfect degeneracy of the primary and secondary vibration modes is achieved through electrostatic frequency tuning, which also enables the phase and frequency of the parametric coupling to be varied, and we show that the resulting phase and frequency dependence of the amplification follow the theory of parametric resonance. We expect that this phenomenon will be useful for both fundamental studies of dynamic systems with low dissipation and for increasing signal-to-noise ratio in practical applications such as gyroscopes.

Non-linear elastic deformations

CERN Document Server

Ogden, R W

1997-01-01

Classic in the field covers application of theory of finite elasticity to solution of boundary-value problems, analysis of mechanical properties of solid materials capable of large elastic deformations. Problems. References.

Manipulating acoustic wave reflection by a nonlinear elastic metasurface

Science.gov (United States)

Guo, Xinxin; Gusev, Vitalyi E.; Bertoldi, Katia; Tournat, Vincent

2018-03-01

The acoustic wave reflection properties of a nonlinear elastic metasurface, derived from resonant nonlinear elastic elements, are theoretically and numerically studied. The metasurface is composed of a two degree-of-freedom mass-spring system with quadratic elastic nonlinearity. The possibility of converting, during the reflection process, most of the fundamental incoming wave energy into the second harmonic wave is shown, both theoretically and numerically, by means of a proper design of the nonlinear metasurface. The theoretical results from the harmonic balance method for a monochromatic source are compared with time domain simulations for a wave packet source. This protocol allows analyzing the dynamics of the nonlinear reflection process in the metasurface as well as exploring the limits of the operating frequency bandwidth. The reported methodology can be applied to a wide variety of nonlinear metasurfaces, thus possibly extending the family of exotic nonlinear reflection processes.

Resonant Column Tests and Nonlinear Elasticity in Simulated Rocks

Science.gov (United States)

Sebastian, Resmi; Sitharam, T. G.

2018-01-01

Rocks are generally regarded as linearly elastic even though the manifestations of nonlinearity are prominent. The variations of elastic constants with varying strain levels and stress conditions, disagreement between static and dynamic moduli, etc., are some of the examples of nonlinear elasticity in rocks. The grain-to-grain contact, presence of pores and joints along with other compliant features induce the nonlinear behavior in rocks. The nonlinear elastic behavior of rocks is demonstrated through resonant column tests and numerical simulations in this paper. Resonant column tests on intact and jointed gypsum samples across varying strain levels have been performed in laboratory and using numerical simulations. The paper shows the application of resonant column apparatus to obtain the wave velocities of stiff samples at various strain levels under long wavelength condition, after performing checks and incorporating corrections to the obtained resonant frequencies. The numerical simulation and validation of the resonant column tests using distinct element method are presented. The stiffness reductions of testing samples under torsional and flexural vibrations with increasing strain levels have been analyzed. The nonlinear elastic behavior of rocks is reflected in the results, which is enhanced by the presence of joints. The significance of joint orientation and influence of joint spacing during wave propagation have also been assessed and presented using the numerical simulations. It has been found that rock joints also exhibit nonlinear behavior within the elastic limit.

Nonlinear transverse vibrations of elastic beams under tension

International Nuclear Information System (INIS)

Ichikawa, Y.H.; Konno, Kimiaki; Wadati, Miki.

1980-02-01

Nonlinear transverse vibrations of elastic beams under end-thrust have been examined with full account of the rigorous nonlinear relation of curvature and deformation of elastic beams. When the beams are subject to tension, the derived equation is shown to be reduced to one of the new integrable evolution equations discovered by us. (author)

Large deflection analysis of laminated composite plates resting on nonlinear elastic foundations by the method of discrete singular convolution

International Nuclear Information System (INIS)

Baltacioglu, A.K.; Civalek, O.; Akgoez, B.; Demir, F.

2011-01-01

This paper presents nonlinear static analysis of a rectangular laminated composite thick plate resting on nonlinear two-parameter elastic foundation with cubic nonlinearity. The plate formulation is based on first-order shear deformation theory (FSDT). The governing equation of motion for a rectangular laminated composite thick plate is derived by using the von Karman equation. The nonlinear static deflections of laminated plates on elastic foundation are investigated using the discrete singular convolution method. The effects of foundation and geometric parameters of plates on nonlinear deflections are investigated. The validity of the present method is demonstrated by comparing the present results with those available in the literature. - Highlights: → Large deflection analysis of laminated composite plates are investigated. → As foundation, nonlinear elastic models have been used firstly. → The effects of three-parameter foundation are investigated in detail.

Morphoelasticity: A theory of elastic growth

KAUST Repository

Goriely, Alain; Moulton, Derek

2011-01-01

This chapter is concerned with the modelling of growth processes in the framework of continuum mechanics and nonlinear elasticity. It begins by considering growth and deformation in a one-dimensional setting, illustrating the key relationship between growth, the elastic response of the material, and the generation of residual stresses. The general three-dimensional theory of morphoelasticity is then developed from conservation of mass and momentum balance equations. In the formulation, the multiplicative decomposition of the deformation tensor, the standard approach in morphoelasticity, is derived in a new way. A discussion of continuous growth is also included. The chapter concludes by working through a sample problem of a growing cylindrical tube. A stability analysis is formulated, and the effect of growth on mucosal folding, a commonly seen instability in biological tubes, is demonstrated.

Morphoelasticity: A theory of elastic growth

KAUST Repository

Goriely, Alain

2011-10-11

This chapter is concerned with the modelling of growth processes in the framework of continuum mechanics and nonlinear elasticity. It begins by considering growth and deformation in a one-dimensional setting, illustrating the key relationship between growth, the elastic response of the material, and the generation of residual stresses. The general three-dimensional theory of morphoelasticity is then developed from conservation of mass and momentum balance equations. In the formulation, the multiplicative decomposition of the deformation tensor, the standard approach in morphoelasticity, is derived in a new way. A discussion of continuous growth is also included. The chapter concludes by working through a sample problem of a growing cylindrical tube. A stability analysis is formulated, and the effect of growth on mucosal folding, a commonly seen instability in biological tubes, is demonstrated.

Elasticity theory and applications

CERN Document Server

Saada, Adel S; Hartnett, James P; Hughes, William F

2013-01-01

Elasticity: Theory and Applications reviews the theory and applications of elasticity. The book is divided into three parts. The first part is concerned with the kinematics of continuous media; the second part focuses on the analysis of stress; and the third part considers the theory of elasticity and its applications to engineering problems. This book consists of 18 chapters; the first of which deals with the kinematics of continuous media. The basic definitions and the operations of matrix algebra are presented in the next chapter, followed by a discussion on the linear transformation of points. The study of finite and linear strains gradually introduces the reader to the tensor concept. Orthogonal curvilinear coordinates are examined in detail, along with the similarities between stress and strain. The chapters that follow cover torsion; the three-dimensional theory of linear elasticity and the requirements for the solution of elasticity problems; the method of potentials; and topics related to cylinders, ...

Nonlinear Subincremental Method for Determination of Elastic-Plastic-Creep Behaviour

DEFF Research Database (Denmark)

Ottosen, N. Saabye; Gunneskov, O.

1985-01-01

to general elastic-plastic-creep behaviour including problems with a highly nonlinear total strain path caused by the occurrence of creep hardening. This nonlinear method degenerates to the linear approach for elastic-plastic behaviour and when secondary creep is present. It is also linear during step......The frequently used subincremental method has so far been used on a linear interpolation of the total strain path within each main step. This method has proven successful when elastic-plastic behaviour and secondary creep is involved. The authors propose a nonlinear subincremental method applicable...

Mathematical theory of elastic and elasto-plastic bodies an introduction

CERN Document Server

Necas, J

2013-01-01

The book acquaints the reader with the basic concepts and relations of elasticity and plasticity, and also with the contemporary state of the theory, covering such aspects as the nonlinear models of elasto-plastic bodies and of large deflections of plates, unilateral boundary value problems, variational principles, the finite element method, and so on.

On Maximally Dissipative Shock Waves in Nonlinear Elasticity

OpenAIRE

Knowles, James K.

2010-01-01

Shock waves in nonlinearly elastic solids are, in general, dissipative. We study the following question: among all plane shock waves that can propagate with a given speed in a given one-dimensional nonlinearly elastic bar, which one—if any—maximizes the rate of dissipation? We find that the answer to this question depends strongly on the qualitative nature of the stress-strain relation characteristic of the given material. When maximally dissipative shocks do occur, they propagate according t...

Dynamic nonlinear interaction of elastic plates on discrete supports

International Nuclear Information System (INIS)

Coutinho, A.L.G.A.; Landau, L.; Lima, E.C.P. de; Ebecken, N.F.F.

1984-01-01

A study on the dynamic nonlinear interaction of elastic plates using the finite element method is presented. The elastic plate is discretized by 4-node isoparametric Mindlin elements. The constitutive relation of the discrete supports can be any nonlinear curve given by pairs of force-displacement points. The nonlinear behaviour is represented by the overlay approach. This model also allows the simulation of a progressive decrease on the supports stiffnesses during load cycles. The dynamic nonlinear incremental movement equations are integrated by the Newmark implicit operator. Two alternatives for the incremental-iterative formulation are compared. The paper ends with a discussion of the advantages and limitations of the presented numerical models. (Author) [pt

A New Theory of Non-Linear Thermo-Elastic Constitutive Equation of Isotropic Hyperelastic Materials

Science.gov (United States)

Li, Chen; Liao, Yufei

2018-03-01

Considering the influence of temperature and strain variables on materials. According to the relationship of conjugate stress-strain, a complete and irreducible non-linear constitutive equation of isotropic hyperelastic materials is derived and the constitutive equations of 16 types of isotropic hyperelastic materials are given we study the transformation methods and routes of 16 kinds of constitutive equations and the study proves that transformation of two forms of constitutive equation. As an example of application, the non-linear thermo-elastic constitutive equation of isotropic hyperelastic materials is combined with the natural vulcanized rubber experimental data in the existing literature base on MATLAB, The results show that the fitting accuracy is satisfactory.

Development of a nonlinear unsteady transonic flow theory

Science.gov (United States)

Stahara, S. S.; Spreiter, J. R.

1973-01-01

A nonlinear, unsteady, small-disturbance theory capable of predicting inviscid transonic flows about aerodynamic configurations undergoing both rigid body and elastic oscillations was developed. The theory is based on the concept of dividing the flow into steady and unsteady components and then solving, by method of local linearization, the coupled differential equation for unsteady surface pressure distribution. The equations, valid at all frequencies, were derived for two-dimensional flows, numerical results, were obtained for two classses of airfoils and two types of oscillatory motions.

A nonlinear approach of elastic reflection waveform inversion

KAUST Repository

Guo, Qiang

2016-09-06

Elastic full waveform inversion (EFWI) embodies the original intention of waveform inversion at its inception as it is a better representation of the mostly solid Earth. However, compared with the acoustic P-wave assumption, EFWI for P- and S-wave velocities using multi-component data admitted mixed results. Full waveform inversion (FWI) is a highly nonlinear problem and this nonlinearity only increases under the elastic assumption. Reflection waveform inversion (RWI) can mitigate the nonlinearity by relying on transmissions from reflections focused on inverting low wavenumber components of the model. In our elastic endeavor, we split the P- and S-wave velocities into low wavenumber and perturbation components and propose a nonlinear approach to invert for both of them. The new optimization problem is built on an objective function that depends on both background and perturbation models. We utilize an equivalent stress source based on the model perturbation to generate reflection instead of demigrating from an image, which is applied in conventional RWI. Application on a slice of an ocean-bottom data shows that our method can efficiently update the low wavenumber parts of the model, but more so, obtain perturbations that can be added to the low wavenumbers for a high resolution output.

A nonlinear approach of elastic reflection waveform inversion

KAUST Repository

Guo, Qiang; Alkhalifah, Tariq Ali

2016-01-01

Elastic full waveform inversion (EFWI) embodies the original intention of waveform inversion at its inception as it is a better representation of the mostly solid Earth. However, compared with the acoustic P-wave assumption, EFWI for P- and S-wave velocities using multi-component data admitted mixed results. Full waveform inversion (FWI) is a highly nonlinear problem and this nonlinearity only increases under the elastic assumption. Reflection waveform inversion (RWI) can mitigate the nonlinearity by relying on transmissions from reflections focused on inverting low wavenumber components of the model. In our elastic endeavor, we split the P- and S-wave velocities into low wavenumber and perturbation components and propose a nonlinear approach to invert for both of them. The new optimization problem is built on an objective function that depends on both background and perturbation models. We utilize an equivalent stress source based on the model perturbation to generate reflection instead of demigrating from an image, which is applied in conventional RWI. Application on a slice of an ocean-bottom data shows that our method can efficiently update the low wavenumber parts of the model, but more so, obtain perturbations that can be added to the low wavenumbers for a high resolution output.

Astronomical optics and elasticity theory

CERN Document Server

Lemaitre, Gerard Rene

2008-01-01

Astronomical Optics and Elasticity Theory provides a very thorough and comprehensive account of what is known in this field. After an extensive introduction to optics and elasticity, the book discusses variable curvature and multimode deformable mirrors, as well as, in depth, active optics, its theory and applications. Further, optical design utilizing the Schmidt concept and various types of Schmidt correctors, as well as the elasticity theory of thin plates and shells are elaborated upon. Several active optics methods are developed for obtaining aberration corrected diffraction gratings. Further, a weakly conical shell theory of elasticity is elaborated for the aspherization of grazing incidence telescope mirrors. The very didactic and fairly easy-to-read presentation of the topic will enable PhD students and young researchers to actively participate in challenging astronomical optics and instrumentation projects.

Nonlinear surface elastic modes in crystals

Science.gov (United States)

Gorentsveig, V. I.; Kivshar, Yu. S.; Kosevich, A. M.; Syrkin, E. S.

1990-03-01

The influence of nonlinearity on shear horizontal surface elastic waves in crystals is described on the basis of the effective nonlinear Schrödinger equation. It is shown that the corresponding solutions form a set of surface modes and the simplest mode coincides with the solution proposed by Mozhaev. The higher order modes have internal frequencies caused by the nonlinearity. All these modes decay in the crystal as uoexp(- z/ zo) atz≫ zo- u o-1 ( z is the distance from the crystal surface, uo the wave amplitude at the surface). The creation of the modes from a localized surface excitation has a threshold. The stability of the modes is discussed.

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.

On the geometrically nonlinear elastic response of class θ = 1 tensegrity prisms

Science.gov (United States)

Mascolo, Ida; Amendola, Ada; Zuccaro, Giulio; Feo, Luciano; Fraternali, Fernando

2018-03-01

The present work studies the geometrically nonlinear response of class ϑ=1 tensegrity prisms modeled as a collection of elastic springs reacting in tension (strings or cables) or compression (bars), under uniform uniaxial loading. The incremental equilibrium equations of the structure are numerically solved through a path-following procedure, with the aim of modeling the mechanical behavior of the structure in the large displacement regime. Several numerical results are presented with reference to a variety of physical models, which use two different materials for the cables and the bars, and show different aspect ratios associated with either 'standard' or 'expanded' configurations. An experimental validation of the predicted constitutive response is conducted with reference to a 'thick' and a 'slender' model, observing rather good theory vs. experiment matching. The given numerical and experimental results highlight that the elastic response of the examined structures may switch from stiffening to softening, depending on the geometry of the system, the magnitude of the external load, and the applied prestress. The outcomes of the current study confirm previous literature results on the elastic response of minimal tensegrity prisms, and pave the way to the use of tensegrity systems as nonlinear spring units forming tunable mechanical metamaterials.

Elasticity theory of ultrathin nanofilms

International Nuclear Information System (INIS)

Li, Jiangang; Yun, Guohong; Narsu, B; Yao, Haiyan

2015-01-01

A self-consistent theoretical scheme for describing the elastic behavior of ultrathin nanofilms (UTNFs) was proposed. Taking into account the lower symmetry of an UTNF compared to its bulk counterpart, additional elastic and magnetoelastic parameters were introduced to model the elasticity rigorously. The applications of current theory to several elastic and magnetoelastic systems gave excellent agreement with experiments. More importantly, the surface elastic and magnetoelastic parameters used to fit the experimental results are physically reasonable and in close agreement with those obtained from experiment and simulation. This fact suggests that the additional elastic (magnetoelastic) constants due to symmetry breaking are of great importance in theoretical description of the mechanical properties of UTNFs. And we proved that the elasticity of UTNFs should be described by a three-dimensional model just including the intrinsic surface and bulk parameters, but not the effective surface parameters. It is believed that the theory reported here is a universal strategy for elasticity and magnetoelasticity of ultrathin films. (paper)

NONLINEAR SPECTRAL IMAGING OF ELASTIC CARTILAGE IN RABBIT EARS

Directory of Open Access Journals (Sweden)

JING CHEN

2013-07-01

Full Text Available Elastic cartilage in the rabbit external ear is an important animal model with attractive potential value for researching the physiological and pathological states of cartilages especially during wound healing. In this work, nonlinear optical microscopy based on two-photon excited fluorescence and second harmonic generation were employed for imaging and quantifying the intact elastic cartilage. The morphology and distribution of main components in elastic cartilage including cartilage cells, collagen and elastic fibers were clearly observed from the high-resolution two-dimensional nonlinear optical images. The areas of cell nuclei, a parameter related to the pathological changes of normal or abnormal elastic cartilage, can be easily quantified. Moreover, the three-dimensional structure of chondrocytes and matrix were displayed by constructing three-dimensional image of cartilage tissue. At last, the emission spectra from cartilage were obtained and analyzed. We found that the different ratio of collagen over elastic fibers can be used to locate the observed position in the elastic cartilage. The redox ratio based on the ratio of nicotinamide adenine dinucleotide (NADH over flavin adenine dinucleotide (FAD fluorescence can also be calculated to analyze the metabolic state of chondrocytes in different regions. Our results demonstrated that this technique has the potential to provide more accurate and comprehensive information for the physiological states of elastic cartilage.

An Enhanced Asymptotic Expansion for the Stability of Nonlinear Elastic Structures

DEFF Research Database (Denmark)

Christensen, Claus Dencker; Byskov, Esben

2010-01-01

A new, enhanced asymptotic expansion applicable to stability of structures made of nonlinear elastic materials is established. The method utilizes “hyperbolic” terms instead of the conventional polynomial terms, covers full kinematic nonlinearity and is applied to nonlinear elastic Euler columns...... with two different types of cross-section. Comparison with numerical results show that our expansion provides more accurate predictions of the behavior than usual expansions. The method is based on an extended version of the principle of virtual displacements that covers cases with auxiliary conditions...

Nonlinear to Linear Elastic Code Coupling in 2-D Axisymmetric Media.

Energy Technology Data Exchange (ETDEWEB)

Preston, Leiph [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2017-08-01

Explosions within the earth nonlinearly deform the local media, but at typical seismological observation distances, the seismic waves can be considered linear. Although nonlinear algorithms can simulate explosions in the very near field well, these codes are computationally expensive and inaccurate at propagating these signals to great distances. A linearized wave propagation code, coupled to a nonlinear code, provides an efficient mechanism to both accurately simulate the explosion itself and to propagate these signals to distant receivers. To this end we have coupled Sandia's nonlinear simulation algorithm CTH to a linearized elastic wave propagation code for 2-D axisymmetric media (axiElasti) by passing information from the nonlinear to the linear code via time-varying boundary conditions. In this report, we first develop the 2-D axisymmetric elastic wave equations in cylindrical coordinates. Next we show how we design the time-varying boundary conditions passing information from CTH to axiElasti, and finally we demonstrate the coupling code via a simple study of the elastic radius.

Nonlinear elastic properties of superconducting antiperovskites MNNi 3 (M =Zn, Cd, Mg, Al, Ga, and In) from first principles

KAUST Repository

Liu, Lili; Wu, Xiaozhi; Wang, Rui; Gan, Liyong; Wei, Qunyi

2014-01-01

We present theoretical studies for the third-order elastic constants (TOECs) of superconducting antiperovskites MNNi 3 (M = Zn, Cd, Mg, Al, Ga, and In) using the density functional theory (DFT) and homogeneous deformation method. From the nonlinear least-square fitting, the elastic constants are extracted from a polynomial fit to the calculated strain-energy data. Calculated second-order elastic constants (SOECs) are compared with the previous theoretical calculations, and a very good agreement was found. The nonlinear effects often play an important role when the finite strains are larger than approximately 2.5 %. Besides, we have computed the pressure derivatives of SOECs and provided rough estimations for the Grüneisen constants of long-wavelength acoustic modes by using the calculated TOECs. © 2014 Springer Science+Business Media New York.

Nonlinear elastic properties of superconducting antiperovskites MNNi 3 (M =Zn, Cd, Mg, Al, Ga, and In) from first principles

KAUST Repository

Liu, Lili

2014-05-22

We present theoretical studies for the third-order elastic constants (TOECs) of superconducting antiperovskites MNNi 3 (M = Zn, Cd, Mg, Al, Ga, and In) using the density functional theory (DFT) and homogeneous deformation method. From the nonlinear least-square fitting, the elastic constants are extracted from a polynomial fit to the calculated strain-energy data. Calculated second-order elastic constants (SOECs) are compared with the previous theoretical calculations, and a very good agreement was found. The nonlinear effects often play an important role when the finite strains are larger than approximately 2.5 %. Besides, we have computed the pressure derivatives of SOECs and provided rough estimations for the Grüneisen constants of long-wavelength acoustic modes by using the calculated TOECs. © 2014 Springer Science+Business Media New York.

DYNAMICS OF VIBRATION FEEDERS WITH A NONLINEAR ELASTIC CHARACTERISTIC

Directory of Open Access Journals (Sweden)

V. I. Dyrda

2017-04-01

Full Text Available Purpose. Subject to the smooth and efficient operation of each production line, is the use of vehicles transporting high specification. It worked well in practice for transporting construction machines, which are used during the vibration. The use of vibration machines requires optimization of their operation modes. In the form of elastic link in them are increasingly using rubber-metallic elements, which are characterized by nonlinear damping properties. So it is necessary to search for new, more modern, methods of calculation of dynamic characteristics of the vibration machines on the properties of rubber as a cushioning material. Methodology. The dynamics of vibration machine that is as elastic rubber block units and buffer shock absorbers limiting the amplitude of the vibrations of the working body. The method of determining amplitude-frequency characteristics of the vibrating feeder is based on the principle of Voltaire, who in the calculations of the damping properties of the dampers will allow for elastic-hereditary properties of rubber. When adjusting the basic dynamic stiffness of the elastic ties and vibratory buffers, using the principle of heredity rubber properties, determine the dependence of the amplitude of the working body of the machine vibrations. This method is called integro-operator using the fractional-exponential kernels of relaxation. Findings. Using the derived formula for determining the amplitude of the resonance curve is constructed one-mass nonlinear system. It is established that the use of the proposed method of calculation will provide a sufficiently complete description of the damping parameters of rubber-metallic elements and at the same time be an effective means of calculating the amplitude-frequency characteristics of nonlinear vibration systems. Originality. The authors improved method of determining damping characteristics of rubber-metallic elements and the amplitude-frequency characteristics of nonlinear

Wave propagation in elastic medium with heterogeneous quadratic nonlinearity

International Nuclear Information System (INIS)

Tang Guangxin; Jacobs, Laurence J.; Qu Jianmin

2011-01-01

This paper studies the one-dimensional wave propagation in an elastic medium with spatially non-uniform quadratic nonlinearity. Two problems are solved analytically. One is for a time-harmonic wave propagating in a half-space where the displacement is prescribed on the surface of the half-space. It is found that spatial non-uniformity of the material nonlinearity causes backscattering of the second order harmonic, which when combined with the forward propagating waves generates a standing wave in steady-state wave motion. The second problem solved is the reflection from and transmission through a layer of finite thickness embedded in an otherwise linearly elastic medium of infinite extent, where it is assumed that the layer has a spatially non-uniform quadratic nonlinearity. The results show that the transmission coefficient for the second order harmonic is proportional to the spatial average of the nonlinearity across the thickness of the layer, independent of the spatial distribution of the nonlinearity. On the other hand, the coefficient of reflection is proportional to a weighted average of the nonlinearity across the layer thickness. The weight function in this weighted average is related to the propagating phase, thus making the coefficient of reflection dependent on the spatial distribution of the nonlinearity. Finally, the paper concludes with some discussions on how to use the reflected and transmitted second harmonic waves to evaluate the variance and autocorrelation length of nonlinear parameter β when the nonlinearity distribution in the layer is a stochastic process.

Composite Beam Theory with Material Nonlinearities and Progressive Damage

Science.gov (United States)

Jiang, Fang

Beam has historically found its broad applications. Nowadays, many engineering constructions still rely on this type of structure which could be made of anisotropic and heterogeneous materials. These applications motivate the development of beam theory in which the impact of material nonlinearities and damage on the global constitutive behavior has been a focus in recent years. Reliable predictions of these nonlinear beam responses depend on not only the quality of the material description but also a comprehensively generalized multiscale methodology which fills the theoretical gaps between the scales in an efficient yet high-fidelity manner. The conventional beam modeling methodologies which are built upon ad hoc assumptions are in lack of such reliability in need. Therefore, the focus of this dissertation is to create a reliable yet efficient method and the corresponding tool for composite beam modeling. A nonlinear beam theory is developed based on the Mechanics of Structure Genome (MSG) using the variational asymptotic method (VAM). The three-dimensional (3D) nonlinear continuum problem is rigorously reduced to a one-dimensional (1D) beam model and a two-dimensional (2D) cross-sectional analysis featuring both geometric and material nonlinearities by exploiting the small geometric parameter which is an inherent geometric characteristic of the beam. The 2D nonlinear cross-sectional analysis utilizes the 3D material models to homogenize the beam cross-sectional constitutive responses considering the nonlinear elasticity and progressive damage. The results from such a homogenization are inputs as constitutive laws into the global nonlinear 1D beam analysis. The theoretical foundation is formulated without unnecessary kinematic assumptions. Curvilinear coordinates and vector calculus are utilized to build the 3D deformation gradient tensor, of which the components are formulated in terms of cross-sectional coordinates, generalized beam strains, unknown warping

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

Elastic Nonlinear Response in Granular Media Under Resonance Conditions

Science.gov (United States)

Jia, X.; Johnson, P. A.

2004-12-01

We are studying the elastic linear and nonlinear behavior of granular media using dynamic wave methods. In the work presented here, our goal is to quantify the elastic nonlinear response by applying wave resonance. Resonance studies are desirable because they provide the means to easily study amplitude dependencies of elastic nonlinear behavior and thus to characterize the physical nature of the elastic nonlinearity. This work has implications for a variety of topics, in particular, the in situ nonlinear response of surface sediments. For this work we constructed an experimental cell in which high sensitivity dynamic resonance studies were conducted using granular media under controlled effective pressure. We limit our studies here to bulk modes but have the capability to employ shear waves as well. The granular media are composed of glass beads held under pressure by a piston, while applying resonance waves from transducers as both the excitation and the material probe. The container is closed with two fitted pistons and a normal load is applied to the granular sample across the top piston. Force and displacement are measured directly. Resonant frequency sweeps with frequencies corresponding to the fundamental bulk mode are applied to the longitudinal source transducer. The pore pressure in the system is 1 atm. The glass beads used in our experiments are of diameter 0.5 mm, randomly deposited in a duralumin cylinder of diameter 30 mm and height of 15 mm. This corresponds to a granular skeleton acoustic wave velocity of v ª 750m/s under 50 N of force [0.07 Mpa]. The loaded system gives fundamental mode resonances in the audio frequency band at half a wavelength where resonance frequency is effective-pressure dependent. The volume fraction of glass beads thus obtained is found to be 0.63 ± 0.01. Plane-wave generating and detecting transducers of diameter 30 mm are placed on axis at the top and bottom of the cylindrical container in direct contact with the glass

Nucleon-nucleon scattering in the functional quantum theory of the nonlinear spinor field

International Nuclear Information System (INIS)

Haegele, G.

1979-01-01

The author calculates the S matrix for the elastic nucleon-nucleon scattering in the lowest approximation using the quantum theory of nonlinear spinor fields with special emphasis to the ghost configuration of this theory. Introducing a general scalar product a new functional channel calculus is considered. From the results the R and T matrix elements and the differential and integral cross sections are derived. (HSI)

Power laws and elastic nonlinearity in materials with complex microstructure

Energy Technology Data Exchange (ETDEWEB)

Scalerandi, M., E-mail: marco.scalerandi@infm.polito.it

2016-01-28

Nonlinear ultrasonic methods have been widely used to characterize the microstructure of damaged solids and consolidated granular media. Besides distinguishing between materials exhibiting classical nonlinear behaviors from those exhibiting hysteresis, it could be of importance the discrimination between ultrasonic indications from different physical sources (scatterers). Elastic hysteresis could indeed be due to dislocations, grain boundaries, stick-slip at interfaces, etc. Analyzing data obtained on various concrete samples, we show that the power law behavior of the nonlinear indicator vs. the energy of excitation could be used to classify different microscopic features. In particular, the power law exponent ranges between 1 and 3, depending on the nature of nonlinearity. We also provide a theoretical interpretation of the collected data using models for clapping and hysteretic nonlinearities. - Highlights: • Several materials exhibit a nontrivial nonlinear elastic behavior which can be ascribed to different physical sources. • The quantitative nonlinear response is dependent on the type of microstructure present in the material. • A nonlinear indicator could be defined which depends on the excitation energy of the sample. • Assuming a power law dependence, the exponent depends on the microstructure of the material and could evolve in time. • Experimental results on concrete are discussed and a theoretical description is proposed.

A general one-dimension nonlinear magneto-elastic coupled constitutive model for magnetostrictive materials

International Nuclear Information System (INIS)

Zhang, Da-Guang; Li, Meng-Han; Zhou, Hao-Miao

2015-01-01

For magnetostrictive rods under combined axial pre-stress and magnetic field, a general one-dimension nonlinear magneto-elastic coupled constitutive model was built in this paper. First, the elastic Gibbs free energy was expanded into polynomial, and the relationship between stress and strain and the relationship between magnetization and magnetic field with the polynomial form were obtained with the help of thermodynamic relations. Then according to microscopic magneto-elastic coupling mechanism and some physical facts of magnetostrictive materials, a nonlinear magneto-elastic constitutive with concise form was obtained when the relations of nonlinear strain and magnetization in the polynomial constitutive were instead with transcendental functions. The comparisons between the prediction and the experimental data of different magnetostrictive materials, such as Terfenol-D, Metglas and Ni showed that the predicted magnetostrictive strain and magnetization curves were consistent with experimental results under different pre-stresses whether in the region of low and moderate field or high field. Moreover, the model can fully reflect the nonlinear magneto-mechanical coupling characteristics between magnetic, magnetostriction and elasticity, and it can effectively predict the changes of material parameters with pre-stress and bias field, which is useful in practical applications

On the Geometrically Nonlinear Elastic Response of Class θ = 1 Tensegrity Prisms

Directory of Open Access Journals (Sweden)

Ida Mascolo

2018-03-01

Full Text Available The present work studies the geometrically nonlinear response of class θ = 1 tensegrity prisms modeled as a collection of elastic springs reacting in tension (strings or cables or compression (bars, under uniform uniaxial loading. The incremental equilibrium equations of the structure are numerically solved through a path-following procedure, with the aim of modeling the mechanical behavior of the structure in the large displacement regime. Several numerical results are presented with reference to a variety of physical models, which use two different materials for the cables and the bars, and show different aspect ratios associated with either “standard” or “expanded” configurations. An experimental validation of the predicted constitutive response is conducted with reference to a “thick” and a “slender” model, observing rather good theory vs. experiment matching. The given numerical and experimental results highlight that the elastic response of the examined structures may switch from stiffening to softening, depending on the geometry of the system, the magnitude of the external load, and the applied prestress. The outcomes of the current study confirm previous literature results on the elastic response of minimal tensegrity prisms, and pave the way to the use of tensegrity systems as nonlinear spring units forming tunable mechanical metamaterials.

Hamilton-Ostrogradsky principle in the theory of nonlinear elasticity with the combined approach

International Nuclear Information System (INIS)

Sporykhin, A.N.

1995-01-01

The assignment of a portion of the edge conditions in the deformed state and a portion of them in the initial state so that the initial and deformed states of the body are unknowns is a characteristic feature of the statement of a number of technological problems. Haber and Haber and Abel have performed studies in this direction, where constitutive relationships have been constructed within the framework of a linearly elastic material. Use of the displacements of individual particles as variable parameters in these relationships has required additional conditions that do not follow from the formulated problem. Use of familiar variational principles described in Euler coordinates is rendered difficult by the complexity of edge-condition formulation in the special case when the initial state is unknown. The latter is governed by the fact that variational principles are derived from the initial formulations open-quotes in Lagrangian coordinates,close quotes by recalculating the operation functional. Using Lagrange's principle, Novikov and Sporykhin constructed constitutive equations in the general case of a nonlinearly elastic body with edge conditions assigned in different configurations. An analogous problem is solved in this paper using the Hamilton-Ostrogradsky principle

Non-linear elastic thermal stress analysis with phase changes

International Nuclear Information System (INIS)

Amada, S.; Yang, W.H.

1978-01-01

The non-linear elastic, thermal stress analysis with temperature induced phase changes in the materials is presented. An infinite plate (or body) with a circular hole (or tunnel) is subjected to a thermal loading on its inner surface. The peak temperature around the hole reaches beyond the melting point of the material. The non-linear diffusion equation is solved numerically using the finite difference method. The material properties change rapidly at temperatures where the change of crystal structures and solid-liquid transition occur. The elastic stresses induced by the transient non-homogeneous temperature distribution are calculated. The stresses change remarkably when the phase changes occur and there are residual stresses remaining in the plate after one cycle of thermal loading. (Auth.)

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

Solitary waves on nonlinear elastic rods. II

DEFF Research Database (Denmark)

Sørensen, Mads Peter; Christiansen, Peter Leth; Lomdahl, P. S.

1987-01-01

In continuation of an earlier study of propagation of solitary waves on nonlinear elastic rods, numerical investigations of blowup, reflection, and fission at continuous and discontinuous variation of the cross section for the rod and reflection at the end of the rod are presented. The results ar...... are compared with predictions of conservation theorems for energy and momentum....

Nonlinear Dispersive Elastic Waves in Solids: Exact, Approximate, and Numerical Solutions

Science.gov (United States)

Khajehtourian, Romik

Wave motion lies at the heart of many disciplines in the physical sciences and engineering. For example, problems and applications involving light, sound, heat, or fluid flow are all likely to involve wave dynamics at some level. A particular class of problems is concerned with the propagation of elastic waves in a solid medium, such as a fiber-reinforced composite material responding to vibratory excitations, or soil and rock admitting seismic waves moments after the onset of an earthquake, or phonon transport in a semiconducting crystal like silicon. Regardless of the type of wave, the dispersion relation provides a fundamental characterization of the elastodynamic properties of the medium. The first part of the dissertation examines the propagation of a large-amplitude elastic wave in a one-dimensional homogeneous medium with a focus on the effects of inherent nonlinearities on the dispersion relation. Considering a thin rod, where the thickness is small compared to the wavelength, an exact, closed-form formulation is presented for the treatment of two types of nonlinearity in the strain-displacement gradient relation: Green-Lagrange and Hencky. The derived relation is then verified by direct time-domain simulations, examining both instantaneous dispersion (by direct observation) and short-term, pre-breaking dispersion (by Fourier transformation). A high-order perturbation analysis is also conducted yielding an explicit analytical space-time solution, which is shown to be spectrally accurate. The results establish a perfect match between theory and simulation and reveal that regardless of the strength of the nonlinearity, the dispersion relation fully embodies all information pertaining to the nonlinear harmonic generation mechanism that unfolds as an arbitrary-profiled wave evolves in the medium. In the second part of the dissertation, the analysis is extended to a continuous periodic thin rod exhibiting multiple phases or embedded local resonators. The

Bulk nonlinear elastic strain waves in a bar with nanosize inclusions

DEFF Research Database (Denmark)

Gula, Igor A.; Samsonov (†), Alexander M.

2018-01-01

We propose a mathematical model for propagation of the long nonlinearly elastic longitudinal strain waves in a bar, which contains nanoscale structural inclusions. The model is governed by a nonlinear doubly dispersive equation (DDE) with respect to the one unknown longitudinal strain function. We...

A new type of surface acoustic waves in solids due to nonlinear elasticity

International Nuclear Information System (INIS)

Mozhaev, V.G.

1988-12-01

It is shown that in nonlinear elastic semi-infinite medium possessing a property of self focusing of shear waves, besides bulk non-linear shear waves, new surface acoustic waves exist, localization of which near the boundary is entirely due to nonlinear effects. (author). 8 refs

Nonlinear constitutive relations for anisotropic elastic materials

Science.gov (United States)

Sokolova, Marina; Khristich, Dmitrii

2018-03-01

A general approach to constructing of nonlinear variants of connection between stresses and strains in anisotropic materials with different types of symmetry of properties is considered. This approach is based on the concept of elastic proper subspaces of anisotropic materials introduced in the mechanics of solids by J. Rychlewski and on the particular postulate of isotropy proposed by A. A. Il’yushin. The generalization of the particular postulate on the case of nonlinear anisotropic materials is formulated. Systems of invariants of deformations as lengths of projections of the strain vector into proper subspaces are developed. Some variants of nonlinear constitutive relations for anisotropic materials are offered. The analysis of these relations from the point of view of their satisfaction to general and limit forms of generalization of partial isotropy postulate on anisotropic materials is performed. The relations for particular cases of anisotropy are written.

Special discontinuities in nonlinearly elastic media

Science.gov (United States)

Chugainova, A. P.

2017-06-01

Solutions of a nonlinear hyperbolic system of equations describing weakly nonlinear quasitransverse waves in a weakly anisotropic elastic medium are studied. The influence of small-scale processes of dissipation and dispersion is investigated. The small-scale processes determine the structure of discontinuities (shocks) and a set of discontinuities with a stationary structure. Among the discontinuities with a stationary structure, there are special ones that, in addition to relations following from conservation laws, satisfy additional relations required for the existence of their structure. In the phase plane, the structure of such discontinuities is represented by an integral curve joining two saddles. Special discontinuities lead to nonunique self-similar solutions of the Riemann problem. Asymptotics of non-self-similar problems for equations with dissipation and dispersion are found numerically. These asymptotics correspond to self-similar solutions of the problems.

Rayleigh scattering and nonlinear inversion of elastic waves

Energy Technology Data Exchange (ETDEWEB)

Gritto, Roland [Univ. of California, Berkeley, CA (United States)

1995-12-01

Rayleigh scattering of elastic waves by an inclusion is investigated and the limitations determined. In the near field of the inhomogeneity, the scattered waves are up to a factor of 300 stronger than in the far field, excluding the application of the far field Rayleigh approximation for this range. The investigation of the relative error as a function of parameter perturbation shows a range of applicability broader than previously assumed, with errors of 37% and 17% for perturbations of -100% and +100%, respectively. The validity range for the Rayleigh limit is controlled by large inequalities, and therefore, the exact limit is determined as a function of various parameter configurations, resulting in surprisingly high values of up to k_pR = 0.9. The nonlinear scattering problem can be solved by inverting for equivalent source terms (moments) of the scatterer, before the elastic parameters are determined. The nonlinear dependence between the moments and the elastic parameters reveals a strong asymmetry around the origin, which will produce different results for weak scattering approximations depending on the sign of the anomaly. Numerical modeling of cross hole situations shows that near field terms are important to yield correct estimates of the inhomogeneities in the vicinity of the receivers, while a few well positioned sources and receivers considerably increase the angular coverage, and thus the model resolution of the inversion parameters. The pattern of scattered energy by an inhomogeneity is complicated and varies depending on the object, the wavelength of the incident wave, and the elastic parameters involved. Therefore, it is necessary to investigate the direction of scattered amplitudes to determine the best survey geometry.

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

Modeling fracture in the context of a strain-limiting theory of elasticity: a single anti-plane shear crack

KAUST Repository

Rajagopal, K. R.

2011-01-06

This paper is the first part of an extended program to develop a theory of fracture in the context of strain-limiting theories of elasticity. This program exploits a novel approach to modeling the mechanical response of elastic, that is non-dissipative, materials through implicit constitutive relations. The particular class of models studied here can also be viewed as arising from an explicit theory in which the displacement gradient is specified to be a nonlinear function of stress. This modeling construct generalizes the classical Cauchy and Green theories of elasticity which are included as special cases. It was conjectured that special forms of these implicit theories that limit strains to physically realistic maximum levels even for arbitrarily large stresses would be ideal for modeling fracture by offering a modeling paradigm that avoids the crack-tip strain singularities characteristic of classical fracture theories. The simplest fracture setting in which to explore this conjecture is anti-plane shear. It is demonstrated herein that for a specific choice of strain-limiting elasticity theory, crack-tip strains do indeed remain bounded. Moreover, the theory predicts a bounded stress field in the neighborhood of a crack-tip and a cusp-shaped opening displacement. The results confirm the conjecture that use of a strain limiting explicit theory in which the displacement gradient is given as a function of stress for modeling the bulk constitutive behavior obviates the necessity of introducing ad hoc modeling constructs such as crack-tip cohesive or process zones in order to correct the unphysical stress and strain singularities predicted by classical linear elastic fracture mechanics. © 2011 Springer Science+Business Media B.V.

A non-linear elastic constitutive framework for replicating plastic deformation in solids.

Energy Technology Data Exchange (ETDEWEB)

Roberts, Scott Alan; Schunk, Peter Randall

2014-02-01

Ductile metals and other materials typically deform plastically under large applied loads; a behavior most often modeled using plastic deformation constitutive models. However, it is possible to capture some of the key behaviors of plastic deformation using only the framework for nonlinear elastic mechanics. In this paper, we develop a phenomenological, hysteretic, nonlinear elastic constitutive model that captures many of the features expected of a plastic deformation model. This model is based on calculating a secant modulus directly from a materials stress-strain curve. Scalar stress and strain values are obtained in three dimensions by using the von Mises invariants. Hysteresis is incorporated by tracking an additional history variable and assuming an elastic unloading response. This model is demonstrated in both single- and multi-element simulations under varying strain conditions.

Ultrasound Shear Wave Simulation of Breast Tumor Using Nonlinear Tissue Elasticity

Directory of Open Access Journals (Sweden)

Dae Woo Park

2016-01-01

Full Text Available Shear wave elasticity imaging (SWEI can assess the elasticity of tissues, but the shear modulus estimated in SWEI is often less sensitive to a subtle change of the stiffness that produces only small mechanical contrast to the background tissues. Because most soft tissues exhibit mechanical nonlinearity that differs in tissue types, mechanical contrast can be enhanced if the tissues are compressed. In this study, a finite element- (FE- based simulation was performed for a breast tissue model, which consists of a circular (D: 10 mm, hard tumor and surrounding tissue (soft. The SWEI was performed with 0% to 30% compression of the breast tissue model. The shear modulus of the tumor exhibited noticeably high nonlinearity compared to soft background tissue above 10% overall applied compression. As a result, the elastic modulus contrast of the tumor to the surrounding tissue was increased from 0.46 at 0% compression to 1.45 at 30% compression.

Ultrasound Shear Wave Simulation of Breast Tumor Using Nonlinear Tissue Elasticity.

Science.gov (United States)

Park, Dae Woo

2015-01-01

Shear wave elasticity imaging (SWEI) can assess the elasticity of tissues, but the shear modulus estimated in SWEI is often less sensitive to a subtle change of the stiffness that produces only small mechanical contrast to the background tissues. Because most soft tissues exhibit mechanical nonlinearity that differs in tissue types, mechanical contrast can be enhanced if the tissues are compressed. In this study, a finite element- (FE-) based simulation was performed for a breast tissue model, which consists of a circular (D: 10 mm, hard) tumor and surrounding tissue (soft). The SWEI was performed with 0% to 30% compression of the breast tissue model. The shear modulus of the tumor exhibited noticeably high nonlinearity compared to soft background tissue above 10% overall applied compression. As a result, the elastic modulus contrast of the tumor to the surrounding tissue was increased from 0.46 at 0% compression to 1.45 at 30% compression.

Nonlinear modulation of torsional waves in elastic rod. [Instability

Energy Technology Data Exchange (ETDEWEB)

Hirao, M; Sugimoto, N [Osaka Univ., Toyonaka (Japan). Faculty of Engineering Science

1977-06-01

Nonlinear Schroedinger equation, which describes the nonlinear modulation of dispersive torsional waves in an elastic rod of circular cross-section, is derived by the derivative expansion method. It is found, for the lowest dispersive mode, that the modulational instability occurs except in the range of the carrier wavenumber, 2.799nonlinear Schroedinger equation is no longer valid. In this case, another system of equations is derived, which governs both the wave amplitudes involved in this resonance between the fundamental torsional and its second-harmonic longitudinal modes.

Phononic Crystal Waveguide Transducers for Nonlinear Elastic Wave Sensing.

Science.gov (United States)

Ciampa, Francesco; Mankar, Akash; Marini, Andrea

2017-11-07

Second harmonic generation is one of the most sensitive and reliable nonlinear elastic signatures for micro-damage assessment. However, its detection requires powerful amplification systems generating fictitious harmonics that are difficult to discern from pure nonlinear elastic effects. Current state-of-the-art nonlinear ultrasonic methods still involve impractical solutions such as cumbersome signal calibration processes and substantial modifications of the test component in order to create material-based tunable harmonic filters. Here we propose and demonstrate a valid and sensible alternative strategy involving the development of an ultrasonic phononic crystal waveguide transducer that exhibits both single and multiple frequency stop-bands filtering out fictitious second harmonic frequencies. Remarkably, such a sensing device can be easily fabricated and integrated on the surface of the test structure without altering its mechanical and geometrical properties. The design of the phononic crystal structure is supported by a perturbative theoretical model predicting the frequency band-gaps of periodic plates with sinusoidal corrugation. We find our theoretical findings in excellent agreement with experimental testing revealing that the proposed phononic crystal waveguide transducer successfully attenuates second harmonics caused by the ultrasonic equipment, thus demonstrating its wide range of potential applications for acousto/ultrasonic material damage inspection.

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.

Nonlinear problems of the theory of heterogeneous slightly curved shells

Science.gov (United States)

Kantor, B. Y.

1973-01-01

An account if given of the variational method of the solution of physically and geometrically nonlinear problems of the theory of heterogeneous slightly curved shells. Examined are the bending and supercritical behavior of plates and conical and spherical cupolas of variable thickness in a temperature field, taking into account the dependence of the elastic parameters on temperature. The bending, stability in general and load-bearing capacity of flexible isotropic elastic-plastic shells with different criteria of plasticity, taking into account compressibility and hardening. The effect of the plastic heterogeneity caused by heat treatment, surface work hardening and irradiation by fast neutron flux is investigated. Some problems of the dynamic behavior of flexible shells are solved. Calculations are performed in high approximations. Considerable attention is given to the construction of a machine algorithm and to the checking of the convergence of iterative processes.

Introduction to nonlinear finite element analysis

CERN Document Server

Kim, Nam-Ho

2015-01-01

This book introduces the key concepts of nonlinear finite element analysis procedures. The book explains the fundamental theories of the field and provides instructions on how to apply the concepts to solving practical engineering problems. Instead of covering many nonlinear problems, the book focuses on three representative problems: nonlinear elasticity, elastoplasticity, and contact problems. The book is written independent of any particular software, but tutorials and examples using four commercial programs are included as appendices: ANSYS, NASTRAN, ABAQUS, and MATLAB. In particular, the MATLAB program includes all source codes so that students can develop their own material models, or different algorithms. This book also: ·         Presents clear explanations of nonlinear finite element analysis for elasticity, elastoplasticity, and contact problems ·         Includes many informative examples of nonlinear analyses so that students can clearly understand the nonlinear theory ·    ...

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

A REMARK ON FORMAL MODELS FOR NONLINEARLY ELASTIC MEMBRANE SHELLS

Institute of Scientific and Technical Information of China (English)

无

2001-01-01

This paper gives all the two-dimensional membrane models obtained from formal asymptotic analysis of the three-dimensional geometrically exact nonlinear model of a thin elastic shell made with a Saint Venant-Kirchhoff material. Therefore, the other models can be quoted as flexural nonlinear ones. The author also gives the formal equations solved by the associated stress tensor and points out that only one of those models leads, by linearization, to the “classical” linear limiting membrane model, whose juetification has already been established by a convergence theorem.

An introduction to the theory of elasticity

CERN Document Server

Atkin, R J

2005-01-01

Thanks to intense research activity in the field of continuum mechanics, the teaching of subjects such as elasticity theory has attained a high degree of clarity and simplicity. This introductory volume offers upper-level undergraduates a perspective based on modern developments that also takes into account the limited mathematical tools they are likely to have at their disposal. It also places special emphasis on areas that students often find difficult upon first encounter. An Introduction to the Theory of Elasticity provides an accessible guide to the subject in a form that will instill a f

The elastic theory of a single DNA molecule

Indian Academy of Sciences (India)

methods and Monte Carlo simulations to understand the entropic elasticity, ... DNA; elastic theory; stacking interaction; supercoiling; hairpin-coil transition. .... the probability distribution of t and ϕ along the DNA chain [14,15], is governed by.

On the dynamic buckling of a weakly damped nonlinear elastic ...

African Journals Online (AJOL)

In this paper we determine the dynamic buckling load of a strictly nonlinear but weakly damped elastic oscillatory model structure subjected to small perturbations The loading history is explicitly time dependent and varies slowly with time over a natural period of oscillation of the structure. A multiple timing regular ...

Free-vibration acoustic resonance of a nonlinear elastic bar

Science.gov (United States)

Tarumi, Ryuichi; Oshita, Yoshihito

2011-02-01

Free-vibration acoustic resonance of a one-dimensional nonlinear elastic bar was investigated by direct analysis in the calculus of variations. The Lagrangian density of the bar includes a cubic term of the deformation gradient, which is responsible for both geometric and constitutive nonlinearities. By expanding the deformation function into a complex Fourier series, we derived the action integral in an analytic form and evaluated its stationary conditions numerically with the Ritz method for the first three resonant vibration modes. This revealed that the bar shows the following prominent nonlinear features: (i) amplitude dependence of the resonance frequency; (ii) symmetry breaking in the vibration pattern; and (iii) excitation of the high-frequency mode around nodal-like points. Stability of the resonant vibrations was also addressed in terms of a convex condition on the strain energy density.

Spectral theory and nonlinear functional analysis

CERN Document Server

Lopez-Gomez, Julian

2001-01-01

This Research Note addresses several pivotal problems in spectral theory and nonlinear functional analysis in connection with the analysis of the structure of the set of zeroes of a general class of nonlinear operators. It features the construction of an optimal algebraic/analytic invariant for calculating the Leray-Schauder degree, new methods for solving nonlinear equations in Banach spaces, and general properties of components of solutions sets presented with minimal use of topological tools. The author also gives several applications of the abstract theory to reaction diffusion equations and systems.The results presented cover a thirty-year period and include recent, unpublished findings of the author and his coworkers. Appealing to a broad audience, Spectral Theory and Nonlinear Functional Analysis contains many important contributions to linear algebra, linear and nonlinear functional analysis, and topology and opens the door for further advances.

A nonlinear magneto-thermo-elastic coupled hysteretic constitutive model for magnetostrictive alloys

International Nuclear Information System (INIS)

Jin Ke; Kou Yong; Zheng Xiaojing

2012-01-01

This paper presents a general hysteretic constitutive law of nonlinear magneto-thermo-elastic coupling for magnetostrictive alloys. The model considered here is thermodynamically motivated and based on the Gibbs free energy function. A nonlinear part of the elastic strain arising from magnetic domain rotation induced by the pre-stress is taken into account. Furthermore, the movement of the domain walls is incorporated to describe hysteresis based on Jiles–Atherton's model. Then a set of closed and analytical expressions of the constitutive law for the magnetostrictive rods and films are obtained, and the parameters appearing in the model can be determined by those measurable experiments in mechanics and physics. Comparing this model with other existing models in this field, the quantitative results show that the relationships obtained here are more effective to describe the effects of the pre-stress or in-plane residual stress and ambient temperature on the magnetization or the magnetostriction hysteresis loops. - Highlights: ► A general hysteretic constitutive law of nonlinear magneto-thermo-elastic coupling for magnetostrictive materials is proposed. ► Model is thermodynamically motivated and the reversible magnetic domain rotation and irreversible domain wall motion are taken. ► The predictions are in good accordance with the experimental data including both rods and films. ► Magnetostrictive alloys are sensitive to environment temperature and pre-stress or residual stress.

Adaptive, Small-Rotation-Based, Corotational Technique for Analysis of 2D Nonlinear Elastic Frames

Directory of Open Access Journals (Sweden)

Jaroon Rungamornrat

2014-01-01

Full Text Available This paper presents an efficient and accurate numerical technique for analysis of two-dimensional frames accounted for both geometric nonlinearity and nonlinear elastic material behavior. An adaptive remeshing scheme is utilized to optimally discretize a structure into a set of elements where the total displacement can be decomposed into the rigid body movement and one possessing small rotations. This, therefore, allows the force-deformation relationship for the latter part to be established based on small-rotation-based kinematics. Nonlinear elastic material model is integrated into such relation via the prescribed nonlinear moment-curvature relationship. The global force-displacement relation for each element can be derived subsequently using corotational formulations. A final system of nonlinear algebraic equations along with its associated gradient matrix for the whole structure is obtained by a standard assembly procedure and then solved numerically by Newton-Raphson algorithm. A selected set of results is then reported to demonstrate and discuss the computational performance including the accuracy and convergence of the proposed technique.

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

Geometrically nonlinear dynamic and static analysis of shallow spherical shell resting on two-parameters elastic foundations

International Nuclear Information System (INIS)

Civalek, Ö.

2014-01-01

In the present study nonlinear static and dynamic responses of shallow spherical shells resting on Winkler–Pasternak elastic foundations are carried out. The formulation of the shells is based on the Donnell theory. The nonlinear governing equations of motion of shallow shells are discretized in space and time domains using the discrete singular convolution and the differential quadrature methods, respectively. The validity of the present method is demonstrated by comparing the present results with those available in the open literature. The effects of the Winkler and Pasternak foundation parameters on nonlinear static and dynamic response of shells are investigated. Some results are also presented for circular plate as special case. Damping effect on nonlinear dynamic response of shells is studied. It is important to state that the increase in damping parameter causes decrease in the dynamic response of the shells. It is shown that the shear parameter of the foundation has a significant influence on the dynamic and static response of the shells. Also, the response of the shell is decreased with the increasing value of the shear parameter of the foundation. Parametric studies considering different geometric variables have also been investigated. -- Highlights: • Nonlinear responses of shallow spherical shells are presented. • The effects of foundation parameters are investigated. • Damping effect on nonlinear dynamic response of shells is also studied

Experimental and theoretical studies of spectral alteration in ultrasonic waves resulting from nonlinear elastic response in rock

Energy Technology Data Exchange (ETDEWEB)

Johnson, P.A.; McCall, K.R.; Meegan, G.D. Jr. [Los Alamos National Lab., NM (United States)

1993-11-01

Experiments in rock show a large nonlinear elastic wave response, far greater than that of gases, liquids and most other solids. The large response is attributed to structural defects in rock including microcracks and grain boundaries. In the earth, a large nonlinear response may be responsible for significant spectral alteration at amplitudes and distances currently considered to be well within the linear elastic regime.

Experimental and theoretical studies of spectral alteration in ultrasonic waves resulting from nonlinear elastic response in rock

International Nuclear Information System (INIS)

Johnson, P.A.; McCall, K.R.; Meegan, G.D. Jr.

1993-01-01

Experiments in rock show a large nonlinear elastic wave response, far greater than that of gases, liquids and most other solids. The large response is attributed to structural defects in rock including microcracks and grain boundaries. In the earth, a large nonlinear response may be responsible for significant spectral alteration at amplitudes and distances currently considered to be well within the linear elastic regime

On the general theory of thermo-elastic friction

NARCIS (Netherlands)

Alblas, J.B.

1961-01-01

A theory of the thermo-elastic dissipation in vibrating bodies is developed, starting from the three-dimensional thermo-elastic equations. After a discussion of the basic thermodynamical foundations, some general considerations on the problem of the conversion of mechanical energy into heat are

Interfacial elastic fingering in Hele-Shaw cells: A weakly nonlinear study

KAUST Repository

Carvalho, Gabriel D.

2013-11-11

We study a variant of the classic viscous fingering instability in Hele-Shaw cells where the interface separating the fluids is elastic, and presents a curvature-dependent bending rigidity. By employing a second-order mode-coupling approach we investigate how the elastic nature of the interface influences the morphology of emerging interfacial patterns. This is done by focusing our attention on a conventionally stable situation in which the fluids involved have the same viscosity. In this framework, we show that the inclusion of nonlinear effects plays a crucial role in inducing sizable interfacial instabilities, as well as in determining the ultimate shape of the pattern-forming structures. Particularly, we have found that the emergence of either narrow or wide fingers can be regulated by tuning a rigidity fraction parameter. Our weakly nonlinear findings reinforce the importance of the so-called curvature weakening effect, which favors the development of fingers in regions of lower rigidity. © 2013 American Physical Society.

Interfacial elastic fingering in Hele-Shaw cells: A weakly nonlinear study

KAUST Repository

Carvalho, Gabriel D.; Miranda, José A.; Gadê lha, Hermes

2013-01-01

We study a variant of the classic viscous fingering instability in Hele-Shaw cells where the interface separating the fluids is elastic, and presents a curvature-dependent bending rigidity. By employing a second-order mode-coupling approach we investigate how the elastic nature of the interface influences the morphology of emerging interfacial patterns. This is done by focusing our attention on a conventionally stable situation in which the fluids involved have the same viscosity. In this framework, we show that the inclusion of nonlinear effects plays a crucial role in inducing sizable interfacial instabilities, as well as in determining the ultimate shape of the pattern-forming structures. Particularly, we have found that the emergence of either narrow or wide fingers can be regulated by tuning a rigidity fraction parameter. Our weakly nonlinear findings reinforce the importance of the so-called curvature weakening effect, which favors the development of fingers in regions of lower rigidity. © 2013 American Physical Society.

Theory of the change of elastic constants by interstitials

International Nuclear Information System (INIS)

Breuer, N.; Dederichs, P.H.; Lehmann, C.; Leibfried, G.; Scholz, A.

1975-01-01

The theory of the change of elastic constants by point-defects, in particular by interstitials, is briefly summarized. The typical effects of spring changes in a defect lattice on the elastic data are discussed qualitatively. Numerical results for the change of elastic constants by self-interstitials and vacancies are given and compared with experimental data for Cu and Al

Nonlinear morphoelastic plates II: Exodus to buckled states

KAUST Repository

McMahon, J.

2011-05-11

Morphoelasticity is the theory of growing elastic materials. The theory is based on the multiplicative decomposition of the deformation gradient and provides a formulation of the deformation and stresses induced by growth. Following a companion paper, a general theory of growing non-linear elastic Kirchhoff plate is described. First, a complete geometric description of incompatibility with simple examples is given. Second, the stability of growing Kirchhoff plates is analyzed. © SAGE Publications 2011.

Nonlinear morphoelastic plates II: Exodus to buckled states

KAUST Repository

McMahon, J.; Goriely, A.; Tabor, M.

2011-01-01

Morphoelasticity is the theory of growing elastic materials. The theory is based on the multiplicative decomposition of the deformation gradient and provides a formulation of the deformation and stresses induced by growth. Following a companion paper, a general theory of growing non-linear elastic Kirchhoff plate is described. First, a complete geometric description of incompatibility with simple examples is given. Second, the stability of growing Kirchhoff plates is analyzed. © SAGE Publications 2011.

Waves and Structures in Nonlinear Nondispersive Media General Theory and Applications to Nonlinear Acoustics

CERN Document Server

Gurbatov, S N; Saichev, A I

2012-01-01

"Waves and Structures in Nonlinear Nondispersive Media: General Theory and Applications to Nonlinear Acoustics” is devoted completely to nonlinear structures. The general theory is given here in parallel with mathematical models. Many concrete examples illustrate the general analysis of Part I. Part II is devoted to applications to nonlinear acoustics, including specific nonlinear models and exact solutions, physical mechanisms of nonlinearity, sawtooth-shaped wave propagation, self-action phenomena, nonlinear resonances and engineering application (medicine, nondestructive testing, geophysics, etc.). This book is designed for graduate and postgraduate students studying the theory of nonlinear waves of various physical nature. It may also be useful as a handbook for engineers and researchers who encounter the necessity of taking nonlinear wave effects into account of their work. Dr. Gurbatov S.N. is the head of Department, and Vice Rector for Research of Nizhny Novgorod State University. Dr. Rudenko O.V. is...

A preconditioner for the finite element computation of incompressible, nonlinear elastic deformations

Science.gov (United States)

Whiteley, J. P.

2017-10-01

Large, incompressible elastic deformations are governed by a system of nonlinear partial differential equations. The finite element discretisation of these partial differential equations yields a system of nonlinear algebraic equations that are usually solved using Newton's method. On each iteration of Newton's method, a linear system must be solved. We exploit the structure of the Jacobian matrix to propose a preconditioner, comprising two steps. The first step is the solution of a relatively small, symmetric, positive definite linear system using the preconditioned conjugate gradient method. This is followed by a small number of multigrid V-cycles for a larger linear system. Through the use of exemplar elastic deformations, the preconditioner is demonstrated to facilitate the iterative solution of the linear systems arising. The number of GMRES iterations required has only a very weak dependence on the number of degrees of freedom of the linear systems.

A Lagrangian meshfree method applied to linear and nonlinear elasticity.

Science.gov (United States)

Walker, Wade A

2017-01-01

The repeated replacement method (RRM) is a Lagrangian meshfree method which we have previously applied to the Euler equations for compressible fluid flow. In this paper we present new enhancements to RRM, and we apply the enhanced method to both linear and nonlinear elasticity. We compare the results of ten test problems to those of analytic solvers, to demonstrate that RRM can successfully simulate these elastic systems without many of the requirements of traditional numerical methods such as numerical derivatives, equation system solvers, or Riemann solvers. We also show the relationship between error and computational effort for RRM on these systems, and compare RRM to other methods to highlight its strengths and weaknesses. And to further explain the two elastic equations used in the paper, we demonstrate the mathematical procedure used to create Riemann and Sedov-Taylor solvers for them, and detail the numerical techniques needed to embody those solvers in code.

On the vibrations of a simply supported square plate on a weakly nonlinear elastic foundation

NARCIS (Netherlands)

Zarubinskaya, M.A.; Van Horssen, W.T.

2003-01-01

In this paper an initial-boundary value problem for a weakly nonlinear plate equation with a quadratic nonlinearity will be studied. This initial-boundary value problem can be regarded as a simple model describing free oscillations of a simply supported square plate on an elastic foundation. It is

Transient response of nonlinear polymer networks: A kinetic theory

Science.gov (United States)

Vernerey, Franck J.

2018-06-01

Dynamic networks are found in a majority of natural materials, but also in engineering materials, such as entangled polymers and physically cross-linked gels. Owing to their transient bond dynamics, these networks display a rich class of behaviors, from elasticity, rheology, self-healing, or growth. Although classical theories in rheology and mechanics have enabled us to characterize these materials, there is still a gap in our understanding on how individuals (i.e., the mechanics of each building blocks and its connection with others) affect the emerging response of the network. In this work, we introduce an alternative way to think about these networks from a statistical point of view. More specifically, a network is seen as a collection of individual polymer chains connected by weak bonds that can associate and dissociate over time. From the knowledge of these individual chains (elasticity, transient attachment, and detachment events), we construct a statistical description of the population and derive an evolution equation of their distribution based on applied deformation and their local interactions. We specifically concentrate on nonlinear elastic response that follows from the strain stiffening response of individual chains of finite size. Upon appropriate averaging operations and using a mean field approximation, we show that the distribution can be replaced by a so-called chain distribution tensor that is used to determine important macroscopic measures such as stress, energy storage and dissipation in the network. Prediction of the kinetic theory are then explored against known experimental measurement of polymer responses under uniaxial loading. It is found that even under the simplest assumptions of force-independent chain kinetics, the model is able to reproduce complex time-dependent behaviors of rubber and self-healing supramolecular polymers.

Bulk solitary waves in elastic solids

Science.gov (United States)

Samsonov, A. M.; Dreiden, G. V.; Semenova, I. V.; Shvartz, A. G.

2015-10-01

A short and object oriented conspectus of bulk solitary wave theory, numerical simulations and real experiments in condensed matter is given. Upon a brief description of the soliton history and development we focus on bulk solitary waves of strain, also known as waves of density and, sometimes, as elastic and/or acoustic solitons. We consider the problem of nonlinear bulk wave generation and detection in basic structural elements, rods, plates and shells, that are exhaustively studied and widely used in physics and engineering. However, it is mostly valid for linear elasticity, whereas dynamic nonlinear theory of these elements is still far from being completed. In order to show how the nonlinear waves can be used in various applications, we studied the solitary elastic wave propagation along lengthy wave guides, and remarkably small attenuation of elastic solitons was proven in physical experiments. Both theory and generation for strain soliton in a shell, however, remained unsolved problems until recently, and we consider in more details the nonlinear bulk wave propagation in a shell. We studied an axially symmetric deformation of an infinite nonlinearly elastic cylindrical shell without torsion. The problem for bulk longitudinal waves is shown to be reducible to the one equation, if a relation between transversal displacement and the longitudinal strain is found. It is found that both the 1+1D and even the 1+2D problems for long travelling waves in nonlinear solids can be reduced to the Weierstrass equation for elliptic functions, which provide the solitary wave solutions as appropriate limits. We show that the accuracy in the boundary conditions on free lateral surfaces is of crucial importance for solution, derive the only equation for longitudinal nonlinear strain wave and show, that the equation has, amongst others, a bidirectional solitary wave solution, which lead us to successful physical experiments. We observed first the compression solitary wave in the

Imperfection Sensitivity of Nonlinear Vibration of Curved Single-Walled Carbon Nanotubes Based on Nonlocal Timoshenko Beam Theory

Directory of Open Access Journals (Sweden)

Iman Eshraghi

2016-09-01

Full Text Available Imperfection sensitivity of large amplitude vibration of curved single-walled carbon nanotubes (SWCNTs is considered in this study. The SWCNT is modeled as a Timoshenko nano-beam and its curved shape is included as an initial geometric imperfection term in the displacement field. Geometric nonlinearities of von Kármán type and nonlocal elasticity theory of Eringen are employed to derive governing equations of motion. Spatial discretization of governing equations and associated boundary conditions is performed using differential quadrature (DQ method and the corresponding nonlinear eigenvalue problem is iteratively solved. Effects of amplitude and location of the geometric imperfection, and the nonlocal small-scale parameter on the nonlinear frequency for various boundary conditions are investigated. The results show that the geometric imperfection and non-locality play a significant role in the nonlinear vibration characteristics of curved SWCNTs.

A dynamic elastic and inelastic scattering theory of high-energy electrons

International Nuclear Information System (INIS)

Wang Zhonglin

1990-01-01

A review is given on the applications of elastic multislice theory for simulating the images and diffractions of reflection electron microscopy. The limitation of this theory is illustrated according to some experimental observations. A generalized elastic and inelastic multislice theory is then introduced from quantum mechanics; its applications for approaching inelastic plasmon excitation and phonon excitation (or thermal diffuse scattering) are discussed. The energy-filtered inelastic high resolution images can be simulated based on this theory

Equivalent Representation Form of Oscillators with Elastic and Damping Nonlinear Terms

Directory of Open Access Journals (Sweden)

Alex Elías-Zúñiga

2013-01-01

Full Text Available In this work we consider the nonlinear equivalent representation form of oscillators that exhibit nonlinearities in both the elastic and the damping terms. The nonlinear damping effects are considered to be described by fractional power velocity terms which provide better predictions of the dissipative effects observed in some physical systems. It is shown that their effects on the system dynamics response are equivalent to a shift in the coefficient of the linear damping term of a Duffing oscillator. Then, its numerical integration predictions, based on its equivalent representation form given by the well-known forced, damped Duffing equation, are compared to the numerical integration values of its original equations of motion. The applicability of the proposed procedure is evaluated by studying the dynamics response of four nonlinear oscillators that arise in some engineering applications such as nanoresonators, microresonators, human wrist movements, structural engineering design, and chain dynamics of polymeric materials at high extensibility, among others.

Equations of motion for anisotropic nonlinear elastic continuum in gravitational field

International Nuclear Information System (INIS)

Sokolov, S.N.

1994-01-01

Equations of motion for anisotropic nonlinear elastic continuum in the gravitational field are written in the form convenient for numerical calculations. The energy-stress tensor is expressed through scalar and tensor products of three vectors frozen in the continuum. Examples of expansion of the energy-stress tensor into scalar and tensor invariants corresponding to some crystal classes are given. 47 refs

Weakly nonlinear dispersion and stop-band effects for periodic structures

DEFF Research Database (Denmark)

Sorokin, Vladislav; Thomsen, Jon Juel

of frequency band-gaps, i.e. frequency ranges in which elastic waves cannot propagate. Most existing analytical methods in the field are based on Floquet theory [1]; e.g. this holds for the classical Hill’s method of infinite determinants [1,2], and themethod of space-harmonics [3]. However, application...... of these methods for studying nonlinear problems isimpossible or cumbersome, since Floquet theory is applicable only for linear systems. Thus the nonlinear effects for periodic structures are not yet fully uncovered, while at the same time applications may demand effects of nonlinearity on structural response...... to be accounted for.The paper deals with analytically predicting dynamic response for nonlinear elastic structures with a continuous periodic variation in structural properties. Specifically, for a Bernoulli-Euler beam with aspatially continuous modulation of structural properties in the axial direction...

Oscillations of a Beam on a Non-Linear Elastic Foundation under Periodic Loads

Directory of Open Access Journals (Sweden)

Donald Mark Santee

2006-01-01

Full Text Available The complexity of the response of a beam resting on a nonlinear elastic foundation makes the design of this structural element rather challenging. Particularly because, apparently, there is no algebraic relation for its load bearing capacity as a function of the problem parameters. Such an algebraic relation would be desirable for design purposes. Our aim is to obtain this relation explicitly. Initially, a mathematical model of a flexible beam resting on a non-linear elastic foundation is presented, and its non-linear vibrations and instabilities are investigated using several numerical methods. At a second stage, a parametric study is carried out, using analytical and semi-analytical perturbation methods. So, the influence of the various physical and geometrical parameters of the mathematical model on the non-linear response of the beam is evaluated, in particular, the relation between the natural frequency and the vibration amplitude and the first period doubling and saddle-node bifurcations. These two instability phenomena are the two basic mechanisms associated with the loss of stability of the beam. Finally Melnikov's method is used to determine an algebraic expression for the boundary that separates a safe from an unsafe region in the force parameters space. It is shown that this can be used as a basis for a reliable engineering design criterion.

Nonlinear elastic longitudinal strain-wave propagation in a plate with nonequilibrium laser-generated point defects

International Nuclear Information System (INIS)

Mirzade, Fikret Kh.

2005-01-01

The propagation of longitudinal strain wave in a plate with quadratic nonlinearity of elastic continuum was studied in the context of a model that takes into account the joint dynamics of elastic displacements in the medium and the concentration of the nonequilibrium laser-induced point defects. The input equations of the problem are reformulated in terms of only the total displacements of the medium points. In this case, the presence of structural defects manifests itself in the emergence of a delayed response of the system to the propagation of the strain-related perturbations, which is characteristic of media with relaxation or memory. The model equations describing the nonlinear displacement wave were derived with allowance made for the values of the relaxation parameter. The influence of the generation and relaxation of lattice defects on the propagation of this wave was analyzed. It is shown that, for short relaxation times of defects, the strain can propagate in the form of shock fronts. In the case of longer relaxation times, shock waves do not form and the strain wave propagates only in the form of solitary waves or a train of solitons. The contributions of the finiteness of the defect-recombination rate to linear and nonlinear elastic modulus, and spatial dispersion are determined

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

An enstrophy-based linear and nonlinear receptivity theory

Science.gov (United States)

Sengupta, Aditi; Suman, V. K.; Sengupta, Tapan K.; Bhaumik, Swagata

2018-05-01

In the present research, a new theory of instability based on enstrophy is presented for incompressible flows. Explaining instability through enstrophy is counter-intuitive, as it has been usually associated with dissipation for the Navier-Stokes equation (NSE). This developed theory is valid for both linear and nonlinear stages of disturbance growth. A previously developed nonlinear theory of incompressible flow instability based on total mechanical energy described in the work of Sengupta et al. ["Vortex-induced instability of an incompressible wall-bounded shear layer," J. Fluid Mech. 493, 277-286 (2003)] is used to compare with the present enstrophy based theory. The developed equations for disturbance enstrophy and disturbance mechanical energy are derived from NSE without any simplifying assumptions, as compared to other classical linear/nonlinear theories. The theory is tested for bypass transition caused by free stream convecting vortex over a zero pressure gradient boundary layer. We explain the creation of smaller scales in the flow by a cascade of enstrophy, which creates rotationality, in general inhomogeneous flows. Linear and nonlinear versions of the theory help explain the vortex-induced instability problem under consideration.

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.

Mechanical characterization and non-linear elastic modeling of poly(glycerol sebacate) for soft tissue engineering.

Science.gov (United States)

Mitsak, Anna G; Dunn, Andrew M; Hollister, Scott J

2012-07-01

Scaffold tissue engineering strategies for repairing and replacing soft tissue aim to improve reconstructive and corrective surgical techniques whose limitations include suboptimal mechanical properties, fibrous capsule formation and volume loss due to graft resorption. An effective tissue engineering strategy requires a scaffolding material with low elastic modulus that behaves similarly to soft tissue, which has been characterized as a nonlinear elastic material. The material must also have the ability to be manufactured into specifically designed architectures. Poly(glycerol sebacate) (PGS) is a thermoset elastomer that meets these criteria. We hypothesize that the mechanical properties of PGS can be modulated through curing condition and architecture to produce materials with a range of stiffnesses. To evaluate this hypothesis, we manufactured PGS constructs cured under various conditions and having one of two architectures (solid or porous). Specimens were then tensile tested according to ASTM standards and the data were modeled using a nonlinear elastic Neo-Hookean model. Architecture and testing conditions, including elongation rate and wet versus dry conditions, affected the mechanical properties. Increasing curing time and temperature led to increased tangent modulus and decreased maximum strain for solid constructs. Porous constructs had lower nonlinear elastic properties, as did constructs of both architectures tested under simulated physiological conditions (wetted at 37 °C). Both solid and porous PGS specimens could be modeled well with the Neo-Hookean model. Future studies include comparing PGS properties to other biological tissue types and designing and characterizing PGS scaffolds for regenerating these tissues. Copyright © 2012 Elsevier Ltd. All rights reserved.

Nonlinear structural mechanics theory, dynamical phenomena and modeling

CERN Document Server

Lacarbonara, Walter

2013-01-01

Nonlinear Structural Mechanics: Theory, Dynamical Phenomena and Modeling offers a concise, coherent presentation of the theoretical framework of nonlinear structural mechanics, computational methods, applications, parametric investigations of nonlinear phenomena and their mechanical interpretation towards design. The theoretical and computational tools that enable the formulation, solution, and interpretation of nonlinear structures are presented in a systematic fashion so as to gradually attain an increasing level of complexity of structural behaviors, under the prevailing assumptions on the geometry of deformation, the constitutive aspects and the loading scenarios. Readers will find a treatment of the foundations of nonlinear structural mechanics towards advanced reduced models, unified with modern computational tools in the framework of the prominent nonlinear structural dynamic phenomena while tackling both the mathematical and applied sciences. Nonlinear Structural Mechanics: Theory, Dynamical Phenomena...

Detecting Damage in Composite Material Using Nonlinear Elastic Wave Spectroscopy Methods

Science.gov (United States)

Meo, Michele; Polimeno, Umberto; Zumpano, Giuseppe

2008-05-01

Modern aerospace structures make increasing use of fibre reinforced plastic composites, due to their high specific mechanical properties. However, due to their brittleness, low velocity impact can cause delaminations beneath the surface, while the surface may appear to be undamaged upon visual inspection. Such damage is called barely visible impact damage (BVID). Such internal damages lead to significant reduction in local strengths and ultimately could lead to catastrophic failures. It is therefore important to detect and monitor damages in high loaded composite components to receive an early warning for a well timed maintenance of the aircraft. Non-linear ultrasonic spectroscopy methods are promising damage detection and material characterization tools. In this paper, two different non-linear elastic wave spectroscopy (NEWS) methods are presented: single mode nonlinear resonance ultrasound (NRUS) and nonlinear wave modulation technique (NWMS). The NEWS methods were applied to detect delamination damage due to low velocity impact (<12 J) on various composite plates. The results showed that the proposed methodology appear to be highly sensitive to the presence of damage with very promising future NDT and structural health monitoring applications.

Purely elastic scattering theories and their ultraviolet limits

International Nuclear Information System (INIS)

Klassen, T.R.; Chicago Univ., IL; Melzer, E.

1990-01-01

We use the thermodynamic Bethe ansatz to find the finite-size corrections to the ground-state energy in an arbitrary (1+1)-dimensional purely elastic scattering theory. The leading finite-size effects are characterized by tilde c=c-12d 0 , where c and d 0 are the central charge and the lowest scaling dimension, respectively, of the (possibly nonunitary) CFT describing the ultraviolet limit of the massive scattering theory. After presenting the purely elastic S-matrix theories that emerged in recent discussions of perturbed CFTs, we calculate their finite-size scaling coefficient tilde c. Our results show that the UV limits of the 'minimal' S-matrix theories are the unperturbed CFTs in question. On the other hand, the S-matrices which have been suggested to describe affine Toda field theories, differing from the minimal S-matrices by coupling-dependent factors, are seen to have free bosonic CFTs as their UV limits. We also discuss some interesting properties of tilde c. In particular, we suggest that tilde c is a measure of the number of degrees of freedom of an arbitrary two-dimensional CFT. (orig.)

Nonlinear classical theory of electromagnetism

International Nuclear Information System (INIS)

Pisello, D.

1977-01-01

A topological theory of electric charge is given. Einstein's criteria for the completion of classical electromagnetic theory are summarized and their relation to quantum theory and the principle of complementarity is indicated. The inhibiting effect that this principle has had on the development of physical thought is discussed. Developments in the theory of functions on nonlinear spaces provide the conceptual framework required for the completion of electromagnetism. The theory is based on an underlying field which is a continuous mapping of space-time into points on the two-sphere. (author)

Dynamic acousto-elastic testing of concrete with a coda-wave probe: comparison with standard linear and nonlinear ultrasonic techniques.

Science.gov (United States)

Shokouhi, Parisa; Rivière, Jacques; Lake, Colton R; Le Bas, Pierre-Yves; Ulrich, T J

2017-11-01

The use of nonlinear acoustic techniques in solids consists in measuring wave distortion arising from compliant features such as cracks, soft intergrain bonds and dislocations. As such, they provide very powerful nondestructive tools to monitor the onset of damage within materials. In particular, a recent technique called dynamic acousto-elasticity testing (DAET) gives unprecedented details on the nonlinear elastic response of materials (classical and non-classical nonlinear features including hysteresis, transient elastic softening and slow relaxation). Here, we provide a comprehensive set of linear and nonlinear acoustic responses on two prismatic concrete specimens; one intact and one pre-compressed to about 70% of its ultimate strength. The two linear techniques used are Ultrasonic Pulse Velocity (UPV) and Resonance Ultrasound Spectroscopy (RUS), while the nonlinear ones include DAET (fast and slow dynamics) as well as Nonlinear Resonance Ultrasound Spectroscopy (NRUS). In addition, the DAET results correspond to a configuration where the (incoherent) coda portion of the ultrasonic record is used to probe the samples, as opposed to a (coherent) first arrival wave in standard DAET tests. We find that the two visually identical specimens are indistinguishable based on parameters measured by linear techniques (UPV and RUS). On the contrary, the extracted nonlinear parameters from NRUS and DAET are consistent and orders of magnitude greater for the damaged specimen than those for the intact one. This compiled set of linear and nonlinear ultrasonic testing data including the most advanced technique (DAET) provides a benchmark comparison for their use in the field of material characterization. Copyright © 2017 Elsevier B.V. All rights reserved.

Three dimensional vibration and bending analysis of carbon nanotubes embedded in elastic medium based on theory of elasticity

Directory of Open Access Journals (Sweden)

M. Shaban

Full Text Available This paper studies free vibration and bending behavior of singlewalled carbon nanotubes (SWCNTs embedded on elastic medium based on three-dimensional theory of elasticity. To accounting the size effect of carbon nanotubes, non-local theory is adopted to shell model. The nonlocal parameter is incorporated into all constitutive equations in three dimensions. The surrounding medium is modeled as two-parameter elastic foundation. By using Fourier series expansion in axial and circumferential direction, the set of coupled governing equations are reduced to the ordinary differential equations in thickness direction. Then, the state-space method as an efficient and accurate method is used to solve the resulting equations analytically. Comprehensive parametric studies are carried out to show the influences of the nonlocal parameter, radial and shear elastic stiffness, thickness-to-radius ratio and radiusto-length ratio.

Geometrical nonlinear deformation model and its experimental study on bimorph giant magnetostrictive thin film

Institute of Scientific and Technical Information of China (English)

Wei LIU; Zhenyuan JIA; Fuji WANG; Yongshun ZHANG; Dongming GUO

2008-01-01

The geometrical nonlinearity of a giant magne-tostrictive thin film (GMF) can be clearly detected under the magnetostriction effect. Thus, using geometrical linear elastic theory to describe the strain, stress, and constitutive relationship of GMF is inaccurate. According to nonlinear elastic theory, a nonlinear deformation model of the bimorph GMF is established based on assumptions that the magnetostriction effect is equivalent to the effect of body force loaded on the GMF. With Taylor series method, the numerical solution is deduced. Experiments on TbDyFe/Polyimide (PI)/SmFe and TbDyFe/Cu/SmFe are then conducted to verify the proposed model, respectively. Results indicate that the nonlinear deflection curve model is in good conformity with the experimental data.

Measuring the linear and nonlinear elastic properties of brain tissue with shear waves and inverse analysis.

Science.gov (United States)

Jiang, Yi; Li, Guoyang; Qian, Lin-Xue; Liang, Si; Destrade, Michel; Cao, Yanping

2015-10-01

We use supersonic shear wave imaging (SSI) technique to measure not only the linear but also the nonlinear elastic properties of brain matter. Here, we tested six porcine brains ex vivo and measured the velocities of the plane shear waves induced by acoustic radiation force at different states of pre-deformation when the ultrasonic probe is pushed into the soft tissue. We relied on an inverse method based on the theory governing the propagation of small-amplitude acoustic waves in deformed solids to interpret the experimental data. We found that, depending on the subjects, the resulting initial shear modulus [Formula: see text] varies from 1.8 to 3.2 kPa, the stiffening parameter [Formula: see text] of the hyperelastic Demiray-Fung model from 0.13 to 0.73, and the third- [Formula: see text] and fourth-order [Formula: see text] constants of weakly nonlinear elasticity from [Formula: see text]1.3 to [Formula: see text]20.6 kPa and from 3.1 to 8.7 kPa, respectively. Paired [Formula: see text] test performed on the experimental results of the left and right lobes of the brain shows no significant difference. These values are in line with those reported in the literature on brain tissue, indicating that the SSI method, combined to the inverse analysis, is an efficient and powerful tool for the mechanical characterization of brain tissue, which is of great importance for computer simulation of traumatic brain injury and virtual neurosurgery.

Perturbation Theory for Open Two-Level Nonlinear Quantum Systems

International Nuclear Information System (INIS)

Zhang Zhijie; Jiang Dongguang; Wang Wei

2011-01-01

Perturbation theory is an important tool in quantum mechanics. In this paper, we extend the traditional perturbation theory to open nonlinear two-level systems, treating decoherence parameter γ as a perturbation. By this virtue, we give a perturbative solution to the master equation, which describes a nonlinear open quantum system. The results show that for small decoherence rate γ, the ratio of the nonlinear rate C to the tunneling coefficient V (i.e., r = C/V) determines the validity of the perturbation theory. For small ratio r, the perturbation theory is valid, otherwise it yields wrong results. (general)

Some Differential Geometric Relations in the Elastic Shell

Directory of Open Access Journals (Sweden)

Xiaoqin Shen

2016-01-01

Full Text Available The theory of the elastic shells is one of the most important parts of the theory of solid mechanics. The elastic shell can be described with its middle surface; that is, the three-dimensional elastic shell with equal thickness comprises a series of overlying surfaces like middle surface. In this paper, the differential geometric relations between elastic shell and its middle surface are provided under the curvilinear coordinate systems, which are very important for forming two-dimensional linear and nonlinear elastic shell models. Concretely, the metric tensors, the determinant of metric matrix field, the Christoffel symbols, and Riemann tensors on the three-dimensional elasticity are expressed by those on the two-dimensional middle surface, which are featured by the asymptotic expressions with respect to the variable in the direction of thickness of the shell. Thus, the novelty of this work is that we can further split three-dimensional mechanics equations into two-dimensional variation problems. Finally, two kinds of special shells, hemispherical shell and semicylindrical shell, are provided as the examples.

Nonlinear free vibration analysis of elastically supported carbon nanotube-reinforced composite beam with the thermal environment in non-deterministic framework

Directory of Open Access Journals (Sweden)

Chaudhari Virendra Kumar

2017-01-01

Full Text Available This paper deals with the investigation of nonlinear free vibration behavior of elastically supported carbon nanotube reinforced composite (CNTRC beam subjected to thermal loading with random system properties. Material properties of each constituent’s material, volume fraction exponent and foundation parameters are considered as uncorrelated Gaussian random input variables. The beam is supported by a Pasternak foundation with Winkler cubic nonlinearity. The higher order shear deformation theory (HSDT with von-Karman non-linearity is used to formulate the governing equation using Hamilton principle. Convergence and validation study is carried out through the comparison with the available results in the literature for authenticity and accuracy of the present approach used in the analysis. First order perturbation technique (FOPT,Second order perturbation technique (SOPT and Monte Carlo simulation (MCS methods are employed to investigate the effect of geometric configuration, volume fraction exponent, foundation parameters, distribution of reinforcement and thermal loading on nonlinear vibration characteristics CNTRC beam.The present work signifies the accurate analysis of vibrational behaviour influences by different random variables. Results are presented in terms of mean, variance (COV and probability density function (PDF for various aforementioned parameters.

A Linear Theory for Pretwisted Elastic Beams

DEFF Research Database (Denmark)

Krenk, Steen

1983-01-01

contains a general system of differential equations and gives explicit solutions for homogenous extension, torsion, and bending. The theory accounts explicitly for the shear center, the elastic center, and the axis of pretwist. The resulting torsion-extension coupling is in agreement with a recent...

Non-linear waves in heterogeneous elastic rods via homogenization

KAUST Repository

Quezada de Luna, Manuel

2012-03-01

We consider the propagation of a planar loop on a heterogeneous elastic rod with a periodic microstructure consisting of two alternating homogeneous regions with different material properties. The analysis is carried out using a second-order homogenization theory based on a multiple scale asymptotic expansion. © 2011 Elsevier Ltd. All rights reserved.

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.

FEATURES APPLICATION CIRCUIT MOMENT FINITE ELEMENT (MSSE) NONLINEAR CALCULATIONS OF PLATES AND SHELLS

OpenAIRE

Bazhenov V.A.; Sacharov A.S.; Guliar A. I.; Pyskunov S.O.; Maksymiuk Y.V.

2014-01-01

Based MSSE created shell CE general type, which allows you to analyze the stress-strain state of axisymmetrical shells and plates in problems of physical and geometric nonlinearity. The principal nonlinear elasticity theory, algorithms for solving systems of nonlinear equations for determining the temperature and plastic deformation.

Spectral theory and nonlinear analysis with applications to spatial ecology

CERN Document Server

Cano-Casanova, S; Mora-Corral , C

2005-01-01

This volume details some of the latest advances in spectral theory and nonlinear analysis through various cutting-edge theories on algebraic multiplicities, global bifurcation theory, non-linear Schrödinger equations, non-linear boundary value problems, large solutions, metasolutions, dynamical systems, and applications to spatial ecology. The main scope of the book is bringing together a series of topics that have evolved separately during the last decades around the common denominator of spectral theory and nonlinear analysis - from the most abstract developments up to the most concrete applications to population dynamics and socio-biology - in an effort to fill the existing gaps between these fields.

A 2D nonlinear multiring model for blood flow in large elastic arteries

Science.gov (United States)

Ghigo, Arthur R.; Fullana, Jose-Maria; Lagrée, Pierre-Yves

2017-12-01

In this paper, we propose a two-dimensional nonlinear ;multiring; model to compute blood flow in axisymmetric elastic arteries. This model is designed to overcome the numerical difficulties of three-dimensional fluid-structure interaction simulations of blood flow without using the over-simplifications necessary to obtain one-dimensional blood flow models. This multiring model is derived by integrating over concentric rings of fluid the simplified long-wave Navier-Stokes equations coupled to an elastic model of the arterial wall. The resulting system of balance laws provides a unified framework in which both the motion of the fluid and the displacement of the wall are dealt with simultaneously. The mathematical structure of the multiring model allows us to use a finite volume method that guarantees the conservation of mass and the positivity of the numerical solution and can deal with nonlinear flows and large deformations of the arterial wall. We show that the finite volume numerical solution of the multiring model provides at a reasonable computational cost an asymptotically valid description of blood flow velocity profiles and other averaged quantities (wall shear stress, flow rate, ...) in large elastic and quasi-rigid arteries. In particular, we validate the multiring model against well-known solutions such as the Womersley or the Poiseuille solutions as well as against steady boundary layer solutions in quasi-rigid constricted and expanded tubes.

Key Elasticities in Job Search Theory : International Evidence

OpenAIRE

Addison, John T.; Centeno, Mário; Portugal, Pedro

2004-01-01

This paper exploits the informational value of search theory, after Lancaster and Chesher (1983), in conjunction with survey data on the unemployed to calculate key reservation wage and duration elasticities for most EU-15 nations.

Mathematical Systems Theory : from Behaviors to Nonlinear Control

CERN Document Server

Julius, A; Pasumarthy, Ramkrishna; Rapisarda, Paolo; Scherpen, Jacquelien

2015-01-01

This treatment of modern topics related to mathematical systems theory forms the proceedings of a workshop, Mathematical Systems Theory: From Behaviors to Nonlinear Control, held at the University of Groningen in July 2015. The workshop celebrated the work of Professors Arjan van der Schaft and Harry Trentelman, honouring their 60th Birthdays. The first volume of this two-volume work covers a variety of topics related to nonlinear and hybrid control systems. After giving a detailed account of the state of the art in the related topic, each chapter presents new results and discusses new directions. As such, this volume provides a broad picture of the theory of nonlinear and hybrid control systems for scientists and engineers with an interest in the interdisciplinary field of systems and control theory. The reader will benefit from the expert participants’ ideas on exciting new approaches to control and system theory and their predictions of future directions for the subject that were discussed at the worksho...

The Nonlinear Field Space Theory

Energy Technology Data Exchange (ETDEWEB)

Mielczarek, Jakub, E-mail: jakub.mielczarek@uj.edu.pl [Institute of Physics, Jagiellonian University, ul. Łojasiewicza 11, 30-348 Kraków (Poland); Trześniewski, Tomasz, E-mail: tbwbt@ift.uni.wroc.pl [Institute of Physics, Jagiellonian University, ul. Łojasiewicza 11, 30-348 Kraków (Poland); Institute for Theoretical Physics, University of Wrocław, pl. Borna 9, 50-204 Wrocław (Poland)

2016-08-10

In recent years the idea that not only the configuration space of particles, i.e. spacetime, but also the corresponding momentum space may have nontrivial geometry has attracted significant attention, especially in the context of quantum gravity. The aim of this letter is to extend this concept to the domain of field theories, by introducing field spaces (i.e. phase spaces of field values) that are not affine spaces. After discussing the motivation and general aspects of our approach we present a detailed analysis of the prototype (quantum) Nonlinear Field Space Theory of a scalar field on the Minkowski background. We show that the nonlinear structure of a field space leads to numerous interesting predictions, including: non-locality, generalization of the uncertainty relations, algebra deformations, constraining of the maximal occupation number, shifting of the vacuum energy and renormalization of the charge and speed of propagation of field excitations. Furthermore, a compact field space is a natural way to implement the “Principle of finiteness” of physical theories, which once motivated the Born–Infeld theory. Thus the presented framework has a variety of potential applications in the theories of fundamental interactions (e.g. quantum gravity), as well as in condensed matter physics (e.g. continuous spin chains), and can shed new light on the issue of divergences in quantum field theories.

The Nonlinear Field Space Theory

International Nuclear Information System (INIS)

Mielczarek, Jakub; Trześniewski, Tomasz

2016-01-01

In recent years the idea that not only the configuration space of particles, i.e. spacetime, but also the corresponding momentum space may have nontrivial geometry has attracted significant attention, especially in the context of quantum gravity. The aim of this letter is to extend this concept to the domain of field theories, by introducing field spaces (i.e. phase spaces of field values) that are not affine spaces. After discussing the motivation and general aspects of our approach we present a detailed analysis of the prototype (quantum) Nonlinear Field Space Theory of a scalar field on the Minkowski background. We show that the nonlinear structure of a field space leads to numerous interesting predictions, including: non-locality, generalization of the uncertainty relations, algebra deformations, constraining of the maximal occupation number, shifting of the vacuum energy and renormalization of the charge and speed of propagation of field excitations. Furthermore, a compact field space is a natural way to implement the “Principle of finiteness” of physical theories, which once motivated the Born–Infeld theory. Thus the presented framework has a variety of potential applications in the theories of fundamental interactions (e.g. quantum gravity), as well as in condensed matter physics (e.g. continuous spin chains), and can shed new light on the issue of divergences in quantum field theories.

An introduction to nonlinear analysis and fixed point theory

CERN Document Server

Pathak, Hemant Kumar

2018-01-01

This book systematically introduces the theory of nonlinear analysis, providing an overview of topics such as geometry of Banach spaces, differential calculus in Banach spaces, monotone operators, and fixed point theorems. It also discusses degree theory, nonlinear matrix equations, control theory, differential and integral equations, and inclusions. The book presents surjectivity theorems, variational inequalities, stochastic game theory and mathematical biology, along with a large number of applications of these theories in various other disciplines. Nonlinear analysis is characterised by its applications in numerous interdisciplinary fields, ranging from engineering to space science, hydromechanics to astrophysics, chemistry to biology, theoretical mechanics to biomechanics and economics to stochastic game theory. Organised into ten chapters, the book shows the elegance of the subject and its deep-rooted concepts and techniques, which provide the tools for developing more realistic and accurate models for ...

An Laudau-Lifschitz theory based algorithm on calculating post-buckling configuration of a rod buckling in elastic media

Science.gov (United States)

Huang, Shicheng; Tan, Likun; Hu, Nan; Grover, Hannah; Chu, Kevin; Chen, Zi

This reserach introduces a new numerical approach of calculating the post-buckling configuration of a thin rod embedded in elastic media. The theoretical base is the governing ODEs describing the balance of forces and moments, the length conservation, and the physics of bending and twisting by Laudau and Lifschitz. The numerical methods applied in the calculation are continuation method and Newton's method of iteration in combination with spectrum method. To the authors' knowledge, it is the first trial of directly applying the L-L theory to numerically studying the phenomenon of rod buckling in elastic medium. This method accounts for nonlinearity of geometry, thus is capable of calculating large deformation. The stability of this method is another advantage achieved by expressing the governing equations in a set of first-order derivative form. The wave length, amplitude, and decay effect all agree with the experiment without any further assumptions. This program can be applied to different occasions with varying stiffness of the elastic medai and rigidity of the rod.

Nonlinear continuum mechanics and large inelastic deformations

CERN Document Server

Dimitrienko, Yuriy I

2010-01-01

This book provides a rigorous axiomatic approach to continuum mechanics under large deformation. In addition to the classical nonlinear continuum mechanics - kinematics, fundamental laws, the theory of functions having jump discontinuities across singular surfaces, etc. - the book presents the theory of co-rotational derivatives, dynamic deformation compatibility equations, and the principles of material indifference and symmetry, all in systematized form. The focus of the book is a new approach to the formulation of the constitutive equations for elastic and inelastic continua under large deformation. This new approach is based on using energetic and quasi-energetic couples of stress and deformation tensors. This approach leads to a unified treatment of large, anisotropic elastic, viscoelastic, and plastic deformations. The author analyses classical problems, including some involving nonlinear wave propagation, using different models for continua under large deformation, and shows how different models lead t...

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...

Nonlinear optimal control theory

CERN Document Server

Berkovitz, Leonard David

2012-01-01

Nonlinear Optimal Control Theory presents a deep, wide-ranging introduction to the mathematical theory of the optimal control of processes governed by ordinary differential equations and certain types of differential equations with memory. Many examples illustrate the mathematical issues that need to be addressed when using optimal control techniques in diverse areas. Drawing on classroom-tested material from Purdue University and North Carolina State University, the book gives a unified account of bounded state problems governed by ordinary, integrodifferential, and delay systems. It also dis

Riemann-Cartan geometry of nonlinear disclination mechanics

KAUST Repository

Yavari, A.; Goriely, A.

2012-01-01

In the continuous theory of defects in nonlinear elastic solids, it is known that a distribution of disclinations leads, in general, to a non-trivial residual stress field. To study this problem, we consider the particular case of determining

Nonlinearity and disorder: Theory and applications

DEFF Research Database (Denmark)

Bang, Ole; Sørensen, Mads Peter

Proceedings of the NATO Advanced Research Workshop (ARW) entitled Nonlinearity and Disorder: Theory and Applications, held in Tashkent, Uzbekistan, October 2-6, 2001. Phenomena of coherent structures in nonlinear systems and disorder are considered opposite in nature. For example one of the most...... of the photorefractive solitons. Another very fast growing area induced by the technological development is statistical phenomena in nonlinear pulse propagation in optical fibers. Intrinsic randomness of existing optical communication systems has an important impact on the performance of planned soliton communication...

Modeling Pseudo-elastic Behavior of Springback

International Nuclear Information System (INIS)

Xia, Z. Cedric

2005-01-01

constant. In the context of this investigation we refer psuedoelastic behavior in the most general sense as any deviation from linearity in the unloading curve. The non-linearity leads to a hysteresis loop upon reloading. The approach is based on the non-conventional theory with a vanishing elastic region as advanced by Dafalias and Popov. The treatment is purely phenomenological where we don't distinguish between macroscopic plasticity and micro-plasticity. The macroscopic uniaxial stress-strain curve is used to define effective plastic response in the same manner as classical plasticity theory except that the nonlinearity during unloading and reloading are incorporated into plasticity. It is shown that such models can be easily formulated within the context of elastoplasticity without violating any physical mechanisms of deformation. Springback for a plane strain bending model is used to demonstrate the potential effect if such a model is applied

Non-linear elasticity of extracellular matrices enables contractile cells to communicate local position and orientation.

Directory of Open Access Journals (Sweden)

Jessamine P Winer

2009-07-01

Full Text Available Most tissue cells grown in sparse cultures on linearly elastic substrates typically display a small, round phenotype on soft substrates and become increasingly spread as the modulus of the substrate increases until their spread area reaches a maximum value. As cell density increases, individual cells retain the same stiffness-dependent differences unless they are very close or in molecular contact. On nonlinear strain-stiffening fibrin gels, the same cell types become maximally spread even when the low strain elastic modulus would predict a round morphology, and cells are influenced by the presence of neighbors hundreds of microns away. Time lapse microscopy reveals that fibroblasts and human mesenchymal stem cells on fibrin deform the substrate by several microns up to five cell lengths away from their plasma membrane through a force limited mechanism. Atomic force microscopy and rheology confirm that these strains locally and globally stiffen the gel, depending on cell density, and this effect leads to long distance cell-cell communication and alignment. Thus cells are acutely responsive to the nonlinear elasticity of their substrates and can manipulate this rheological property to induce patterning.

FEATURES APPLICATION CIRCUIT MOMENT FINITE ELEMENT (MSSE NONLINEAR CALCULATIONS OF PLATES AND SHELLS

Directory of Open Access Journals (Sweden)

Bazhenov V.A.

2014-06-01

Full Text Available Based MSSE created shell CE general type, which allows you to analyze the stress-strain state of axisymmetrical shells and plates in problems of physical and geometric nonlinearity. The principal nonlinear elasticity theory, algorithms for solving systems of nonlinear equations for determining the temperature and plastic deformation.

Nonlinear elastic inclusions in isotropic solids

KAUST Repository

Yavari, A.

2013-10-16

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 be described by distributed eigenstrains. Geometrically, the eigenstrains define a Riemannian 3-manifold in which the body is stress-free by construction. The problem of residual stress calculation is then reduced to finding a mapping from the Riemannian material manifold to the ambient Euclidean space. Using this construction, we find the residual stress fields of three model systems with spherical and cylindrical symmetries in both incompressible and compressible isotropic elastic solids. In particular, we consider a finite spherical ball with a spherical inclusion with uniform pure dilatational eigenstrain and we show that the stress in the inclusion is uniform and hydrostatic. We also show how singularities in the stress distribution emerge as a consequence of a mismatch between radial and circumferential eigenstrains at the centre of a sphere or the axis of a cylinder.

Two-velocity elasticity theory and facet growth

OpenAIRE

Andreev, A. F.; Melnikovsky, L. A.

2002-01-01

We explain the linear growth of smooth solid helium facets by the presence of lattice point defects. To implement this task, the framework of very general two-velocity elasticity theory equations is developed. Boundary conditions for these equations for various surface types are derived. We also suggest additional experiments to justify the concept.

The Khachaturyan theory of elastic inclusions: Recollections and results

Science.gov (United States)

Morris, J. W.

2010-01-01

In keeping with the assignment, this paper has two parts. The first is a personal recollection of my interactions with Professor Armen Khachaturyan since he first visited Berkeley in the 1970s. The second part is a review of the Khachaturyan formulation of the theory of elastic inclusions, with emphasis on results found since his classic monograph on the Theory of Structural Transformations in Solids [Wiley, New York, 1983]. The focus here is on the shapes and habits of coherent inclusions. The basic theory is presented, briefly, to exhibit Khachaturyan's results for the strain and energy within a coherent inclusion and show that the elastic energy is minimal for a thin-plate morphology with a definite habit. The preferred habit of the thin-plate inclusion is then discussed and computed for inclusions with dyadic strain (including the dislocation loop) and coherent inclusions with orthorhombic or simpler symmetry. This is followed by a discussion of the evolution of precipitate shape during coarsening, including the theory of the spontaneous splitting of coarsening precipitates and the development of octahedral or tetrahedral shapes.

Frequency tuning, nonlinearities and mode coupling in circular mechanical graphene resonators

International Nuclear Information System (INIS)

Eriksson, A M; Midtvedt, D; Croy, A; Isacsson, A

2013-01-01

We study circular nanomechanical graphene resonators by means of continuum elasticity theory, treating them as membranes. We derive dynamic equations for the flexural mode amplitudes. Due to the geometrical nonlinearity the mode dynamics can be modeled by coupled Duffing equations. By solving the Airy stress problem we obtain analytic expressions for the eigenfrequencies and nonlinear coefficients as functions of the radius, suspension height, initial tension, back-gate voltage and elastic constants, which we compare with finite element simulations. Using perturbation theory, we show that it is necessary to include the effects of the non-uniform stress distribution for finite deflections. This correctly reproduces the spectrum and frequency tuning of the resonator, including frequency crossings. (paper)

Using strong nonlinearity and high-frequency vibrations to control effective properties of discrete elastic waveguides

DEFF Research Database (Denmark)

Lazarov, Boyan Stefanov; Thomsen, Jon Juel; Snaeland, Sveinn Orri

2008-01-01

The aim of this article is to investigate how highfrequency (HF) excitation, combined with strong nonlinear elastic material behavior, influences the effective material or structural properties for low-frequency excitation and wave propagation. The HF effects are demonstrated on discrete linear s...

Experimental Observation of Two Features Unexpected from the Classical Theories of Rubber Elasticity

Science.gov (United States)

Nishi, Kengo; Fujii, Kenta; Chung, Ung-il; Shibayama, Mitsuhiro; Sakai, Takamasa

2017-12-01

Although the elastic modulus of a Gaussian chain network is thought to be successfully described by classical theories of rubber elasticity, such as the affine and phantom models, verification experiments are largely lacking owing to difficulties in precisely controlling of the network structure. We prepared well-defined model polymer networks experimentally, and measured the elastic modulus G for a broad range of polymer concentrations and connectivity probabilities, p . In our experiment, we observed two features that were distinct from those predicted by classical theories. First, we observed the critical behavior G ˜|p -pc|1.95 near the sol-gel transition. This scaling law is different from the prediction of classical theories, but can be explained by analogy between the electric conductivity of resistor networks and the elasticity of polymer networks. Here, pc is the sol-gel transition point. Furthermore, we found that the experimental G -p relations in the region above C* did not follow the affine or phantom theories. Instead, all the G /G0-p curves fell onto a single master curve when G was normalized by the elastic modulus at p =1 , G0. We show that the effective medium approximation for Gaussian chain networks explains this master curve.

Metamaterials-based sensor to detect and locate nonlinear elastic sources

Energy Technology Data Exchange (ETDEWEB)

Gliozzi, Antonio S.; Scalerandi, Marco [Department of Applied Science and Technology, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino (Italy); Miniaci, Marco; Bosia, Federico [Department of Physics, University of Torino, Via Pietro Giuria 1, 10125 Torino (Italy); Pugno, Nicola M. [Laboratory of Bio-Inspired and Graphene Nanomechanics, Department of Civil, Environmental and Mechanical Engineering, University of Trento, Via Mesiano 77, 38123 Trento (Italy); Center for Materials and Microsystems, Fondazione Bruno Kessler, Via Sommarive 18, 38123 Povo (Trento) (Italy); School of Engineering and Materials Science, Queen Mary University of London, Mile End Road, London E1 4NS (United Kingdom)

2015-10-19

In recent years, acoustic metamaterials have attracted increasing scientific interest for very diverse technological applications ranging from sound abatement to ultrasonic imaging, mainly due to their ability to act as band-stop filters. At the same time, the concept of chaotic cavities has been recently proposed as an efficient tool to enhance the quality of nonlinear signal analysis, particularly in the ultrasonic/acoustic case. The goal of the present paper is to merge the two concepts in order to propose a metamaterial-based device that can be used as a natural and selective linear filter for the detection of signals resulting from the propagation of elastic waves in nonlinear materials, e.g., in the presence of damage, and as a detector for the damage itself in time reversal experiments. Numerical simulations demonstrate the feasibility of the approach and the potential of the device in providing improved signal-to-noise ratios and enhanced focusing on the defect locations.

Metamaterials-based sensor to detect and locate nonlinear elastic sources

International Nuclear Information System (INIS)

Gliozzi, Antonio S.; Scalerandi, Marco; Miniaci, Marco; Bosia, Federico; Pugno, Nicola M.

2015-01-01

In recent years, acoustic metamaterials have attracted increasing scientific interest for very diverse technological applications ranging from sound abatement to ultrasonic imaging, mainly due to their ability to act as band-stop filters. At the same time, the concept of chaotic cavities has been recently proposed as an efficient tool to enhance the quality of nonlinear signal analysis, particularly in the ultrasonic/acoustic case. The goal of the present paper is to merge the two concepts in order to propose a metamaterial-based device that can be used as a natural and selective linear filter for the detection of signals resulting from the propagation of elastic waves in nonlinear materials, e.g., in the presence of damage, and as a detector for the damage itself in time reversal experiments. Numerical simulations demonstrate the feasibility of the approach and the potential of the device in providing improved signal-to-noise ratios and enhanced focusing on the defect locations

A new integrability theory for certain nonlinear physical problems

International Nuclear Information System (INIS)

Berger, M.S.

1993-01-01

A new mathematically sound integrability theory for certain nonlinear problems defined by ordinary or partial differential equations is defined. The new theory works in an arbitrary finite number of space dimensions. Moreover, if a system is integrable in the new sense described here, it has a remarkable stability property that distinguishes if from any previously known integrability ideas. The new theory proceeds by establishing a ''global normal form'' for the problem at hand. This normal form holds subject to canonical coordinate transformations, extending such classical ideas by using new nonlinear methods of infinite dimensional functional analysis. The global normal form in question is related to the mathematical theory of singularities of mappings of H. Whitney and R. Thom extended globally and form finite to infinite dimensions. Thus bifurcation phenomena are naturally included in the new integrability theory. Typical examples include the classically nonintegrable Riccati equation, certain non-Euclidean mean field theories, certain parabolic reaction diffusion equations and the hyperbolic nonlinear telegrapher's equation. (Author)

Nonlinear Lorentz-invariant theory of gravitation

International Nuclear Information System (INIS)

Petry, W.

1976-01-01

A nonlinear Lorentz-invariant theory of gravitation and a Lorentz-invariant Hamiltonian for a particle with spin in the gravitational field are developed. The equations of motions are studied. The theory is applied to the three well known tests of General Relativity. In the special case of the red shift of spectral lines and of the deflection of light, the theory gives the same results as the General Theory of Relativity, whereas in the case of the perihelion of the Mercury, the theory gives 40,3'', in good agreement with experimental results of Dicke. (author)

Nonlinear isochrones in murine left ventricular pressure-volume loops: how well does the time-varying elastance concept hold?

Science.gov (United States)

Claessens, T E; Georgakopoulos, D; Afanasyeva, M; Vermeersch, S J; Millar, H D; Stergiopulos, N; Westerhof, N; Verdonck, P R; Segers, P

2006-04-01

The linear time-varying elastance theory is frequently used to describe the change in ventricular stiffness during the cardiac cycle. The concept assumes that all isochrones (i.e., curves that connect pressure-volume data occurring at the same time) are linear and have a common volume intercept. Of specific interest is the steepest isochrone, the end-systolic pressure-volume relationship (ESPVR), of which the slope serves as an index for cardiac contractile function. Pressure-volume measurements, achieved with a combined pressure-conductance catheter in the left ventricle of 13 open-chest anesthetized mice, showed a marked curvilinearity of the isochrones. We therefore analyzed the shape of the isochrones by using six regression algorithms (two linear, two quadratic, and two logarithmic, each with a fixed or time-varying intercept) and discussed the consequences for the elastance concept. Our main observations were 1) the volume intercept varies considerably with time; 2) isochrones are equally well described by using quadratic or logarithmic regression; 3) linear regression with a fixed intercept shows poor correlation (R(2) volume intercept of the ESPVR. In conclusion, the linear time-varying elastance fails to provide a sufficiently robust model to account for changes in pressure and volume during the cardiac cycle in the mouse ventricle. A new framework accounting for the nonlinear shape of the isochrones needs to be developed.

Riemann–Cartan Geometry of Nonlinear Dislocation Mechanics

KAUST Repository

Yavari, Arash

2012-03-09

We present a geometric theory of nonlinear solids with distributed dislocations. In this theory the material manifold-where the body is stress free-is a Weitzenböck manifold, that is, a manifold with a flat affine connection with torsion but vanishing non-metricity. Torsion of the material manifold is identified with the dislocation density tensor of nonlinear dislocation mechanics. Using Cartan\\'s moving frames we construct the material manifold for several examples of bodies with distributed dislocations. We also present non-trivial examples of zero-stress dislocation distributions. More importantly, in this geometric framework we are able to calculate the residual stress fields, assuming that the nonlinear elastic body is incompressible. We derive the governing equations of nonlinear dislocation mechanics covariantly using balance of energy and its covariance. © 2012 Springer-Verlag.

A Study of Nonlinear Elasticity Effects on Permeability of Stress Sensitive Shale Rocks Using an Improved Coupled Flow and Geomechanics Model: A Case Study of the Longmaxi Shale in China

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Chenji Wei

2018-02-01

Full Text Available Gas transport in shale gas reservoirs is largely affected by rock properties such as permeability. These properties are often sensitive to the in-situ stress state changes. Accurate modeling of shale gas transport in shale reservoir rocks considering the stress sensitive effects on rock petrophysical properties is important for successful shale gas extraction. Nonlinear elasticity in stress sensitive reservoir rocks depicts the nonlinear stress-strain relationship, yet it is not thoroughly studied in previous reservoir modeling works. In this study, an improved coupled flow and geomechanics model that considers nonlinear elasticity is proposed. The model is based on finite element methods, and the nonlinear elasticity in the model is validated with experimental data on shale samples selected from the Longmaxi Formation in Sichuan Basin China. Numerical results indicate that, in stress sensitive shale rocks, nonlinear elasticity affects shale permeability, shale porosity, and distributions of effective stress and pore pressure. Elastic modulus change is dependent on not only in-situ stress state but also stress history path. Without considering nonlinear elasticity, the modeling of shale rock permeability in Longmaxi Formation can overestimate permeability values by 1.6 to 53 times.

An analysis of hypercritical states in elastic and inelastic systems

Science.gov (United States)

Kowalczk, Maciej

The author raises a wide range of problems whose common characteristic is an analysis of hypercritical states in elastic and inelastic systems. the article consists of two basic parts. The first part primarily discusses problems of modelling hypercritical states, while the second analyzes numerical methods (so-called continuation methods) used to solve non-linear problems. The original approaches for modelling hypercritical states found in this article include the combination of plasticity theory and an energy condition for cracking, accounting for the variability and cyclical nature of the forms of fracture of a brittle material under a die, and the combination of plasticity theory and a simplified description of the phenomenon of localization along a discontinuity line. The author presents analytical solutions of three non-linear problems for systems made of elastic/brittle/plastic and elastic/ideally plastic materials. The author proceeds to discuss the analytical basics of continuation methods and analyzes the significance of the parameterization of non-linear problems, provides a method for selecting control parameters based on an analysis of the rank of a rectangular matrix of a uniform system of increment equations, and also provides a new method for selecting an equilibrium path originating from a bifurcation point. The author provides a general outline of continuation methods based on an analysis of the rank of a matrix of a corrective system of equations. The author supplements his theoretical solutions with numerical solutions of non-linear problems for rod systems and problems of the plastic disintegration of a notched rectangular plastic plate.

Mathematical theory of elasticity of quasicrystals and its applications

CERN Document Server

Fan, Tianyou

2011-01-01

This book presents a clear-cut, strict and systematic mathematical overview of the continuum mechanics of novel materials, condensed matter physics and partial differential equations, and explores the mathematical theory of elasticity of quasicrystals.

Mathematical theory of elasticity of quasicrystals and its applications

CERN Document Server

Fan, Tian-You

2016-01-01

This interdisciplinary work on condensed matter physics, the continuum mechanics of novel materials, and partial differential equations, discusses the mathematical theory of elasticity and hydrodynamics of quasicrystals, as well as its applications. By establishing new partial differential equations of higher order and their solutions under complicated boundary value and initial value conditions, the theories developed here dramatically simplify the solution of complex elasticity problems. Comprehensive and detailed mathematical derivations guide readers through the work. By combining theoretical analysis and experimental data, mathematical studies and practical applications, readers will gain a systematic, comprehensive and in-depth understanding of condensed matter physics, new continuum mechanics and applied mathematics. This new edition covers the latest developments in quasicrystal studies. In particular, it pays special attention to the hydrodynamics, soft-matter quasicrystals, and the Poisson bracket m...

The theory of elastic waves and waveguides

CERN Document Server

Miklowitz, J

1984-01-01

The primary objective of this book is to give the reader a basic understanding of waves and their propagation in a linear elastic continuum. The studies of elastodynamic theory and its application to fundamental value problems should prepare the reader to tackle many physical problems of general interest in engineering and geophysics, and of particular interest in mechanics and seismology.

A Geometrically—Nonlinear Plate Theory 12

Institute of Scientific and Technical Information of China (English)

AlbertC.J.LUO

1999-01-01

An approximate plate theory developed in this paper is based on an assumed displacement field,the strains described by a Taylor series in the normal distance from the middle surface,the exact strains of the middle surface and the equations of equilibrium governing the exact configuration of the deformed middle surface,In this theory the exact geometry of the deformed middle surface is used to derive the strains and equilibrium of the plate.Application of this theory does not depend on the constitutive law.THis theory can reduce to some existing nonlinear theories through imposition of constraints.

Hydro-elastic complementarity in black branes at large D

Energy Technology Data Exchange (ETDEWEB)

Emparan, Roberto [ICREA, Passeig Lluís Companys 23, E-08010 Barcelona (Spain); Departament de Física Fonamental, Institut de Ciències del Cosmos, Universitat de Barcelona,Martí i Franquès 1, E-08028 Barcelona (Spain); Izumi, Keisuke; Luna, Raimon [Departament de Física Fonamental, Institut de Ciències del Cosmos, Universitat de Barcelona,Martí i Franquès 1, E-08028 Barcelona (Spain); Suzuki, Ryotaku [Department of Physics, Osaka City University, Osaka 558-8585 (Japan); Tanabe, Kentaro [Theory Center, Institute of Particles and Nuclear Studies, KEK,Tsukuba, Ibaraki, 305-0801 (Japan)

2016-06-21

We obtain the effective theory for the non-linear dynamics of black branes — both neutral and charged, in asymptotically flat or Anti-deSitter spacetimes — to leading order in the inverse-dimensional expansion. We find that black branes evolve as viscous fluids, but when they settle down they are more naturally viewed as solutions of an elastic soap-bubble theory. The two views are complementary: the same variable is regarded in one case as the energy density of the fluid, in the other as the deformation of the elastic membrane. The large-D theory captures finite-wavelength phenomena beyond the conventional reach of hydrodynamics. For asymptotically flat charged black branes (either Reissner-Nordstrom or p-brane-charged black branes) it yields the non-linear evolution of the Gregory-Laflamme instability at large D and its endpoint at stable non-uniform black branes. For Reissner-Nordstrom AdS black branes we find that sound perturbations do not propagate (have purely imaginary frequency) when their wavelength is below a certain charge-dependent value. We also study the polarization of black branes induced by an external electric field.

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.

Effect of reorientation of anisotropic point defects on relaxation of crystal elastic coefficients of high order

International Nuclear Information System (INIS)

Topchyan, I.I.; Dokhner, R.D.

1977-01-01

The effect of reorientation of anisotropic point defects in uniform fields of elastic stresses on the relaxation of the elastic coefficients of a crystal was investigated in the nonlinear elasticity theory approximation. In calculating the interaction of point defects with elastic-stress fields was taken into consideration. The expression for the relaxations of the elasticity coefficients are obtained in an analytical form. The relaxation of the second-order elasticity coefficients is due to the dimentional interaction of a point defect with an applied-stress field, whereas the relaxation of the higher-order elasticity coefficients is determined both by dimentional and module effects

Scattering theory of nonlinear thermoelectricity in quantum coherent conductors.

Science.gov (United States)

Meair, Jonathan; Jacquod, Philippe

2013-02-27

We construct a scattering theory of weakly nonlinear thermoelectric transport through sub-micron scale conductors. The theory incorporates the leading nonlinear contributions in temperature and voltage biases to the charge and heat currents. Because of the finite capacitances of sub-micron scale conducting circuits, fundamental conservation laws such as gauge invariance and current conservation require special care to be preserved. We do this by extending the approach of Christen and Büttiker (1996 Europhys. Lett. 35 523) to coupled charge and heat transport. In this way we write relations connecting nonlinear transport coefficients in a manner similar to Mott's relation between the linear thermopower and the linear conductance. We derive sum rules that nonlinear transport coefficients must satisfy to preserve gauge invariance and current conservation. We illustrate our theory by calculating the efficiency of heat engines and the coefficient of performance of thermoelectric refrigerators based on quantum point contacts and resonant tunneling barriers. We identify, in particular, rectification effects that increase device performance.

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.)

Theory of Nonlinear Dispersive Waves and Selection of the Ground State

International Nuclear Information System (INIS)

Soffer, A.; Weinstein, M.I.

2005-01-01

A theory of time-dependent nonlinear dispersive equations of the Schroedinger or Gross-Pitaevskii and Hartree type is developed. The short, intermediate and large time behavior is found, by deriving nonlinear master equations (NLME), governing the evolution of the mode powers, and by a novel multitime scale analysis of these equations. The scattering theory is developed and coherent resonance phenomena and associated lifetimes are derived. Applications include Bose-Einstein condensate large time dynamics and nonlinear optical systems. The theory reveals a nonlinear transition phenomenon, 'selection of the ground state', and NLME predicts the decay of excited state, with half its energy transferred to the ground state and half to radiation modes. Our results predict the recent experimental observations of Mandelik et al. in nonlinear optical waveguides

Elastic properties of Gum Metal

International Nuclear Information System (INIS)

Kuramoto, Shigeru; Furuta, Tadahiko; Hwang, Junghwan; Nishino, Kazuaki; Saito, Takashi

2006-01-01

In situ X-ray diffraction measurements under tensile loading and dynamic mechanical analysis were performed to investigate the mechanisms of elastic deformation in Gum Metal. Tensile stress-strain curves for Gum Metal indicate that cold working substantially decreases the elastic modulus while increasing the yield strength, thereby confirming nonlinearity in the elastic range. The gradient of each curve decreased continuously to about one-third its original value near the elastic limit. As a result of this decrease in elastic modulus and nonlinearity, elastic deformability reaches 2.5% after cold working. Superelasticity is attributed to stress-induced martensitic transformations, although the large elastic deformation in Gum Metal is not accompanied by a phase transformation

Sensitivity theory for general non-linear algebraic equations with constraints

International Nuclear Information System (INIS)

Oblow, E.M.

1977-04-01

Sensitivity theory has been developed to a high state of sophistication for applications involving solutions of the linear Boltzmann equation or approximations to it. The success of this theory in the field of radiation transport has prompted study of possible extensions of the method to more general systems of non-linear equations. Initial work in the U.S. and in Europe on the reactor fuel cycle shows that the sensitivity methodology works equally well for those non-linear problems studied to date. The general non-linear theory for algebraic equations is summarized and applied to a class of problems whose solutions are characterized by constrained extrema. Such equations form the basis of much work on energy systems modelling and the econometrics of power production and distribution. It is valuable to have a sensitivity theory available for these problem areas since it is difficult to repeatedly solve complex non-linear equations to find out the effects of alternative input assumptions or the uncertainties associated with predictions of system behavior. The sensitivity theory for a linear system of algebraic equations with constraints which can be solved using linear programming techniques is discussed. The role of the constraints in simplifying the problem so that sensitivity methodology can be applied is highlighted. The general non-linear method is summarized and applied to a non-linear programming problem in particular. Conclusions are drawn in about the applicability of the method for practical problems

Corrugated Membrane Nonlinear Deformation Process Calculation

Directory of Open Access Journals (Sweden)

A. S. Nikolaeva

2015-01-01

Full Text Available Elastic elements are widely used in instrumentation. They are used to create a particular interference between the parts, for accumulating mechanical energy, as the motion transmission elements, elastic supports, and sensing elements of measuring devices. Device reliability and quality depend on the calculation accuracy of the elastic elements. A corrugated membrane is rather common embodiment of the elastic element.The corrugated membrane properties depend largely on its profile i.e. a generatrix of the meridian surface.Unlike other types of pressure elastic members (bellows, tube spring, the elastic characteristics of which are close to linear, an elastic characteristic of the corrugated membrane (typical movement versus external load is nonlinear. Therefore, the corrugated membranes can be used to measure quantities, nonlinearly related to the pressure (e.g., aircraft air speed, its altitude, pipeline fluid or gas flow rate. Another feature of the corrugated membrane is that significant movements are possible within the elastic material state. However, a significant non-linearity of membrane characteristics leads to severe complicated calculation.This article is aimed at calculating the corrugated membrane to obtain the elastic characteristics and the deformed shape of the membrane meridian, as well as at investigating the processes of buckling. As the calculation model, a thin-walled axisymmetric shell rotation is assumed. The material properties are linearly elastic. We consider a corrugated membrane of sinusoidal profile. The membrane load is a uniform pressure.The algorithm for calculating the mathematical model of an axisymmetric corrugated membrane of constant thickness, based on the Reissner’s theory of elastic thin shells, was realized as the author's program in C language. To solve the nonlinear problem were used a method of changing the subspace of control parameters, developed by S.S., Gavriushin, and a parameter marching method

Finite elements of nonlinear continua

CERN Document Server

Oden, John Tinsley

1972-01-01

Geared toward undergraduate and graduate students, this text extends applications of the finite element method from linear problems in elastic structures to a broad class of practical, nonlinear problems in continuum mechanics. It treats both theory and applications from a general and unifying point of view.The text reviews the thermomechanical principles of continuous media and the properties of the finite element method, and then brings them together to produce discrete physical models of nonlinear continua. The mathematical properties of these models are analyzed, along with the numerical s

Geometric Theory of Reduction of Nonlinear Control Systems

Science.gov (United States)

Elkin, V. I.

2018-02-01

The foundations of a differential geometric theory of nonlinear control systems are described on the basis of categorical concepts (isomorphism, factorization, restrictions) by analogy with classical mathematical theories (of linear spaces, groups, etc.).

On a Geometric Theory of Generalized Chiral Elasticity with Discontinuities

Directory of Open Access Journals (Sweden)

Suhendro I.

2008-01-01

Full Text Available In this work we develop, in a somewhat extensive manner, a geometric theory of chiral elasticity which in general is endowed with geometric discontinuities (sometimes referred to as defects. By itself, the present theory generalizes both Cosserat and void elasticity theories to a certain extent via geometrization as well as by taking intoaccount the action of the electromagnetic field, i.e., the incorporation of the electromagnetic field into the description of the so-called microspin (chirality also forms the underlying structure of this work. As we know, the description of the electromagnetic field as a unified phenomenon requires four-dimensional space-time rather than three-dimensional space as its background. For this reason we embed the three-dimensional material space in four-dimensional space-time. This way, the electromagnetic spin is coupled to the non-electromagnetic microspin, both being parts of the completemicrospin to be added to the macrospin in the full description of vorticity. In short, our objective is to generalize the existing continuum theories by especially describing microspin phenomena in a fully geometric way.

The elasticity and failure of fluid-filled cellular solids: Theory and experiment

Science.gov (United States)

Warner, M.; Thiel, B. L.; Donald, A. M.

2000-02-01

We extend and apply theories of filled foam elasticity and failure to recently available data on foods. The predictions of elastic modulus and failure mode dependence on internal pressure and on wall integrity are borne out by photographic evidence of distortion and failure under compressive loading and under the localized stress applied by a knife blade, and by mechanical data on vegetables differing only in their turgor pressure. We calculate the dry modulus of plate-like cellular solids and the cross over between dry-like and fully fluid-filled elastic response. The bulk elastic properties of limp and aging cellular solids are calculated for model systems and compared with our mechanical data, which also show two regimes of response. The mechanics of an aged, limp beam is calculated, thus offering a practical procedure for comparing experiment and theory. This investigation also thereby offers explanations of the connection between turgor pressure and crispness and limpness of cellular materials.

The elasticity and failure of fluid-filled cellular solids: theory and experiment.

Science.gov (United States)

Warner, M; Thiel, B L; Donald, A M

2000-02-15

We extend and apply theories of filled foam elasticity and failure to recently available data on foods. The predictions of elastic modulus and failure mode dependence on internal pressure and on wall integrity are borne out by photographic evidence of distortion and failure under compressive loading and under the localized stress applied by a knife blade, and by mechanical data on vegetables differing only in their turgor pressure. We calculate the dry modulus of plate-like cellular solids and the cross over between dry-like and fully fluid-filled elastic response. The bulk elastic properties of limp and aging cellular solids are calculated for model systems and compared with our mechanical data, which also show two regimes of response. The mechanics of an aged, limp beam is calculated, thus offering a practical procedure for comparing experiment and theory. This investigation also thereby offers explanations of the connection between turgor pressure and crispness and limpness of cellular materials.

Nonlinear theory of the free-electron laser

International Nuclear Information System (INIS)

Chian, A.C.-L.; Padua Brito Serbeto, A. de.

1984-01-01

A theory of Raman free-electron laser using a circularly polarized electromagnetic pump is investigated. Coupled wave equations that describe both linear and nonlinear evolution of stimulated Raman scattering are derived. The dispersion relation and the growth rate for the parametric instability are obtained. Nonlinear processes that may lead to saturation of the free-electron laser are discussed. (Author) [pt

A numerical homogenization method for heterogeneous, anisotropic elastic media based on multiscale theory

KAUST Repository

Gao, Kai; Chung, Eric T.; Gibson, Richard L.; Fu, Shubin; Efendiev, Yalchin R.

2015-01-01

The development of reliable methods for upscaling fine-scale models of elastic media has long been an important topic for rock physics and applied seismology. Several effective medium theories have been developed to provide elastic parameters

Nonlinear transport theory in the metal with tunnel barrier

Science.gov (United States)

Zubov, E. E.

2018-02-01

Within the framework of the scattering matrix formalism, the nonlinear Kubo theory for electron transport in the metal with a tunnel barrier has been considered. A general expression for the mean electrical current was obtained. It significantly simplifies the calculation of nonlinear contributions to the conductivity of various hybrid structures. In the model of the tunnel Hamiltonian, all linear and nonlinear contributions to a mean electrical current are evaluated. The linear approximation agrees with results of other theories. For effective barrier transmission ?, the ballistic transport is realised with a value of the Landauer conductivity equal to ?.

Role of interstitial atoms in the microstructure and non-linear elastic deformation behavior of Ti–Nb alloy

Energy Technology Data Exchange (ETDEWEB)

Tahara, Masaki [Division of Materials Science, University of Tsukuba, Tsukuba, Ibaraki 305-8573 (Japan); Precision and Intelligence Laboratory, Tokyo Institute of Technology, Yokohama 226-8503 (Japan); Kim, Hee Young, E-mail: heeykim@ims.tsukuba.ac.jp [Division of Materials Science, University of Tsukuba, Tsukuba, Ibaraki 305-8573 (Japan); Inamura, Tomonari; Hosoda, Hideki [Precision and Intelligence Laboratory, Tokyo Institute of Technology, Yokohama 226-8503 (Japan); Miyazaki, Shuichi, E-mail: miyazaki@ims.tsukuba.ac.jp [Division of Materials Science, University of Tsukuba, Tsukuba, Ibaraki 305-8573 (Japan); Center of Excellence for Advanced Materials Research, King Abdulaziz University, P.O. Box 80203, Jeddah 21589 (Saudi Arabia); School of Materials Science and Engineering and ERI, Gyeongsang National University, 900 Gazwadong, Jinju, Gyeongnam 660-701 (Korea, Republic of)

2013-11-15

Highlights: ► {110}{sub β}〈11{sup ¯}0〉{sub β} transverse type lattice modulation is confirmed in β phase. ► Nanosized modulated region (nanodomain) distributes homogeneously and randomly. ► Nanodomains act as obstacles against the long-ranged martensitic transformation. ► The origin of non-linear elastic deformation behavior is the continuous increase in lattice distortion strain of the favorable nanodomain variant during tensile deformation. -- Abstract: In order to clarify the effect of interstitial atoms on the non-linear elastic deformation behavior of the Ti–Nb alloy, the microstructure of (Ti–26Nb)–1.0O alloy was closely investigated by transmission electron microscope (TEM) and in situ X-ray diffraction (XRD) measurements. The 〈1 1 0〉{sub β}* rel rods and {1 1 1}{sub β}* rel planes were observed in a reciprocal space for the (Ti–26Nb)–1.0O alloy. Their origin was {110}{sub β}〈11{sup ¯}0〉{sub β} transverse type lattice modulation generated by oxygen atoms. Nanosized modulated domain structure (nanodomain) distributed homogeneously and randomly in the β phase and acted as obstacles for the long-ranged martensitic transformation in the (Ti–26Nb)–1.0O alloy. The non-linear elastic strain of the (Ti–26Nb)–1.0O alloy was generated by the continuous increase in lattice distortion strain of the favorable nanodomain variant during tensile deformation.

Role of interstitial atoms in the microstructure and non-linear elastic deformation behavior of Ti–Nb alloy

International Nuclear Information System (INIS)

Tahara, Masaki; Kim, Hee Young; Inamura, Tomonari; Hosoda, Hideki; Miyazaki, Shuichi

2013-01-01

Highlights: ► {110} β 〈11 ¯ 0〉 β transverse type lattice modulation is confirmed in β phase. ► Nanosized modulated region (nanodomain) distributes homogeneously and randomly. ► Nanodomains act as obstacles against the long-ranged martensitic transformation. ► The origin of non-linear elastic deformation behavior is the continuous increase in lattice distortion strain of the favorable nanodomain variant during tensile deformation. -- Abstract: In order to clarify the effect of interstitial atoms on the non-linear elastic deformation behavior of the Ti–Nb alloy, the microstructure of (Ti–26Nb)–1.0O alloy was closely investigated by transmission electron microscope (TEM) and in situ X-ray diffraction (XRD) measurements. The 〈1 1 0〉 β * rel rods and {1 1 1} β * rel planes were observed in a reciprocal space for the (Ti–26Nb)–1.0O alloy. Their origin was {110} β 〈11 ¯ 0〉 β transverse type lattice modulation generated by oxygen atoms. Nanosized modulated domain structure (nanodomain) distributed homogeneously and randomly in the β phase and acted as obstacles for the long-ranged martensitic transformation in the (Ti–26Nb)–1.0O alloy. The non-linear elastic strain of the (Ti–26Nb)–1.0O alloy was generated by the continuous increase in lattice distortion strain of the favorable nanodomain variant during tensile deformation

A method for determination of X-ray elastic constants of materials showing non-linear sin2ψ diagrams and its application to Zn-Ni-alloy electroplate

International Nuclear Information System (INIS)

Sasaki, Toshihiko; Kuramoto, Makoto; Yoshioka, Yasuo.

1990-01-01

This paper describes the method and the experiment for the determination of the x-ray elastic constants of Zn-Ni-alloy electroplate. For this material, the sin 2 ψ method is not adequate to use because this material shows severely curved sin 2 ψ diagrams. Therefore, a new method developed by the authors was explained first. This new method is effective for materials showing nonlinear sin 2 ψ diagrams. Secondly, the experiment was made on the application of this method to the Zn-Ni-alloy electroplate. And it was found out that the experimental data agreed well to the theory of this method. As a result, the following values were obtained as the x-ray elastic constants of the sample measured: (1+ν)/E=8.44 TPa -1 ν/E=2.02 TPa -1 (author)

Theory of elastic thin shells solid and structural mechanics

CERN Document Server

Gol'Denveizer, A L; Dryden, H L

1961-01-01

Theory of Elastic Thin Shells discusses the mathematical foundations of shell theory and the approximate methods of solution. The present volume was originally published in Russian in 1953, and remains the only text which formulates as completely as possible the different sets of basic equations and various approximate methods of shell analysis emphasizing asymptotic integration. The book is organized into five parts. Part I presents the general formulation and equations of the theory of shells, which are based on the well-known hypothesis of the preservation of the normal element. Part II is

Treatise on classical elasticity theory and related problems

CERN Document Server

Teodorescu, Petre P

2013-01-01

Deformable solids have a particularly complex character; mathematical modeling is not always simple and often leads to inextricable difficulties of computation. One of the simplest mathematical models and, at the same time, the most used model, is that of the elastic body – especially the linear one. But, notwithstanding its simplicity, even this model of a real body may lead to great difficulties of computation. The practical importance of a work about the theory of elasticity, which is also an introduction to the mechanics of deformable solids, consists of the use of scientific methods of computation in a domain in which simplified methods are still used. This treatise takes into account the consideration made above, with special attention to the theoretical study of the state of strain and stress of a deformable solid. The book draws on the known specialized literature, as well as the original results of the author and his 50+ years experience as Professor of Mechanics and Elasticity at the University o...

Energy flow theory of nonlinear dynamical systems with applications

CERN Document Server

Xing, Jing Tang

2015-01-01

This monograph develops a generalised energy flow theory to investigate non-linear dynamical systems governed by ordinary differential equations in phase space and often met in various science and engineering fields. Important nonlinear phenomena such as, stabilities, periodical orbits, bifurcations and chaos are tack-led and the corresponding energy flow behaviors are revealed using the proposed energy flow approach. As examples, the common interested nonlinear dynamical systems, such as, Duffing’s oscillator, Van der Pol’s equation, Lorenz attractor, Rössler one and SD oscillator, etc, are discussed. This monograph lights a new energy flow research direction for nonlinear dynamics. A generalised Matlab code with User Manuel is provided for readers to conduct the energy flow analysis of their nonlinear dynamical systems. Throughout the monograph the author continuously returns to some examples in each chapter to illustrate the applications of the discussed theory and approaches. The book can be used as ...

The constructive approach to nonlinear quantum field theory

International Nuclear Information System (INIS)

Segal, I.

1976-01-01

The general situation in nonlinear quantum field theory is outlined. The author discusses a reversion to the canonical quantization formalism and develops it to the maximal level attainable on the basis of advances in the past decade in nonlinear scattering and functional integration. (B.R.H.)

Alternative theories of the non-linear negative mass instability

International Nuclear Information System (INIS)

Channell, P.J.

1974-01-01

A theory non-linear negative mass instability is extended to include resistance. The basic assumption is explained physically and an alternative theory is offered. The two theories are compared computationally. 7 refs., 8 figs

Buckling Analysis for Stiffened Anisotropic Circular Cylinders Based on Sanders Nonlinear Shell Theory

Science.gov (United States)

Nemeth, Michael P.

2014-01-01

Nonlinear and bifurcation buckling equations for elastic, stiffened, geometrically perfect, right-circular cylindrical, anisotropic shells subjected to combined loads are presented that are based on Sanders' shell theory. Based on these equations, a three-parameter approximate Rayleigh-Ritz solution and a classical solution to the buckling problem are presented for cylinders with simply supported edges. Extensive comparisons of results obtained from these solutions with published results are also presented for a wide range of cylinder constructions. These comparisons include laminated-composite cylinders with a wide variety of shell-wall orthotropies and anisotropies. Numerous results are also given that show the discrepancies between the results obtained by using Donnell's equations and variants of Sanders' equations. For some cases, nondimensional parameters are identified and "master" curves are presented that facilitate the concise representation of results.

A generic double-curvature piezoelectric shell energy harvester: Linear/nonlinear theory and applications

Science.gov (United States)

Zhang, X. F.; Hu, S. D.; Tzou, H. S.

2014-12-01

Converting vibration energy to useful electric energy has attracted much attention in recent years. Based on the electromechanical coupling of piezoelectricity, distributed piezoelectric zero-curvature type (e.g., beams and plates) energy harvesters have been proposed and evaluated. The objective of this study is to develop a generic linear and nonlinear piezoelectric shell energy harvesting theory based on a double-curvature shell. The generic piezoelectric shell energy harvester consists of an elastic double-curvature shell and piezoelectric patches laminated on its surface(s). With a current model in the closed-circuit condition, output voltages and energies across a resistive load are evaluated when the shell is subjected to harmonic excitations. Steady-state voltage and power outputs across the resistive load are calculated at resonance for each shell mode. The piezoelectric shell energy harvesting mechanism can be simplified to shell (e.g., cylindrical, conical, spherical, paraboloidal, etc.) and non-shell (beam, plate, ring, arch, etc.) distributed harvesters using two Lamé parameters and two curvature radii of the selected harvester geometry. To demonstrate the utility and simplification procedures, the generic linear/nonlinear shell energy harvester mechanism is simplified to three specific structures, i.e., a cantilever beam case, a circular ring case and a conical shell case. Results show the versatility of the generic linear/nonlinear shell energy harvesting mechanism and the validity of the simplification procedures.

The elastic theory of shells using geometric algebra.

Science.gov (United States)

Gregory, A L; Lasenby, J; Agarwal, A

2017-03-01

We present a novel derivation of the elastic theory of shells. We use the language of geometric algebra, which allows us to express the fundamental laws in component-free form, thus aiding physical interpretation. It also provides the tools to express equations in an arbitrary coordinate system, which enhances their usefulness. The role of moments and angular velocity, and the apparent use by previous authors of an unphysical angular velocity, has been clarified through the use of a bivector representation. In the linearized theory, clarification of previous coordinate conventions which have been the cause of confusion is provided, and the introduction of prior strain into the linearized theory of shells is made possible.

Nonlinear theory of nonstationary low Mach number channel flows of freely cooling nearly elastic granular gases.

Science.gov (United States)

Meerson, Baruch; Fouxon, Itzhak; Vilenkin, Arkady

2008-02-01

We employ hydrodynamic equations to investigate nonstationary channel flows of freely cooling dilute gases of hard and smooth spheres with nearly elastic particle collisions. This work focuses on the regime where the sound travel time through the channel is much shorter than the characteristic cooling time of the gas. As a result, the gas pressure rapidly becomes almost homogeneous, while the typical Mach number of the flow drops well below unity. Eliminating the acoustic modes and employing Lagrangian coordinates, we reduce the hydrodynamic equations to a single nonlinear and nonlocal equation of a reaction-diffusion type. This equation describes a broad class of channel flows and, in particular, can follow the development of the clustering instability from a weakly perturbed homogeneous cooling state to strongly nonlinear states. If the heat diffusion is neglected, the reduced equation becomes exactly soluble, and the solution develops a finite-time density blowup. The blowup has the same local features at singularity as those exhibited by the recently found family of exact solutions of the full set of ideal hydrodynamic equations [I. Fouxon, Phys. Rev. E 75, 050301(R) (2007); I. Fouxon,Phys. Fluids 19, 093303 (2007)]. The heat diffusion, however, always becomes important near the attempted singularity. It arrests the density blowup and brings about previously unknown inhomogeneous cooling states (ICSs) of the gas, where the pressure continues to decay with time, while the density profile becomes time-independent. The ICSs represent exact solutions of the full set of granular hydrodynamic equations. Both the density profile of an ICS and the characteristic relaxation time toward it are determined by a single dimensionless parameter L that describes the relative role of the inelastic energy loss and heat diffusion. At L>1 the intermediate cooling dynamics proceeds as a competition between "holes": low-density regions of the gas. This competition resembles Ostwald

Approximate Stream Function wavemaker theory for highly non-linear waves in wave flumes

DEFF Research Database (Denmark)

Zhang, H.W.; Schäffer, Hemming Andreas

2007-01-01

An approximate Stream Function wavemaker theory for highly non-linear regular waves in flumes is presented. This theory is based on an ad hoe unified wave-generation method that combines linear fully dispersive wavemaker theory and wave generation for non-linear shallow water waves. This is done...... by applying a dispersion correction to the paddle position obtained for non-linear long waves. The method is validated by a number of wave flume experiments while comparing with results of linear wavemaker theory, second-order wavemaker theory and Cnoidal wavemaker theory within its range of application....

On a Geometric Theory of Generalized Chiral Elasticity with Discontinuities

Directory of Open Access Journals (Sweden)

Suhendro I.

2008-01-01

Full Text Available In this work we develop, in a somewhat extensive manner, a geometric theory of chiral elasticity which in general is endowed with geometric discontinuities (sometimes re- ferred to as defects . By itself, the present theory generalizes both Cosserat and void elasticity theories to a certain extent via geometrization as well as by taking into ac- count the action of the electromagnetic field, i.e., the incorporation of the electromag- netic field into the description of the so-called microspin ( chirality also forms the un- derlying structure of this work. As we know, the description of the electromagnetic field as a unified phenomenon requires four-dimensional space-time rather than three- dimensional space as its background. For this reason we embed the three-dimensional material space in four-dimensional space-time. This way, the electromagnetic spin is coupled to the non-electromagnetic microspin, both being parts of the complete mi- crospin to be added to the macrospin in the full description of vorticity. In short, our objective is to generalize the existing continuum theories by especially describing mi- crospin phenomena in a fully geometric way.

Nonlinear nonlocal vibration of embedded DWCNT conveying fluid using shell model

Energy Technology Data Exchange (ETDEWEB)

Ghorbanpour Arani, A., E-mail: aghorban@kashanu.ac.ir [Faculty of Mechanical Engineering, University of Kashan, Kashan (Iran, Islamic Republic of); Institute of Nanoscience and Nanotechnology, University of Kashan, Kashan (Iran, Islamic Republic of); Zarei, M.Sh.; Amir, S.; Khoddami Maraghi, Z. [Faculty of Mechanical Engineering, University of Kashan, Kashan (Iran, Islamic Republic of)

2013-02-01

In this work nonlinear vibration of double-walled carbon nanotube (DWCNT) embedded in an elastic medium and subjected to an axial fluid flow (incompressible and non-viscose) is investigated. The elastic medium is simulated using Pasternak foundation in which adjacent layer interactions are assumed to have been coupled by van der Waals (VdW) force. The higher-order equation of motion is derived using Hamilton's principle and nonlocal-nonlinear shell theory. Galerkin and averaging methods are adopted to solve the higher-order governing equations. Elastic medium, small scale parameter, velocity and fluid density are taken into account to calculate the effects of axial and circumferential wave numbers in this study. Results reveal that increasing circumferential wave number, leads to enhanced nonlinearity. Critical flow velocities of DWCNT are inversely related to the non-local parameter (e{sub 0}a), so that increase in the later lead to reduced critical flow velocities.

On nonequilibrium many-body systems III: nonlinear transport theory

International Nuclear Information System (INIS)

Luzzi, R.; Vasconcellos, A.R.; Algarte, A.C.S.

1986-01-01

A nonlinear transport theory for many-body systems arbitrarily away from equilibrium, based on the nonequilibrium statistical operator (NSO) method, is presented. Nonlinear transport equations for a basis set of dynamical quantities are derived using two equivalent treatments that may be considered far reaching generalizations of the Hilbert-Chapman-Enskog method and Mori's generalized Langevin equations method. The first case is considered in some detail and the general characteristics of the theory are discussed. (Author) [pt

Modeling of nonlinear responses for reciprocal transducers involving polarization switching

DEFF Research Database (Denmark)

Willatzen, Morten; Wang, Linxiang

2007-01-01

Nonlinearities and hysteresis effects in a reciprocal PZT transducer are examined by use of a dynamical mathematical model on the basis of phase-transition theory. In particular, we consider the perovskite piezoelectric ceramic in which the polarization process in the material can be modeled...... by Landau theory for the first-order phase transformation, in which each polarization state is associated with a minimum of the Landau free-energy function. Nonlinear constitutive laws are obtained by using thermodynamical equilibrium conditions, and hysteretic behavior of the material can be modeled...... intrinsically. The time-dependent Ginzburg-Landau theory is used in the parameter identification involving hysteresis effects. We use the Chebyshev collocation method in the numerical simulations. The elastic field is assumed to be coupled linearly with other fields, and the nonlinearity is in the E-D coupling...

Nonlinear Waves In A Stenosed Elastic Tube Filled With Viscous Fluid: Forced Perturbed Korteweg-De Vries Equation

Science.gov (United States)

Gaik*, Tay Kim; Demiray, Hilmi; Tiong, Ong Chee

In the present work, treating the artery as a prestressed thin-walled and long circularly cylindrical elastic tube with a mild symmetrical stenosis and the blood as an incompressible Newtonian fluid, we have studied the pro pagation of weakly nonlinear waves in such a composite medium, in the long wave approximation, by use of the reductive perturbation method. By intro ducing a set of stretched coordinates suitable for the boundary value type of problems and expanding the field variables into asymptotic series of the small-ness parameter of nonlinearity and dispersion, we obtained a set of nonlinear differential equations governing the terms at various order. By solving these nonlinear differential equations, we obtained the forced perturbed Korteweg-de Vries equation with variable coefficient as the nonlinear evolution equation. By use of the coordinate transformation, it is shown that this type of nonlinear evolution equation admits a progressive wave solution with variable wave speed.

Application of perturbation theory to the non-linear vibration analysis of a string including the bending moment effects

International Nuclear Information System (INIS)

Esmaeilzadeh Khadem, S.; Rezaee, M.

2001-01-01

In this paper the large amplitude and non-linear vibration of a string is considered. The initial tension, lateral vibration amplitude, diameter and the modulus of elasticity of the string have main effects on its natural frequencies. Increasing the lateral vibration amplitude makes the assumption of constant initial tension invalid. In this case, therefore, it is impossible to use the classical equation of string with small amplitude transverse motion assumption. On the other hand, by increasing the string diameter, the bending moment effect will increase dramatically, and acts as an impressive restoring moment. Considering the effects of the bending moments, the nonlinear equation governing the large amplitude transverse vibration of a string is derived. The time dependent portion of the governing equation has the from of Duff ing equation is solved using the perturbation theory. The results of the analysis are shown in appropriate graphs, and the natural frequencies of the string due to the non-linear factors are compared with the natural frequencies of the linear vibration os a string without bending moment effects

Nonlinear mechanics of surface growth for cylindrical and spherical elastic bodies

Science.gov (United States)

Sozio, Fabio; Yavari, Arash

2017-01-01

In this paper we formulate the initial-boundary value problems of accreting cylindrical and spherical nonlinear elastic solids in a geometric framework. It is assumed that the body grows as a result of addition of new (stress-free or pre-stressed) material on part of its boundary. We construct Riemannian material manifolds for a growing body with metrics explicitly depending on the history of applied external loads and deformation during accretion and the growth velocity. We numerically solve the governing equilibrium equations in the case of neo-Hookean solids and compare the accretion and residual stresses with those calculated using the linear mechanics of surface growth.

Two-dimensional linear elasticity theory of magneto-electro-elastic plates considering surface and nonlocal effects for nanoscale device applications

Science.gov (United States)

Wang, Wenjun; Li, Peng; Jin, Feng

2016-09-01

A novel two-dimensional linear elastic theory of magneto-electro-elastic (MEE) plates, considering both surface and nonlocal effects, is established for the first time based on Hamilton’s principle and the Lee plate theory. The equations derived are more general, suitable for static and dynamic analyses, and can also be reduced to the piezoelectric, piezomagnetic, and elastic cases. As a specific application example, the influences of the surface and nonlocal effects, poling directions, piezoelectric phase materials, volume fraction, damping, and applied magnetic field (i.e., constant applied magnetic field and time-harmonic applied magnetic field) on the magnetoelectric (ME) coupling effects are first investigated based on the established two-dimensional plate theory. The results show that the ME coupling coefficient has an obvious size-dependent characteristic owing to the surface effects, and the surface effects increase the ME coupling effects significantly when the plate thickness decreases to its critical thickness. Below this critical thickness, the size-dependent effect is obvious and must be considered. In addition, the output power density of a magnetic energy nanoharvester is also evaluated using the two-dimensional plate theory obtained, with the results showing that a relatively larger output power density can be achieved at the nanoscale. This study provides a mathematical tool which can be used to analyze the mechanical properties of nanostructures theoretically and numerically, as well as evaluating the size effect qualitatively and quantitatively.

A general theory of two-wave mixing in nonlinear media

DEFF Research Database (Denmark)

Chi, Mingjun; Huignard, Jean-Pierre; Petersen, Paul Michael

2009-01-01

A general theory of two-wave mixing in nonlinear media is presented. Assuming a gain (or absorption) grating and a refractive index grating are generated because of the nonlinear process in a nonlinear medium, the coupled-wave equations of two-wave mixing are derived based on the Maxwell’s wave e...

Microscopic origin of nonlinear non-affine deformation in metallic glasses

NARCIS (Netherlands)

Zaccone, A.; Schall, P.; Terentjev, E.M.

2014-01-01

The atomic theory of elasticity of amorphous solids, based on the nonaffine response formalism, is extended into the nonlinear stress-strain regime by coupling with the underlying irreversible many-body dynamics. The latter is implemented in compact analytical form using a qualitative method for the

Flutter analysis of an airfoil with multiple nonlinearities and uncertainties

Directory of Open Access Journals (Sweden)

Haitao Liao

2013-09-01

Full Text Available An original method for calculating the limit cycle oscillations of nonlinear aero-elastic system is presented. The problem of determining the maximum vibration amplitude of limit cycle is transformed into a nonlinear optimization problem. The harmonic balance method and the Floquet theory are selected to construct the general nonlinear equality and inequality constraints. The resulting constrained maximization problem is then solved by using the MultiStart algorithm. Finally, the proposed approach is validated and used to analyse the limit cycle oscillations of an airfoil with multiple nonlinearities and uncertainties. Numerical examples show that the coexistence of multiple nonlinearities may lead to low amplitude limit cycle oscillation.

A numerical homogenization method for heterogeneous, anisotropic elastic media based on multiscale theory

KAUST Repository

Gao, Kai

2015-06-05

The development of reliable methods for upscaling fine-scale models of elastic media has long been an important topic for rock physics and applied seismology. Several effective medium theories have been developed to provide elastic parameters for materials such as finely layered media or randomly oriented or aligned fractures. In such cases, the analytic solutions for upscaled properties can be used for accurate prediction of wave propagation. However, such theories cannot be applied directly to homogenize elastic media with more complex, arbitrary spatial heterogeneity. Therefore, we have proposed a numerical homogenization algorithm based on multiscale finite-element methods for simulating elastic wave propagation in heterogeneous, anisotropic elastic media. Specifically, our method used multiscale basis functions obtained from a local linear elasticity problem with appropriately defined boundary conditions. Homogenized, effective medium parameters were then computed using these basis functions, and the approach applied a numerical discretization that was similar to the rotated staggered-grid finite-difference scheme. Comparisons of the results from our method and from conventional, analytical approaches for finely layered media showed that the homogenization reliably estimated elastic parameters for this simple geometry. Additional tests examined anisotropic models with arbitrary spatial heterogeneity in which the average size of the heterogeneities ranged from several centimeters to several meters, and the ratio between the dominant wavelength and the average size of the arbitrary heterogeneities ranged from 10 to 100. Comparisons to finite-difference simulations proved that the numerical homogenization was equally accurate for these complex cases.

Bending of a nonlinear beam reposing on an unilateral foundation

Directory of Open Access Journals (Sweden)

Machalová J.

2011-06-01

Full Text Available This article is going to deal with bending of a nonlinear beam whose mathematical model was proposed by D. Y. Gao in (Gao, D. Y., Nonlinear elastic beam theory with application in contact problems and variational approaches,Mech. Research Communication, 23 (1 1996. The model is based on the Euler-Bernoulli hypothesis and under assumption of nonzero lateral stress component enables moderately large deflections but with small strains. This is here extended by the unilateralWinkler foundation. The attribution unilateral means that the foundation is not connected with the beam. For this problem we demonstrate a mathematical formulation resulting from its natural decomposition which leads to a saddle-point problem with a proper Lagrangian. Next we are concerned with methods of solution for our problem by means of the finite element method as the paper (Gao, D. Y., Nonlinear elastic beam theory with application in contact problems and variational approaches, Mech. Research Communication, 23 (1 1996 has no mention of it. The main alternatives are here the solution of a system of nonlinear nondifferentiable equations or finding of a saddle point through the use of the augmented Lagrangian method. This is illustrated by an example in the final part of the article.

Nonlinear elastic wave spectroscopy in symbiosis with time reversal for localization of defects: TR-NEWS

Czech Academy of Sciences Publication Activity Database

Dos Santos, S.; Vejvodová, Šárka; Převorovský, Zdeněk

2009-01-01

Roč. 19, č. 2 (2009), s. 14-14 ISSN 1213-3825. [NDT in PROGRESS. 12.11.2009-14.11.2009, Praha] R&D Projects: GA ČR GA106/07/1393; GA MPO(CZ) FR-TI1/274 Institutional research plan: CEZ:AV0Z20760514 Keywords : nonlinear elastic wave spectroscopy (NEWS) * ESAM * time reversal (TR) * TR-NEWS imaging * tomography * DORT Subject RIV: BI - Acoustics

Existence of solutions for quasistatic problems of unilateral contact with nonlocal friction for nonlinear elastic materials

Directory of Open Access Journals (Sweden)

Alain Mignot

2005-09-01

Full Text Available This paper shows the existence of a solution of the quasi-static unilateral contact problem with nonlocal friction law for nonlinear elastic materials. We set up a variational incremental problem which admits a solution, when the friction coefficient is small enough, and then by passing to the limit with respect to time we obtain a solution.

Fully coupled heat conduction and deformation analyses of visco-elastic solids

KAUST Repository

Khan, Kamran

2012-04-21

Visco-elastic materials are known for their capability of dissipating energy. This energy is converted into heat and thus changes the temperature of the materials. In addition to the dissipation effect, an external thermal stimulus can also alter the temperature in a viscoelastic body. The rate of stress relaxation (or the rate of creep) and the mechanical and physical properties of visco-elastic materials, such as polymers, vary with temperature. This study aims at understanding the effect of coupling between the thermal and mechanical response that is attributed to the dissipation of energy, heat conduction, and temperature-dependent material parameters on the overall response of visco-elastic solids. The non-linearly viscoelastic constitutive model proposed by Schapery (Further development of a thermodynamic constitutive theory: stress formulation, 1969,Mech. Time-Depend. Mater. 1:209-240, 1997) is used and modified to incorporate temperature- and stress-dependent material properties. This study also formulates a non-linear energy equation along with a dissipation function based on the Gibbs potential of Schapery (Mech. Time-Depend. Mater. 1:209-240, 1997). A numerical algorithm is formulated for analyzing a fully coupled thermo-visco-elastic response and implemented it in a general finite-element (FE) code. The non-linear stress- and temperature-dependent material parameters are found to have significant effects on the coupled thermo-visco-elastic response of polymers considered in this study. In order to obtain a realistic temperature field within the polymer visco-elastic bodies undergoing a non-uniform heat generation, the role of heat conduction cannot be ignored. © Springer Science+Business Media, B. V. 2012.

Boundary value problems of the circular cylinders in the strain-gradient theory of linear elasticity

International Nuclear Information System (INIS)

Kao, B.G.

1979-11-01

Three boundary value problems in the strain-gradient theory of linear elasticity are solved for circular cylinders. They are the twisting of circular cylinder, uniformly pressuring of concentric circular cylinder, and pure-bending of simply connected cylinder. The comparisons of these solutions with the solutions in classical elasticity and in couple-stress theory reveal the differences in the stress fields as well as the apparent stress fields due to the influences of the strain-gradient. These aspects of the strain-gradient theory could be important in modeling the failure behavior of structural materials

Nonlinear dynamical systems for theory and research in ergonomics.

Science.gov (United States)

Guastello, Stephen J

2017-02-01

Nonlinear dynamical systems (NDS) theory offers new constructs, methods and explanations for phenomena that have in turn produced new paradigms of thinking within several disciplines of the behavioural sciences. This article explores the recent developments of NDS as a paradigm in ergonomics. The exposition includes its basic axioms, the primary constructs from elementary dynamics and so-called complexity theory, an overview of its methods, and growing areas of application within ergonomics. The applications considered here include: psychophysics, iconic displays, control theory, cognitive workload and fatigue, occupational accidents, resilience of systems, team coordination and synchronisation in systems. Although these applications make use of different subsets of NDS constructs, several of them share the general principles of the complex adaptive system. Practitioner Summary: Nonlinear dynamical systems theory reframes problems in ergonomics that involve complex systems as they change over time. The leading applications to date include psychophysics, control theory, cognitive workload and fatigue, biomechanics, occupational accidents, resilience of systems, team coordination and synchronisation of system components.

Thermomechanical theory of materials undergoing large elastic and viscoplastic deformation (AWBA development program)

International Nuclear Information System (INIS)

Martin, S.E.; Newman, J.B.

1980-11-01

A thermomechanical theory of large deformation elastic-inelastic material behavior is developed which is based on a multiplicative decomposition of the strain. Very general assumptions are made for the elastic and inelastic constitutive relations and effects such as thermally-activated creep, fast-neutron-flux-induced creep and growth, annealing, and strain recovery are compatible with the theory. Reduced forms of the constitutive equations are derived by use of the second law of thermodynamics in the form of the Clausius-Duhem inequality. Observer invariant equations are derived by use of an invariance principle which is a generalization of the principle of material frame indifference

New non-linear model of groundwater recharge: Inclusion of memory, heterogeneity and visco-elasticity

Directory of Open Access Journals (Sweden)

Spannenberg Jescica

2017-09-01

Full Text Available Fractional differentiation has adequate use for investigating real world scenarios related to geological formations associated with elasticity, heterogeneity, viscoelasticity, and the memory effect. Since groundwater systems exist in these geological formations, modelling groundwater recharge as a real world scenario is a challenging task to do because existing recharge estimation methods are governed by linear equations which make use of constant field parameters. This is inadequate because in reality these parameters are a function of both space and time. This study therefore concentrates on modifying the recharge equation governing the EARTH model, by application of the Eton approach. Accordingly, this paper presents a modified equation which is non-linear, and accounts for parameters in a way that it is a function of both space and time. To be more specific, herein, recharge and drainage resistance which are parameters within the equation, became a function of both space and time. Additionally, the study entailed solving the non-linear equation using an iterative method as well as numerical solutions by means of the Crank-Nicolson scheme. The numerical solutions were used alongside the Riemann-Liouville, Caputo-Fabrizio, and Atangana-Baleanu derivatives, so that account was taken for elasticity, heterogeneity, viscoelasticity, and the memory effect. In essence, this paper presents a more adequate model for recharge estimation.

Nonlinear elasticity in resonance experiments

Science.gov (United States)

Li, Xun; Sens-Schönfelder, Christoph; Snieder, Roel

2018-04-01

Resonant bar experiments have revealed that dynamic deformation induces nonlinearity in rocks. These experiments produce resonance curves that represent the response amplitude as a function of the driving frequency. We propose a model to reproduce the resonance curves with observed features that include (a) the log-time recovery of the resonant frequency after the deformation ends (slow dynamics), (b) the asymmetry in the direction of the driving frequency, (c) the difference between resonance curves with the driving frequency that is swept upward and downward, and (d) the presence of a "cliff" segment to the left of the resonant peak under the condition of strong nonlinearity. The model is based on a feedback cycle where the effect of softening (nonlinearity) feeds back to the deformation. This model provides a unified interpretation of both the nonlinearity and slow dynamics in resonance experiments. We further show that the asymmetry of the resonance curve is caused by the softening, which is documented by the decrease of the resonant frequency during the deformation; the cliff segment of the resonance curve is linked to a bifurcation that involves a steep change of the response amplitude when the driving frequency is changed. With weak nonlinearity, the difference between the upward- and downward-sweeping curves depends on slow dynamics; a sufficiently slow frequency sweep eliminates this up-down difference. With strong nonlinearity, the up-down difference results from both the slow dynamics and bifurcation; however, the presence of the bifurcation maintains the respective part of the up-down difference, regardless of the sweep rate.

A nonlinear theory of generalized functions

CERN Document Server

1990-01-01

This book provides a simple introduction to a nonlinear theory of generalized functions introduced by J.F. Colombeau, which gives a meaning to any multiplication of distributions. This theory extends from pure mathematics (it presents a faithful generalization of the classical theory of C? functions and provides a synthesis of most existing multiplications of distributions) to physics (it permits the resolution of ambiguities that appear in products of distributions), passing through the theory of partial differential equations both from the theoretical viewpoint (it furnishes a concept of weak solution of pde's leading to existence-uniqueness results in many cases where no distributional solution exists) and the numerical viewpoint (it introduces new and efficient methods developed recently in elastoplasticity, hydrodynamics and acoustics). This text presents basic concepts and results which until now were only published in article form. It is in- tended for mathematicians but, since the theory and applicati...

Laser-based linear and nonlinear guided elastic waves at surfaces (2D) and wedges (1D).

Science.gov (United States)

Hess, Peter; Lomonosov, Alexey M; Mayer, Andreas P

2014-01-01

The characteristic features and applications of linear and nonlinear guided elastic waves propagating along surfaces (2D) and wedges (1D) are discussed. Laser-based excitation, detection, or contact-free analysis of these guided waves with pump-probe methods are reviewed. Determination of material parameters by broadband surface acoustic waves (SAWs) and other applications in nondestructive evaluation (NDE) are considered. The realization of nonlinear SAWs in the form of solitary waves and as shock waves, used for the determination of the fracture strength, is described. The unique properties of dispersion-free wedge waves (WWs) propagating along homogeneous wedges and of dispersive wedge waves observed in the presence of wedge modifications such as tip truncation or coatings are outlined. Theoretical and experimental results on nonlinear wedge waves in isotropic and anisotropic solids are presented. Copyright © 2013 Elsevier B.V. All rights reserved.

Sapphire: A kinking nonlinear elastic solid

Science.gov (United States)

Basu, S.; Barsoum, M. W.; Kalidindi, S. R.

2006-03-01

Kinking nonlinear elastic (KNE) solids are a recently identified large class of solids that deform fully reversibly by the formation of dislocation-based kink bands [Barsoum et al. Phys. Rev. Lett. 92, 255508 (2004)]. We further conjectured that a high c/a ratio-that ensures that only basal slip is operative-is a sufficient condition for a solid to be KNE. The c/a ratio of sapphire is 2.73 and thus, if our conjecture is correct, it should be a KNE solid. Herein by repeatedly loading-up to 30 times-the same location of sapphire single crystals of two orientations-A and C-with a 1 μm radius spherical nanoindenter, followed by atomic force microscopy, we showed that sapphire is indeed a KNE solid. After pop-ins of the order of 100 nm, the repeated loadings give rise to fully reversible, reproducible hysteresis loops wherein the energy dissipated per unit volume per cycle Wd is of the order of 0.5 GJ/m3. Wd is due to the back and fro motion of the dislocations making up the incipient kink bands that are fully reversible. The results presented here strongly suggest that-like in graphite and mica-kink bands play a more critical role in the room temperature constrained deformation of sapphire than had hitherto been appreciated. Our interpretation is also in agreement with, and can explain most, recent nanoindentation results on sapphire.

On the solvability of asymmetric quasilinear finite element approximate problems in nonlinear incompressible elasticity

International Nuclear Information System (INIS)

Ruas, V.

1982-09-01

A class of simplicial finite elements for solving incompressible elasticity problems in n-dimensional space, n=2 or 3, is presented. An asymmetric structure of the shape functions with respect to the centroid of the simplex, renders them particularly stable in the large strain case, in which the incompressibility condition is nonlinear. It is proved that under certain assembling conditions of the elements, there exists a solution to the corresponding discrete problems. Numerical examples illustrate the efficiency of the method. (Author) [pt

Nonlinear turbulence theory and simulation of Buneman instability

International Nuclear Information System (INIS)

Yoon, P. H.; Umeda, T.

2010-01-01

In the present paper, the weak turbulence theory for reactive instabilities, formulated in a companion paper [P. H. Yoon, Phys. Plasmas 17, 112316 (2010)], is applied to the strong electron-ion two-stream (or Buneman) instability. The self-consistent theory involves quasilinear velocity space diffusion equation for the particles and nonlinear wave kinetic equation that includes quasilinear (or induced emission) term as well as nonlinear wave-particle interaction term (or a term that represents an induced scattering off ions). We have also performed one-dimensional electrostatic Vlasov simulation in order to benchmark the theoretical analysis. Under the assumption of self-similar drifting Gaussian distribution function for the electrons it is shown that the current reduction and the accompanying electron heating as well as electric field turbulence generation can be discussed in a self-consistent manner. Upon comparison with the Vlasov simulation result it is found that quasilinear wave kinetic equation alone is insufficient to account for the final saturation amplitude. Upon including the nonlinear scattering term in the wave kinetic equation, however, we find that a qualitative agreement with the simulation is recovered. From this, we conclude that the combined quasilinear particle diffusion plus induced emission and scattering (off ions) processes adequately account for the nonlinear development of the Buneman instability.

Nonlinear analysis of the GFRP material wheel hub

Directory of Open Access Journals (Sweden)

Dong Yun-Feng

2015-01-01

Full Text Available In this paper, the current bicycle wheel was replaced by the ones which composed by the wheel hub with Glassfiber Reinforced Plastic (alkali free thin-walled cylinder material, hereinafter referred to as GFRP material and the protective components made up of rubber outer pneumatic pad. With the help of the basic theory of elastic-plastic mechanics, the finite element “Nonlinear buckling” analysis of the wheel was carried out. The results show that the maximum elastic deformation of the wheel hub and the critical value of buckling failure load were restricted by the elasticity under the condition of external loads. Considering with the tensile strength and elastic modulus of the GFRP value of the material, it is demonstrated that the material is feasible to be used for wheel hub.

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.

Nonlinear gravitons and curved twistor theory

International Nuclear Information System (INIS)

Penrose, R.

1976-01-01

A new approach to the quantization of general relativity is suggested in which a state consisting of just one graviton can be described, but in a way which involves both the curvature and nonlinearities of Einstein's theory. It is felt that this approach can be justified solely on its own merits but it also receives striking encouragement from another direction: a surprising mathematical result enables one to construct the general such nonlinear gravitation state from a curved twistor space, the construction being given in terms of one arbitrary holomorphic function of three complex variables. In this way, the approach fits naturally into the general twistor program for the description of quantized fields. (U.K.)

Linear and Nonlinear Theories of Cosmic Ray Transport

International Nuclear Information System (INIS)

Shalchi, A.

2005-01-01

The transport of charged cosmic rays in plasmawave turbulence is a modern and interesting field of research. We are mainly interested in spatial diffusion parallel and perpendicular to a large scale magnetic field. During the last decades quasilinear theory was the standard tool for the calculation of diffusion coefficients. Through comparison with numerical simulations we found several cases where quasilinear theory is invalid. On could define three major problems of transport theory. I will demonstrate that new nonlinear theories which were proposed recently can solve at least some to these problems

SEACAS Theory Manuals: Part 1. Problem Formulation in Nonlinear Solid Mechancis

Energy Technology Data Exchange (ETDEWEB)

Attaway, S.W.; Laursen, T.A.; Zadoks, R.I.

1998-08-01

This report gives an introduction to the basic concepts and principles involved in the formulation of nonlinear problems in solid mechanics. By way of motivation, the discussion begins with a survey of some of the important sources of nonlinearity in solid mechanics applications, using wherever possible simple one dimensional idealizations to demonstrate the physical concepts. This discussion is then generalized by presenting generic statements of initial/boundary value problems in solid mechanics, using linear elasticity as a template and encompassing such ideas as strong and weak forms of boundary value problems, boundary and initial conditions, and dynamic and quasistatic idealizations. The notational framework used for the linearized problem is then extended to account for finite deformation of possibly inelastic solids, providing the context for the descriptions of nonlinear continuum mechanics, constitutive modeling, and finite element technology given in three companion reports.

Nonlinear many-body reaction theories from nuclear mean field approximations

International Nuclear Information System (INIS)

Griffin, J.J.

1983-01-01

Several methods of utilizing nonlinear mean field propagation in time to describe nuclear reaction have been studied. The property of physical asymptoticity is analyzed in this paper, which guarantees that the prediction by a reaction theory for the physical measurement of internal fragment properties shall not depend upon the precise location of the measuring apparatus. The physical asymptoticity is guaranteed in the Schroedinger collision theory of a scuttering system with translationally invariant interaction by the constancy of the S-matrix elements and by the translational invariance of the internal motion for well-separated fragments. Both conditions are necessary for the physical asymptoticity. The channel asymptotic single-determinantal propagation can be described by the Dirac-TDHF (time dependent Hartree-Fock) time evolution. A new asymptotic Hartree-Fock stationary phase (AHFSP) description together with the S-matrix time-dependent Hartree-Fock (TD-S-HF) theory constitute the second example of a physically asymptotic nonlinear many-body reaction theory. A review of nonlinear mean field many-body reaction theories shows that initial value TDHF is non-asymptotic. The TD-S-HF theory is asymptotic by the construction. The gauge invariant periodic quantized solution of the exact Schroedinger problem has been considered to test whether it includes all of the exact eigenfunctions as it ought to. It did, but included as well an infinity of all spurions solutions. (Kato, T.)

Riemann-Cartan geometry of nonlinear disclination mechanics

KAUST Repository

Yavari, A.

2012-03-23

In the continuous theory of defects in nonlinear elastic solids, it is known that a distribution of disclinations leads, in general, to a non-trivial residual stress field. To study this problem, we consider the particular case of determining the residual stress field of a cylindrically symmetric distribution of parallel wedge disclinations. We first use the tools of differential geometry to construct a Riemannian material manifold in which the body is stress-free. This manifold is metric compatible, has zero torsion, but has non-vanishing curvature. The problem then reduces to embedding this manifold in Euclidean 3-space following the procedure of a classical nonlinear elastic problem. We show that this embedding can be elegantly accomplished by using Cartan\\'s method of moving frames and compute explicitly the residual stress field for various distributions in the case of a neo-Hookean material. © 2012 The Author(s).

Theory of activated glassy dynamics in randomly pinned fluids

Science.gov (United States)

Phan, Anh D.; Schweizer, Kenneth S.

2018-02-01

We generalize the force-level, microscopic, Nonlinear Langevin Equation (NLE) theory and its elastically collective generalization [elastically collective nonlinear Langevin equation (ECNLE) theory] of activated dynamics in bulk spherical particle liquids to address the influence of random particle pinning on structural relaxation. The simplest neutral confinement model is analyzed for hard spheres where there is no change of the equilibrium pair structure upon particle pinning. As the pinned fraction grows, cage scale dynamical constraints are intensified in a manner that increases with density. This results in the mobile particles becoming more transiently localized, with increases of the jump distance, cage scale barrier, and NLE theory mean hopping time; subtle changes of the dynamic shear modulus are predicted. The results are contrasted with recent simulations. Similarities in relaxation behavior are identified in the dynamic precursor regime, including a roughly exponential, or weakly supra-exponential, growth of the alpha time with pinning fraction and a reduction of dynamic fragility. However, the increase of the alpha time with pinning predicted by the local NLE theory is too small and severely so at very high volume fractions. The strong deviations are argued to be due to the longer range collective elasticity aspect of the problem which is expected to be modified by random pinning in a complex manner. A qualitative physical scenario is offered for how the three distinct aspects that quantify the elastic barrier may change with pinning. ECNLE theory calculations of the alpha time are then presented based on the simplest effective-medium-like treatment for how random pinning modifies the elastic barrier. The results appear to be consistent with most, but not all, trends seen in recent simulations. Key open problems are discussed with regard to both theory and simulation.

Overview of nonlinear theory of kinetically driven instabilities

International Nuclear Information System (INIS)

Berk, H.L.; Breizman, B.N.

1998-09-01

An overview is presented of the theory for the nonlinear behavior of instabilities driven by the resonant wave particle interaction. The approach should be applicable to a wide variety of kinetic systems in magnetic fusion devices and accelerators. Here the authors emphasize application to Alfven were driven instability, and the principles of the theory are used to interpret experimental data

Nonlinear PI control of chaotic systems using singular perturbation theory

International Nuclear Information System (INIS)

Wang Jiang; Wang Jing; Li Huiyan

2005-01-01

In this paper, we develop the nonlinear PI controllers for a class of chaotic systems based on singular perturbation theory. The original system is decomposed into two reduced order systems, to which the nonlinear uncertain terms belongs. In order to alleviate the deterioration of these nonlinear uncertainties, the nonlinear PI controllers are applied to each subsystem and combined to construct the composite controller for the full order system. The effectiveness and feasibility of the proposed control scheme is demonstrated through numerical simulations on the chaotic Chua's circuit

Effective-medium theory for nonlinear magneto-optics in magnetic granular alloys: cubic nonlinearity

International Nuclear Information System (INIS)

Granovsky, Alexander B.; Kuzmichov, Michail V.; Clerc, J.-P.; Inoue, Mitsuteru

2003-01-01

We propose a simple effective-medium approach for calculating the effective dielectric function of a magnetic metal-insulator granular alloy in which there is a weakly nonlinear relation between electric displacement D and electric field E for both constituent materials of the form D i =ε i (0) E i +χ i (3) |E i | 2 E i . We assume that linear ε i (0) and cubic nonlinear χ i (3) dielectric functions are diagonal and linear with magnetization non-diagonal components. For such metal-insulator composite magneto-optical effects depend on a light intensity and the effective cubic dielectric function χ eff (3) can be significantly greater (up to 10 3 times) than that for constituent materials. The calculation scheme is based on the Bergman and Stroud-Hui theory of nonlinear optical properties of granular matter. The giant cubic magneto-optical nonlinearity is found for composites with metallic volume fraction close to the percolation threshold and at a resonance of optical conductivity. It is shown that a composite may exhibit nonlinear magneto-optics even when both constituent materials have no cubic magneto-optical nonlinearity

Information theory and stochastics for multiscale nonlinear systems

CERN Document Server

Majda, Andrew J; Grote, Marcus J

2005-01-01

This book introduces mathematicians to the fascinating emerging mathematical interplay between ideas from stochastics and information theory and important practical issues in studying complex multiscale nonlinear systems. It emphasizes the serendipity between modern applied mathematics and applications where rigorous analysis, the development of qualitative and/or asymptotic models, and numerical modeling all interact to explain complex phenomena. After a brief introduction to the emerging issues in multiscale modeling, the book has three main chapters. The first chapter is an introduction to information theory with novel applications to statistical mechanics, predictability, and Jupiter's Red Spot for geophysical flows. The second chapter discusses new mathematical issues regarding fluctuation-dissipation theorems for complex nonlinear systems including information flow, various approximations, and illustrates applications to various mathematical models. The third chapter discusses stochastic modeling of com...

Dynamic Modeling and Control of Electromechanical Coupling for Mechanical Elastic Energy Storage System

Directory of Open Access Journals (Sweden)

Yang Yu

2013-01-01

Full Text Available The structural scheme of mechanical elastic energy storage (MEES system served by permanent magnet synchronous motor (PMSM and bidirectional converters is designed. The aim of the research is to model and control the complex electromechanical system. The mechanical device of the complex system is considered as a node in generalized coordinate system, the terse nonlinear dynamic model of electromechanical coupling for the electromechanical system is constructed through Lagrange-Maxwell energy method, and the detailed deduction of the mathematical model is presented in the paper. The theory of direct feedback linearization (DFL is applied to decouple the nonlinear dynamic model and convert the developed model from nonlinear to linear. The optimal control theory is utilized to accomplish speed tracking control for the linearized system. The simulation results in three different cases show that the proposed nonlinear dynamic model of MEES system is correct; the designed algorithm has a better control performance in contrast with the conventional PI control.

Elastic-plastic analysis of high speed rotors with no plane of symmetry

International Nuclear Information System (INIS)

Anantha Ramu, S.

1981-01-01

A general method of analysis of elastic plastic shells has been developed. The material of the shell is assumed to obey von Mises yield condition and a stress strain law on the basis of deformation theory of plasticity. The method permits an easy iterative solution of the complete set of coupled nonlinear differential equations. The iterative procedure is essentially the solution of the elastic problem several times with different sets of loads. The solution finally yields among other things, the location of the elastic-plastic boundary in the shell wall. The second approach suggested is a three-dimensional hexahedral isoparametric solid element. The computer program developed is capable of modelling perfectly plastic, bilinear as well as nonlinear strain hardening behaviour of materials. As an example, a radial impeller is analysed by both the approaches by idealizing it as a rotating conical shell. The complete history of plastification of the shell wall as the speed increases is determined. The results of both approaches are found to be in good agreement with each other. (orig./HP)

A model of nonlinear strain and damage accumulation in polymer composites

Directory of Open Access Journals (Sweden)

A. N. Ruslantsev

2014-01-01

Full Text Available This paper presents a model to predict a nonlinear strain of the carbon laminate; the model is based on the relations between the theory of laminated plates and the non-linear approximation of deformation curve of unidirectional layer at the shear in the layer plane. The explicit expressions of stiffness and compliance matrices were obtained via multiplying the matrices that correspond to the elastic characteristics by the matrices, considering the non-linear properties of the laminate. The paper suggests an approximation option for the non-linear properties of the layer at the shear using an exponential function. Some considerations on damage accumulation in carbon laminates were made.

Analysis of the elastic behaviour of nonclassical nonlinear mesoscopic materials in quasi-static experiments

International Nuclear Information System (INIS)

Ruffino, E.; Scalerandi, M.

2000-01-01

As discovered by recent quasi-static and dynamic resonance experiments, the classical nonlinear theory fails in describing the hysteretic behaviour of nonlinear mesoscopic materials like rocks, concrete, etc. The paper applies the local interaction simulation approach (LISA) for studying such kind of nonclassical nonlinearity. To this purpose, in the LISA treatment of ultrasonic wave propagation has been included a phenomenological model, based on the PM space approach, of the local mesoscopic features of rocks and other materials with localized damages. A quantitative comparison of simulation and experimental results in quasi-static experiments is also presented

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.)

Theory of atom displacements induced by fast electron elastic scattering in solids

International Nuclear Information System (INIS)

Cruz, C. M.; Pinera, I.; Abreu, Y.; Leyva, A.

2006-01-01

Present contribution deals with the theoretical description of the conditions favoring the occurrence of single fast electron elastic scattering in solids, leading to the displacement of atoms from their crystalline sites. Firstly, the Moliere-Bethe-Goudsmit-Saunderson theory of Multiple Electron Scattering is applied, determining the limiting angle θ l over which the single electron elastic scattering prevails over the multiple one, leading to the evaluation of the total macroscopic cross-section for single electron elastic scattering on the basis of the Mott-Rutherford differential cross-section. On the basis of single electron elastic scattering by atoms in the solid matrix, it was determined the relative number of Atom Displacements produced by the Gamma Radiation as a primary act, as well as the energy and linear momentum of the ejected atoms. The statistical distributions of single electron elastic scattering and of those inducing Atom Displacements at different electron initial energies in comparison with the others electron inelastic scattering channels are discussed, where the statistical sampling methods on the basis of the rejection one where applied simulating different practical situations. (Full text)

Nonlinear system theory: another look at dependence.

Science.gov (United States)

Wu, Wei Biao

2005-10-04

Based on the nonlinear system theory, we introduce previously undescribed dependence measures for stationary causal processes. Our physical and predictive dependence measures quantify the degree of dependence of outputs on inputs in physical systems. The proposed dependence measures provide a natural framework for a limit theory for stationary processes. In particular, under conditions with quite simple forms, we present limit theorems for partial sums, empirical processes, and kernel density estimates. The conditions are mild and easily verifiable because they are directly related to the data-generating mechanisms.

Theory of weakly nonlinear self-sustained detonations

KAUST Repository

Faria, Luiz; Kasimov, Aslan R.; Rosales, Rodolfo R.

2015-01-01

We propose a theory of weakly nonlinear multidimensional self-sustained detonations based on asymptotic analysis of the reactive compressible Navier-Stokes equations. We show that these equations can be reduced to a model consisting of a forced

Theory and design of nonlinear metamaterials

Science.gov (United States)

Rose, Alec Daniel

If electronics are ever to be completely replaced by optics, a significant possibility in the wake of the fiber revolution, it is likely that nonlinear materials will play a central and enabling role. Indeed, nonlinear optics is the study of the mechanisms through which light can change the nature and properties of matter and, as a corollary, how one beam or color of light can manipulate another or even itself within such a material. However, of the many barriers preventing such a lofty goal, the narrow and limited range of properties supported by nonlinear materials, and natural materials in general, stands at the forefront. Many industries have turned instead to artificial and composite materials, with homogenizable metamaterials representing a recent extension of such composites into the electromagnetic domain. In particular, the inclusion of nonlinear elements has caused metamaterials research to spill over into the field of nonlinear optics. Through careful design of their constituent elements, nonlinear metamaterials are capable of supporting an unprecedented range of interactions, promising nonlinear devices of novel design and scale. In this context, I cast the basic properties of nonlinear metamaterials in the conventional formalism of nonlinear optics. Using alternately transfer matrices and coupled mode theory, I develop two complementary methods for characterizing and designing metamaterials with arbitrary nonlinear properties. Subsequently, I apply these methods in numerical studies of several canonical metamaterials, demonstrating enhanced electric and magnetic nonlinearities, as well as predicting the existence of nonlinear magnetoelectric and off-diagonal nonlinear tensors. I then introduce simultaneous design of the linear and nonlinear properties in the context of phase matching, outlining five different metamaterial phase matching methods, with special emphasis on the phase matching of counter propagating waves in mirrorless parametric amplifiers

Effective-medium theory for nonlinear magneto-optics in magnetic granular alloys: cubic nonlinearity

Energy Technology Data Exchange (ETDEWEB)

Granovsky, Alexander B. E-mail: granov@magn.ru; Kuzmichov, Michail V.; Clerc, J.-P.; Inoue, Mitsuteru

2003-03-01

We propose a simple effective-medium approach for calculating the effective dielectric function of a magnetic metal-insulator granular alloy in which there is a weakly nonlinear relation between electric displacement D and electric field E for both constituent materials of the form D{sub i}={epsilon}{sub i}{sup (0)}E{sub i} +{chi}{sub i}{sup (3)}|E{sub i}|{sup 2}E{sub i}. We assume that linear {epsilon}{sub i}{sup (0)} and cubic nonlinear {chi}{sub i}{sup (3)} dielectric functions are diagonal and linear with magnetization non-diagonal components. For such metal-insulator composite magneto-optical effects depend on a light intensity and the effective cubic dielectric function {chi}{sub eff}{sup (3)} can be significantly greater (up to 10{sup 3} times) than that for constituent materials. The calculation scheme is based on the Bergman and Stroud-Hui theory of nonlinear optical properties of granular matter. The giant cubic magneto-optical nonlinearity is found for composites with metallic volume fraction close to the percolation threshold and at a resonance of optical conductivity. It is shown that a composite may exhibit nonlinear magneto-optics even when both constituent materials have no cubic magneto-optical nonlinearity.

Backward stochastic differential equations from linear to fully nonlinear theory

CERN Document Server

Zhang, Jianfeng

2017-01-01

This book provides a systematic and accessible approach to stochastic differential equations, backward stochastic differential equations, and their connection with partial differential equations, as well as the recent development of the fully nonlinear theory, including nonlinear expectation, second order backward stochastic differential equations, and path dependent partial differential equations. Their main applications and numerical algorithms, as well as many exercises, are included. The book focuses on ideas and clarity, with most results having been solved from scratch and most theories being motivated from applications. It can be considered a starting point for junior researchers in the field, and can serve as a textbook for a two-semester graduate course in probability theory and stochastic analysis. It is also accessible for graduate students majoring in financial engineering.

Optical model theory of elastic electron- and positron-atom scattering at intermediate energies

International Nuclear Information System (INIS)

Joachain, C.J.

1977-01-01

It is stated that the basic idea of the optical model theory is to enable analysis of the elastic scattering of a particle from a complex target by replacing the complicated interactions between the beam and the target by an optical potential, or pseudopotential, in which the incident particle moves. Once the optical potential is determined the original many-body elastic scattering problem reduces to a one-body situation. The resulting optical potential is, however, a very complicated operator, and the formal expressions obtained from first principles for the optical potential can only be evaluated approximately in a few simple cases, such as high energy elastic hadron-nucleus scattering, for the the optical potential can be expressed in terms of two-body hadron-nucleon amplitudes, and the non-relativistic elastic scattering of fast charged particles by atoms. The elastic scattering of an electron or positron by a neutral atom at intermediate energies is here considered. Exchange effects between the projectile and the atomic electrons are considered; also absorption and polarisation effects. Applications of the full-wave optical model have so far only been made to the elastic scattering of fast electrons and positrons by atomic H, He, Ne, and Ar. Agreements of the optical model results with absolute measurements of differential cross sections for electron scattering are very good, an agreement that improves as the energy increases, but deteriorates quickly as the incident energy becomes lower than 50 eV for atomic H or 100 eV for He. For more complex atoms the optical model calculations also appear very encouraging. With regard to positron-atom elastic scattering the optical model results for positron-He scattering differ markedly at small angles from the corresponding electron-He values. It would be interesting to have experimental angular distributions of positron-atom elastic scattering in order to check predictions of the optical model theory. (U.K.)

Shaping through buckling in elastic gridshells: from camping tents to architectural roofs

Science.gov (United States)

Reis, Pedro

Elastic gridshells comprise an initially planar network of elastic rods that is actuated into a 3D shell-like structure by loading its extremities. This shaping results from elastic buckling and the subsequent geometrically nonlinear deformation of the grid structure. Architectural elastic gridshells first appeared in the 1970's. However, to date, only a limited number of examples have been constructed around the world, primarily due to the challenges involved in their structural design. Yet, elastic gridshells are highly appealing: they can cover wide spans with low self-weight, they allow for aesthetically pleasing shapes and their construction is typically simple and rapid. We study the mechanics of elastic gridshells by combining precision model experiments that explore their scale invariance, together with computer simulations that employ the Discrete Elastic Rods method. Excellent agreement is found between the two. Upon validation, the numerics are then used to systematically explore parameter space and identify general design principles for specific target final shapes. Our findings are rationalized using the theory of discrete Chebyshev nets, together with the group theory for crystals. Higher buckling modes occur for some configurations due to geometric incompatibility at the boundary and result in symmetry breaking. Along with the systematic classification of the various possible modes of deformation, we provide a reduced model that rationalizes form-finding in elastic gridshells. This work was done in collaboration with Changyeob Baek, Khalid Jawed and Andrew Sageman-Furnas. We are grateful to the NSF for funding (CAREER, CMMI-1351449).

A nonlinear boundary integral equations method for the solving of quasistatic elastic contact problem with Coulomb friction

Directory of Open Access Journals (Sweden)

Yurii M. Streliaiev

2016-06-01

Full Text Available Three-dimensional quasistatic contact problem of two linearly elastic bodies' interaction with Coulomb friction taken into account is considered. The boundary conditions of the problem have been simplified by the modification of the Coulomb's law of friction. This modification is based on the introducing of a delay in normal contact tractions that bound tangent contact tractions in the Coulomb's law of friction expressions. At this statement the problem is reduced to a sequence of similar systems of nonlinear integral equations describing bodies' interaction at each step of loading. A method for an approximate solution of the integral equations system corresponded to each step of loading is applied. This method consists of system regularization, discretization of regularized system and iterative process application for solving the discretized system. A numerical solution of a contact problem of an elastic sphere with an elastic half-space interaction under increasing and subsequently decreasing normal compressive force has been obtained.

Electrodynamic soil plate oscillator: Modeling nonlinear mesoscopic elastic behavior and hysteresis in nonlinear acoustic landmine detection

Science.gov (United States)

Korman, M. S.; Duong, D. V.; Kalsbeck, A. E.

2015-10-01

An apparatus (SPO), designed to study flexural vibrations of a soil loaded plate, consists of a thin circular elastic clamped plate (and cylindrical wall) supporting a vertical soil column. A small magnet attached to the center of the plate is driven by a rigid AC coil (located coaxially below the plate) to complete the electrodynamic soil plate oscillator SPO design. The frequency dependent mechanical impedance Zmech (force / particle velocity, at the plate's center) is inversely proportional to the electrical motional impedance Zmot. Measurements of Zmot are made using the complex output to input response of a Wheatstone bridge that has an identical coil element in one of its legs. Near resonance, measurements of Zmot (with no soil) before and after a slight point mass loading at the center help determine effective mass, spring, damping and coupling constant parameters of the system. "Tuning curve" behavior of real{ Zmot } and imaginary{ Zmot } at successively higher vibration amplitudes of dry sifted masonry sand are measured. They exhibit a decrease "softening" in resonance frequency along with a decrease in the quality Q factor. In soil surface vibration measurements a bilinear hysteresis model predicts the tuning curve shape for this nonlinear mesoscopic elastic SPO behavior - which also models the soil vibration over an actual plastic "inert" VS 1.6 buried landmine. Experiments are performed where a buried 1m cube concrete block supports a 12 inch deep by 30 inch by 30 inch concrete soil box for burying a VS 1.6 in dry sifted masonry sand for on-the-mine and off-the-mine soil vibration experiments. The backbone curve (a plot of the peak amplitude vs. corresponding resonant frequency from a family of tuning curves) exhibits mostly linear behavior for "on target" soil surface vibration measurements of the buried VS 1.6 or drum-like mine simulants for relatively low particle velocities of the soil. Backbone curves for "on target" measurements exhibit

Quantitative theory of driven nonlinear brain dynamics.

Science.gov (United States)

Roberts, J A; Robinson, P A

2012-09-01

Strong periodic stimuli such as bright flashing lights evoke nonlinear responses in the brain and interact nonlinearly with ongoing cortical activity, but the underlying mechanisms for these phenomena are poorly understood at present. The dominant features of these experimentally observed dynamics are reproduced by the dynamics of a quantitative neural field model subject to periodic drive. Model power spectra over a range of drive frequencies show agreement with multiple features of experimental measurements, exhibiting nonlinear effects including entrainment over a range of frequencies around the natural alpha frequency f(α), subharmonic entrainment near 2f(α), and harmonic generation. Further analysis of the driven dynamics as a function of the drive parameters reveals rich nonlinear dynamics that is predicted to be observable in future experiments at high drive amplitude, including period doubling, bistable phase-locking, hysteresis, wave mixing, and chaos indicated by positive Lyapunov exponents. Moreover, photosensitive seizures are predicted for physiologically realistic model parameters yielding bistability between healthy and seizure dynamics. These results demonstrate the applicability of neural field models to the new regime of periodically driven nonlinear dynamics, enabling interpretation of experimental data in terms of specific generating mechanisms and providing new tests of the theory. Copyright © 2012 Elsevier Inc. All rights reserved.

Comparison of classical and modern theories of longitudinal wave propagation in elastic rods

CSIR Research Space (South Africa)

Shatalov, M

2011-01-01

Full Text Available Conference on Computational and Applied Mechanics SACAM10 Pretoria, 10?13 January 2010 ? SACAM COMPARISON OF CLASSICAL AND MODERN THEORIES OF LONGITUDINAL WAVE PROPAGATION IN ELASTIC RODS M. Shatalov*,?,?? , I. Fedotov? 1 , HM. Tenkam? 2, J. Marais..., Pretoria, 0001 FIN-40014, South Africa 1fedotovi@tut.ac.za, 2djouosseutenkamhm@tut.ac.za ?? Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South Africa Keywords: Elastic rod, wave propagation, classical...

Non-linear optical measurement of the twist elastic constant in thermotropic and DNA lyotropic chiral nematics.

Science.gov (United States)

Lucchetti, Liana; Fraccia, Tommaso P; Ciciulla, Fabrizio; Bellini, Tommaso

2017-07-10

Throughout the whole history of liquid crystals science, the balancing of intrinsic elasticity with coupling to external forces has been the key strategy for most application and investigation. While the coupling of the optical field to the nematic director is at the base of a wealth of thoroughly described optical effects, a significant variety of geometries and materials have not been considered yet. Here we show that by adopting a simple cell geometry and measuring the optically induced birefringence, we can readily extract the twist elastic coefficient K 22 of thermotropic and lyotropic chiral nematics (N*). The value of K 22 we obtain for chiral doped 5CB thermotropic N* well matches those reported in the literature. With this same strategy, we could determine for the first time K 22 of the N* phase of concentrated aqueous solutions of DNA oligomers, bypassing the limitations that so far prevented measuring the elastic constants of this class of liquid crystalline materials. The present study also enlightens the significant nonlinear optical response of DNA liquid crystals.

Dependence of the frequency spectrum of small amplitude vibrations superimposed on finite deformations of a nonlinear, cylindrical elastic body on residual stress

KAUST Repository

Gorb, Yuliya; Walton, Jay R.

2010-01-01

We model and analyze the response of nonlinear, residually stressed elastic bodies subjected to small amplitude vibrations superimposed upon large deformations. The problem derives from modeling the use of intravascular ultrasound (IVUS) imaging

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

Nonlinear closed-loop control theory

International Nuclear Information System (INIS)

Perez, R.B.; Otaduy, P.J.; Abdalla, M.

1992-01-01

Traditionally, the control of nuclear power plants has been implemented by the use of proportional-integral (PI) control systems. PI controllers are both simple and, within their calibration range, highly reliable. However, PIs provide little performance information that could be used to diagnose out-of-range events or the nature of unanticipated transients that may occur in the plant. To go beyond the PI controller, the new control algorithms must deal with the physical system nonlinearities and with the reality of uncertain dynamics terms in its mathematical model. The tool to develop a new kind of control algorithm is provided by Optimal Control Theory. In this theory, a norm is minimized which incorporates the constraint that the model equations should be satisfied at all times by means of the Lagrange multipliers. Optimal control algorithms consist of two sets of coupled equations: (1) the model equations, integrated forward in time; and (2) the equations for the Lagrange multipliers (adjoints), integrated backwards in time. There are two challenges: dealing with large sets of coupled nonlinear equations and with a two-point boundary value problem that must be solved iteratively. In this paper, the rigorous conversion of the two-point boundary value problem into an initial value problem is presented. In addition, the incorporation into the control algorithm of ''real world'' constraints such as sensors and actuators, dynamic response functions and time lags introduced by the digitalization of analog signals is presented. (Author)

Nanoparticle amount, and not size, determines chain alignment and nonlinear hardening in polymer nanocomposites

Science.gov (United States)

Varol, H. Samet; Meng, Fanlong; Hosseinkhani, Babak; Malm, Christian; Bonn, Daniel; Bonn, Mischa; Zaccone, Alessio

2017-01-01

Polymer nanocomposites—materials in which a polymer matrix is blended with nanoparticles (or fillers)—strengthen under sufficiently large strains. Such strain hardening is critical to their function, especially for materials that bear large cyclic loads such as car tires or bearing sealants. Although the reinforcement (i.e., the increase in the linear elasticity) by the addition of filler particles is phenomenologically understood, considerably less is known about strain hardening (the nonlinear elasticity). Here, we elucidate the molecular origin of strain hardening using uniaxial tensile loading, microspectroscopy of polymer chain alignment, and theory. The strain-hardening behavior and chain alignment are found to depend on the volume fraction, but not on the size of nanofillers. This contrasts with reinforcement, which depends on both volume fraction and size of nanofillers, potentially allowing linear and nonlinear elasticity of nanocomposites to be tuned independently. PMID:28377517

Geometric methods in the elastic theory of membranes in liquid crystal phases

CERN Document Server

Ji Xing Liu; Yu Zhang Xie

1999-01-01

This book contains a comprehensive description of the mechanical equilibrium and deformation of membranes as a surface problem in differential geometry. Following the pioneering work by W Helfrich, the fluid membrane is seen as a nematic or smectic - A liquid crystal film and its elastic energy form is deduced exactly from the curvature elastic theory of the liquid crystals. With surface variation the minimization of the energy at fixed osmotical pressure and surface tension gives a completely new surface equation in geometry that involves potential interest in mathematics. The investigations

Support minimized inversion of acoustic and elastic wave scattering

International Nuclear Information System (INIS)

Safaeinili, A.

1994-01-01

This report discusses the following topics on support minimized inversion of acoustic and elastic wave scattering: Minimum support inversion; forward modelling of elastodynamic wave scattering; minimum support linearized acoustic inversion; support minimized nonlinear acoustic inversion without absolute phase; and support minimized nonlinear elastic inversion

Unified quantum theory of elastic and inelastic atomic scattering from a physisorbed monolayer solid

DEFF Research Database (Denmark)

Bruch, L. W.; Hansen, Flemming Yssing; Dammann, Bernd

2017-01-01

A unified quantum theory of the elastic and inelastic scattering of low energy He atoms by a physisorbed monolayer solid in the one-phonon approximation is given. It uses a time-dependent wave packet with phonon creation and annihilation components and has a self-consistent feedback between...... the wave functions for elastic and inelastic scattered atoms. An attenuation of diffraction scattering by inelastic processes thus is inherent in the theory. The atomic motion and monolayer vibrations in the harmonic approximation are treated quantum mechanically and unitarity is preserved. The evaluation...... of specific one-phonon events includes contributions from diffuse inelastic scattering in other phonon modes. Effects of thermally excited phonons are included using a mean field approximation. The theory is applied to an incommensurate Xe/Pt(111) monolayer (incident energy Ei = 4-16 meV), a commensurate Xe...

Nonlinear modulation near the Lighthill instability threshold in 2+1 Whitham theory

Science.gov (United States)

Bridges, Thomas J.; Ratliff, Daniel J.

2018-04-01

The dispersionless Whitham modulation equations in 2+1 (two space dimensions and time) are reviewed and the instabilities identified. The modulation theory is then reformulated, near the Lighthill instability threshold, with a slow phase, moving frame and different scalings. The resulting nonlinear phase modulation equation near the Lighthill surfaces is a geometric form of the 2+1 two-way Boussinesq equation. This equation is universal in the same sense as Whitham theory. Moreover, it is dispersive, and it has a wide range of interesting multi-periodic, quasi-periodic and multi-pulse localized solutions. For illustration the theory is applied to a complex nonlinear 2+1 Klein-Gordon equation which has two Lighthill surfaces in the manifold of periodic travelling waves. This article is part of the theme issue `Stability of nonlinear waves and patterns and related topics'.

Nonlinear theory of the collisional Rayleigh-Taylor instability in equatorial spread F

International Nuclear Information System (INIS)

Chaturvedi, P.K.; Ossakow, S.L.

1977-01-01

The nonlinear behavior of the collisional Rayleigh-Taylor instability is studied in equatorial Spread F by including a dominant two-dimensional nonlinearity. It is found that on account of this nonlinearity the instability saturates by generating damped higher spatial harmonics. The saturated power spectrum for the density fluctuations is discussed. A comparison between experimental observations and theory is presented

Nonlinearity in structural and electronic materials

International Nuclear Information System (INIS)

Bishop, A.R.; Beardmore, K.M.; Ben-Naim, E.

1997-01-01

This is the final report of a three-year, Laboratory Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). The project strengthens a nonlinear technology base relevant to a variety of problems arising in condensed matter and materials science, and applies this technology to those problems. In this way the controlled synthesis of, and experiments on, novel electronic and structural materials provide an important focus for nonlinear science, while nonlinear techniques help advance the understanding of the scientific principles underlying the control of microstructure and dynamics in complex materials. This research is primarily focused on four topics: (1) materials microstructure: growth and evolution, and porous media; (2) textures in elastic/martensitic materials; (3) electro- and photo-active polymers; and (4) ultrafast photophysics in complex electronic materials. Accomplishments included the following: organization of a ''Nonlinear Materials'' seminar series and international conferences including ''Fracture, Friction and Deformation,'' ''Nonequilibrium Phase Transitions,'' and ''Landscape Paradigms in Physics and Biology''; invited talks at international conference on ''Synthetic Metals,'' ''Quantum Phase Transitions,'' ''1996 CECAM Euroconference,'' and the 1995 Fall Meeting of the Materials Research Society; large-scale simulations and microscopic modeling of nonlinear coherent energy storage at crack tips and sliding interfaces; large-scale simulation and microscopic elasticity theory for precursor microstructure and dynamics at solid-solid diffusionless phase transformations; large-scale simulation of self-assembling organic thin films on inorganic substrates; analysis and simulation of smoothing of rough atomic surfaces; and modeling and analysis of flux pattern formation in equilibrium and nonequilibrium Josephson junction arrays and layered superconductors

Modelling and Intelligent Control of an Elastic Link Robot Manipulator

Directory of Open Access Journals (Sweden)

Malik Loudini

2013-01-01

Full Text Available In this paper, precise control of the end-point position of a planar single-link elastic manipulator robot is discussed. The Timoshenko beam theory (TBT has been used to characterize the structural link elasticity including important damping mechanisms. A suitable nonlinear model is derived based on the Lagrangian assumed modes method. Elastic link manipulators are classified as systems possessing highly complex dynamics. In addition, the environment in which they operate may have a lot of disturbances. These give rise to special problems that may be solved using intelligent control techniques. The application of two advanced control strategies based on fuzzy set theory is investigated. The first closed-loop control scheme to be applied is the standard Proportional-Derivative (PD type fuzzy logic controller (FLC, also known as PD-type Mamdani's FLC (MPDFLC. Then, a genetic algorithm (GA is used to optimize the MPDFLC parameters with innovative tuning procedures. Both the MPDFLC and the GA optimized FLC (GAOFLC are implemented and tested to achieve a precise control of the manipulator end-point. The performances of the adopted closed-loop intelligent control strategies are examined via simulation experiments.

Theory of plasmonic effects in nonlinear optics: the case of graphene

Science.gov (United States)

Rostami, Habib; Katsnelson, Mikhail I.; Polini, Marco; Mikhail I. Katsnelson Collaboration; Habib Rostami; Marco Polini Collaboration

The nonlinear optical properties of two-dimensional electronic systems are beginning to attract considerable interest both in the theoretical and experimental sectors. Recent experiments on the nonlinear optical properties of graphene reveal considerably strong third harmonic generation and four-wave mixing of this single-atomic-layer electronic system. We develop a large-N theory of electron-electron interaction corrections to multi-legged Feynman diagrams describing second- and third-order nonlinear response functions. Our theory is completely general and is useful to understand all second- and third-order nonlinear effects, including harmonic generation, wave mixing, and photon drag. We apply our theoretical framework to the case of graphene, by carrying out microscopic calculations of the second- and third-order nonlinear response functions of an interacting two-dimensional gas of massless Dirac fermions. We compare our results with recent measurements, where all-optical launching of graphene plasmons has been achieved. This work was supported by Fondazione Istituto Italiano di Tecnologia, the European Union's Horizon 2020 research and innovation programme under Grant agreement No. 696656 GrapheneCore, and the ERC Advanced Grant 338957 FEMTO/NANO (M.I.K.).

SEACAS Theory Manuals: Part II. Nonlinear Continuum Mechanics

Energy Technology Data Exchange (ETDEWEB)

Attaway, S.W.; Laursen, T.A.; Zadoks, R.I.

1998-09-01

This report summarizes the key continuum mechanics concepts required for the systematic prescription and numerical solution of finite deformation solid mechanics problems. Topics surveyed include measures of deformation appropriate for media undergoing large deformations, stress measures appropriate for such problems, balance laws and their role in nonlinear continuum mechanics, the role of frame indifference in description of large deformation response, and the extension of these theories to encompass two dimensional idealizations, structural idealizations, and rigid body behavior. There are three companion reports that describe the problem formulation, constitutive modeling, and finite element technology for nonlinear continuum mechanics systems.

Two-dimensional nonlinear equations of supersymmetric gauge theories

International Nuclear Information System (INIS)

Savel'ev, M.V.

1985-01-01

Supersymmetric generalization of two-dimensional nonlinear dynamical equations of gauge theories is presented. The nontrivial dynamics of a physical system in the supersymmetry and supergravity theories for (2+2)-dimensions is described by the integrable embeddings of Vsub(2/2) superspace into the flat enveloping superspace Rsub(N/M), supplied with the structure of a Lie superalgebra. An equation is derived which describes a supersymmetric generalization of the two-dimensional Toda lattice. It contains both super-Liouville and Sinh-Gordon equations

An introduction to geometric theory of fully nonlinear parabolic equations

International Nuclear Information System (INIS)

Lunardi, A.

1991-01-01

We study a class of nonlinear evolution equations in general Banach space being an abstract version of fully nonlinear parabolic equations. In addition to results of existence, uniqueness and continuous dependence on the data, we give some qualitative results about stability of the stationary solutions, existence and stability of the periodic orbits. We apply such results to some parabolic problems arising from combustion theory. (author). 24 refs

Functional stochastic differential equations: mathematical theory of nonlinear parabolic systems with applications in field theory and statistical mechanics

International Nuclear Information System (INIS)

Doering, C.R.

1985-01-01

Applications of nonlinear parabolic stochastic differential equations with additive colored noise in equilibrium and nonequilibrium statistical mechanics and quantum field theory are developed in detail, providing a new unified mathematical approach to many problems. The existence and uniqueness of solutions to these equations is established, and some of the properties of the solutions are investigated. In particular, asymptotic expansions for the correlation functions of the solutions are introduced and compared to rigorous nonperturbative bounds on the moments. It is found that the perturbative analysis is in qualitative disagreement with the exact result in models corresponding to cut-off self-interacting nonperturbatively renormalizable scalar quantum field theories. For these theories the nonlinearities cannot be considered as perturbations of the linearized theory

Elastic Composite, Reinforced Lightweight Concrete as a Type of Resilient Composite Systems

OpenAIRE

Esmaeili, Kamyar

2015-01-01

. A kind of "Elastic Composite, Reinforced Lightweight Concrete (ECRLC)" with the mentioned specifics is a type of "Resilient Composite Systems (RCS)" in which, contrary to the basic geometrical assumption of flexure theory in Solid Mechanics, "the strain changes in the beam height during bending" is typically "Non-linear". . Through employing this integrated structure, with significant high strain capability and modulus of resilience in bending, we could constructively achieve high bearing c...

Quantum theory of a one-dimensional laser with output coupling. 2. Nonlinear theory

International Nuclear Information System (INIS)

Penaforte, J.C.; Baseia, B.

1984-01-01

A previous paper describing the quantum theory of a laser in linear approximation is here extended to the nonlinear case. Instead of the approach of conventional theory - which deals with discrete 'cavity-modes' and includes artificial mechanisms to simulates radiation field losses due to beam extraction - a more realistic model of optical cavity having output coupling is used that works entirely within the continuous spectrum, allowing one to obtain the equations for the field both inside and outside the laser cavity. Besides the quantum noise due to spontaneous emission, a noise term of classical nature due to transmission losses automatically emerges from the present treatment. For single-collective-mode operation the equations for laser field are solved exactly, yielding the transient and steady-state solutions. Inside the laser cavity, the results of nonlinear analysis agree with those found in conventional theory once the conventional 'mode-amplitude' is reinterpreted as a collective variable. Outside the cavity - unaccessible region in the conventional treatment - the solution for the laser field is also exhibited. Further considerations as concerning the role played by the noise terms in the field buildup are discussed. (Author) [pt

Origin of soft limits from nonlinear supersymmetry in Volkov-Akulov theory

Energy Technology Data Exchange (ETDEWEB)

Kallosh, Renata; Karlsson, Anna; Murli, Divyanshu [Stanford Institute for Theoretical Physics and Department of Physics, Stanford University, Stanford, CA 94305 (United States)

2017-03-15

We apply the background field technique, recently developed for a general class of nonlinear symmetries, at tree level, to the Volkov-Akulov theory with spontaneously broken N=1 supersymmetry. We find that the background field expansion in terms of the free fields to the lowest order reproduces the nonlinear supersymmetry transformation rules. The double soft limit of the background field is, in agreement with the new general identities, defined by the algebra of the nonlinear symmetries.

A hierarchy of high-order theories for modes in an elastic layer

DEFF Research Database (Denmark)

Sorokin, Sergey V.; Chapman, C. John

2015-01-01

A hierarchy of high-order theories for symmetric and skew-symmetric modes in an infinitely long elastic layer of the constant thickness is derived. For each member of the hierarchy, boundary conditions for layers of the finite length are formulated. The forcing problems at several approximation...

Extension of a nonlinear systems theory to general-frequency unsteady transonic aerodynamic responses

Science.gov (United States)

Silva, Walter A.

1993-01-01

A methodology for modeling nonlinear unsteady aerodynamic responses, for subsequent use in aeroservoelastic analysis and design, using the Volterra-Wiener theory of nonlinear systems is presented. The methodology is extended to predict nonlinear unsteady aerodynamic responses of arbitrary frequency. The Volterra-Wiener theory uses multidimensional convolution integrals to predict the response of nonlinear systems to arbitrary inputs. The CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code is used to generate linear and nonlinear unit impulse responses that correspond to each of the integrals for a rectangular wing with a NACA 0012 section with pitch and plunge degrees of freedom. The computed kernels then are used to predict linear and nonlinear unsteady aerodynamic responses via convolution and compared to responses obtained using the CAP-TSD code directly. The results indicate that the approach can be used to predict linear unsteady aerodynamic responses exactly for any input amplitude or frequency at a significant cost savings. Convolution of the nonlinear terms results in nonlinear unsteady aerodynamic responses that compare reasonably well with those computed using the CAP-TSD code directly but at significant computational cost savings.

Single-wave-number representation of nonlinear energy spectrum in elastic-wave turbulence of the Föppl-von Kármán equation: energy decomposition analysis and energy budget.

Science.gov (United States)

Yokoyama, Naoto; Takaoka, Masanori

2014-12-01

A single-wave-number representation of a nonlinear energy spectrum, i.e., a stretching-energy spectrum, is found in elastic-wave turbulence governed by the Föppl-von Kármán (FvK) equation. The representation enables energy decomposition analysis in the wave-number space and analytical expressions of detailed energy budgets in the nonlinear interactions. We numerically solved the FvK equation and observed the following facts. Kinetic energy and bending energy are comparable with each other at large wave numbers as the weak turbulence theory suggests. On the other hand, stretching energy is larger than the bending energy at small wave numbers, i.e., the nonlinearity is relatively strong. The strong correlation between a mode a(k) and its companion mode a(-k) is observed at the small wave numbers. The energy is input into the wave field through stretching-energy transfer at the small wave numbers, and dissipated through the quartic part of kinetic-energy transfer at the large wave numbers. Total-energy flux consistent with energy conservation is calculated directly by using the analytical expression of the total-energy transfer, and the forward energy cascade is observed clearly.

Topics in nonlinear wave theory with applications

International Nuclear Information System (INIS)

Tracy, E.R.

1984-01-01

Selected topics in nonlinear wave theory are discussed, and applications to the study of modulational instabilities are presented. A historical survey is given of topics relating to solitons and modulational problems. A method is then presented for generating exact periodic and quasi-periodic solutions to several nonlinear wave equations, which have important physical applications. The method is then specialized for the purposes of studying the modulational instability of a plane wave solution of the nonlinear Schroedinger equation, an equation with general applicability in one-dimensional modulational problems. Some numerical results obtained in conjunction with the analytic study are presented. The analytic approach explains the recurrence phenomena seen in the numerical studies, and the numerical work of other authors. The method of solution (related to the inverse scattering method) is then analyzed within the context of Hamiltonian dynamics where it is shown that the method can be viewed as simply a pair of canonical transformations. The Abel Transformation, which appears here and in the work of other authors, is shown to be a special form of Liouville's transformation to action-angle variables. The construction of closed form solutions of these nonlinear wave equations, via the solution of Jacobi's inversion problem, is surveyed briefly

Computational Elastic Knots

KAUST Repository

Zhao, Xin

2013-01-01

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

Numerical simulation of shear and the Poynting effects by the finite element method: An application of the generalised empirical inequalities in non-linear elasticity

KAUST Repository

Angela Mihai, L.; Goriely, Alain

2013-01-01

Finite element simulations of different shear deformations in non-linear elasticity are presented. We pay particular attention to the Poynting effects in hyperelastic materials, complementing recent theoretical findings by showing these effects

HAWC2 and BeamDyn: Comparison Between Beam Structural Models for Aero-Servo-Elastic Frameworks: Preprint

Energy Technology Data Exchange (ETDEWEB)

Pavese, Christian; Kim, Taeseong; Wang, Qi; Jonkman, Jason; Sprague, Michael A.

2016-08-01

This work presents a comparison of two beam codes for aero-servo-elastic frameworks: a new structural model for the aeroelastic code HAWC2 and a new nonlinear beam model, BeamDyn, for the aeroelastic modularization framework FAST v8. The main goal is to establish the suitability of the two approaches to model the structural behaviour of modern wind turbine blades in operation. Through a series of benchmarking structural cases of increasing complexity, the capability of the two codes to simulate highly nonlinear effects is investigated and analyzed. Results show that even though the geometrically exact beam theory can better model effects such as very large deflections, rotations, and structural couplings, an approach based on a multi-body formulation assembled through linear elements is capable of computing accurate solutions for typical nonlinear beam theory benchmarking cases.

Nonlinear Hydroelastic Waves Generated due to a Floating Elastic Plate in a Current

Directory of Open Access Journals (Sweden)

Ping Wang

2017-01-01

Full Text Available Effects of underlying uniform current on the nonlinear hydroelastic waves generated due to an infinite floating plate are studied analytically, under the hypotheses that the fluid is homogeneous, incompressible, and inviscid. For the case of irrotational motion, the Laplace equation is the governing equation, with the boundary conditions expressing a balance among the hydrodynamics, the uniform current, and elastic force. It is found that the convergent series solutions, obtained by the homotopy analysis method (HAM, consist of the nonlinear hydroelastic wave profile and the velocity potential. The impacts of important physical parameters are discussed in detail. With the increment of the following current intensity, we find that the amplitudes of the hydroelastic waves decrease very slightly, while the opposing current produces the opposite effect on the hydroelastic waves. Furthermore, the amplitudes of waves increase very obviously for higher opposing current speed but reduce very slightly for higher following current speed. A larger amplitude of the incident wave increases the hydroelastic wave deflections for both opposing and following current, while for Young’s modulus of the plate there is the opposite effect.

Mixing of two co-directional Rayleigh surface waves in a nonlinear elastic material.

Science.gov (United States)

Morlock, Merlin B; Kim, Jin-Yeon; Jacobs, Laurence J; Qu, Jianmin

2015-01-01

The mixing of two co-directional, initially monochromatic Rayleigh surface waves in an isotropic, homogeneous, and nonlinear elastic solid is investigated using analytical, finite element method, and experimental approaches. The analytical investigations show that while the horizontal velocity component can form a shock wave, the vertical velocity component can form a pulse independent of the specific ratios of the fundamental frequencies and amplitudes that are mixed. This analytical model is then used to simulate the development of the fundamentals, second harmonics, and the sum and difference frequency components over the propagation distance. The analytical model is further extended to include diffraction effects in the parabolic approximation. Finally, the frequency and amplitude ratios of the fundamentals are identified which provide maximum amplitudes of the second harmonics as well as of the sum and difference frequency components, to help guide effective material characterization; this approach should make it possible to measure the acoustic nonlinearity of a solid not only with the second harmonics, but also with the sum and difference frequency components. Results of the analytical investigations are then confirmed using the finite element method and the experimental feasibility of the proposed technique is validated for an aluminum specimen.

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...

Nonlinear free vibration of single walled Carbone NanoTubes conveying fluid

Directory of Open Access Journals (Sweden)

Azrar A.

2014-04-01

Full Text Available Nonlinear free vibration of single-walled carbon nanotubes (CNTs conveying fluid are modeled and numerically simulated based on von Kármán geometric nonlinearity and Eringen’s nonlocal elasticity theory. The CNTs are modelled as nanobeams where the effects of transverse shear deformation and rotary inertia are considered within the framework of Timoshenko beam theory. The governing equations and boundary conditions are derived using the Hamilton’s principle and the nonlinear equation of motion is solved by the Galerkin’s method. The small scale parameter and the fluid-tube interaction effects on the dynamic behaviours of the CNT-fluid system as well as the instabilities induced by the fluid-velocity can be investigated. The critical fluid-velocity and frequency-amplitude relationships as well as the flutter and divergence instability types and the associated time responses are obtained based on the presented methodological approach.

Mathematical Modeling of Contact Problems of Elasticity Theory with Continuous Unilateral Contact

Directory of Open Access Journals (Sweden)

I. V. Stankevich

2015-01-01

Full Text Available The work [1] presents the formulation and numerical solution of the problem concerning the unilateral discrete contact interaction of an elastic body and a rigid half-space. However, many parts and components of engineering structures have a pronounced continuous contact within a given surface [2, 3]. In this paper we consider a special case of this option of contact interaction when, the elastic body of finite size, subjected to external forces, is based on a rigid half-space. Contact occurs through a dedicated contact surface, which in general can change their sizes.Developed to solve this problem, a numerical algorithm is a further adaptation and development of the approaches described in [1]. The paper shows results of solving the model problem of the elasticity theory with and without taking friction into account. In the latter case, were additionally obtained numerical data characterizing the convergence of the solution.

An elastic-visco-plastic damage model: from theory to application

International Nuclear Information System (INIS)

Wang, X.C.; Habraken, A.M.

1996-01-01

An energy-based two-variable damage theory is applied to Bodner's model. It gives an elastic-viscoplastic damage model. Some theoretical details are described in this paper. The parameters identification procedure is discussed and a complete set of parameters for an aluminium is presented. Numerical modelling of the laboratory tests are used to validate the model. An industrial aeronautic rod fabrication process is simulated and some numerical results are presented in this paper. (orig.)

A combined dynamic analysis method for geometrically nonlinear vibration isolators with elastic rings

Science.gov (United States)

Hu, Zhan; Zheng, Gangtie

2016-08-01

A combined analysis method is developed in the present paper for studying the dynamic properties of a type of geometrically nonlinear vibration isolator, which is composed of push-pull configuration rings. This method combines the geometrically nonlinear theory of curved beams and the Harmonic Balance Method to overcome the difficulty in calculating the vibration and vibration transmissibility under large deformations of the ring structure. Using the proposed method, nonlinear dynamic behaviors of this isolator, such as the lock situation due to the coulomb damping and the usual jump resulting from the nonlinear stiffness, can be investigated. Numerical solutions based on the primary harmonic balance are first verified by direct integration results. Then, the whole procedure of this combined analysis method is demonstrated and validated by slowly sinusoidal sweeping experiments with different amplitudes of the base excitation. Both numerical and experimental results indicate that this type of isolator behaves as a hardening spring with increasing amplitude of the base excitation, which makes it suitable for isolating both steady-state vibrations and transient shocks.

Influence of quantum confinement on the carrier contribution to the elastic constants in quantum confined heavily doped non-linear optical and optoelectronic materials: simplified theory and the suggestion for experimental determination

International Nuclear Information System (INIS)

Baruah, D; Choudhury, S; Singh, K M; Ghatak, K P

2007-01-01

In this paper we study the carrier contribution to elastic constants in quantum confined heavily doped non-linear optical compounds on the basis of a newly formulated electron dispersion law taking into account the anisotropies of the effective electron masses and spin orbit splitting constants together with the proper inclusion of the crystal field splitting in the Hamiltonian within the framework of k.p formalism. All the results of heavily doped three, and two models of Kane for heavily doped III-V materials form special cases of our generalized analysis. It has been found, taking different heavily doped quantum confined materials that, the carrier contribution to the elastic constants increases with increase in electron statistics and decrease in film thickness in ladder like manners for all types of quantum confinements with different numerical values which are totally dependent on the energy band constants. The said contribution is greatest in quantum dots and least in quantum wells together with the fact the heavy doping enhances the said contributions for all types of quantum confined materials. We have suggested an experimental method of determining the carrier contribution to the elastic constants in nanostructured materials having arbitrary band structures

The effect of non-local higher order stress to predict the nonlinear vibration behavior of carbon nanotube conveying viscous nanoflow

Energy Technology Data Exchange (ETDEWEB)

Mohammadimehr, M., E-mail: mmohammadimehr@kashanu.ac.ir [Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, P.O. Box: 87317-53153, Kashan (Iran, Islamic Republic of); Mohammadi-Dehabadi, A.A. [Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, P.O. Box: 87317-53153, Kashan (Iran, Islamic Republic of); Department of Mechanical Engineering, Iran University of Science and Technology, Narmak, Tehran (Iran, Islamic Republic of); Maraghi, Z. Khoddami [Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, P.O. Box: 87317-53153, Kashan (Iran, Islamic Republic of)

2017-04-01

In this research, the effect of non-local higher order stress on the nonlinear vibration behavior of carbon nanotube conveying viscous nanoflow resting on elastic foundation is investigated. Physical intuition reveals that increasing nanoscale stress leads to decrease the stiffness of nanostructure which firstly established by Eringen's non-local elasticity theory (previous nonlocal method) while many of papers have concluded otherwise at microscale based on modified couple stress, modified strain gradient theories and surface stress effect. The non-local higher order stress model (new nonlocal method) is used in this article that has been studied by few researchers in other fields and the results from the present study show that the trend of the new nonlocal method and size dependent effect including modified couple stress theory is the same. In this regard, the nonlinear motion equations are derived using a variational principal approach considering essential higher-order non-local terms. The surrounded elastic medium is modeled by Pasternak foundation to increase the stability of system where the fluid flow may cause system instability. Effects of various parameters such as non-local parameter, elastic foundation coefficient, and fluid flow velocity on the stability and dimensionless natural frequency of nanotube are investigated. The results of this research show that the small scale parameter based on higher order stress help to increase the natural frequency which has been approved by other small scale theories such as strain gradient theory, modified couple stress theory and experiments, and vice versa for previous nonlocal method. This study may be useful to measure accurately the vibration characteristics of nanotubes conveying viscous nanoflow and to design nanofluidic devices for detecting blood Glucose.

The effect of non-local higher order stress to predict the nonlinear vibration behavior of carbon nanotube conveying viscous nanoflow

International Nuclear Information System (INIS)

Mohammadimehr, M.; Mohammadi-Dehabadi, A.A.; Maraghi, Z. Khoddami

2017-01-01

In this research, the effect of non-local higher order stress on the nonlinear vibration behavior of carbon nanotube conveying viscous nanoflow resting on elastic foundation is investigated. Physical intuition reveals that increasing nanoscale stress leads to decrease the stiffness of nanostructure which firstly established by Eringen's non-local elasticity theory (previous nonlocal method) while many of papers have concluded otherwise at microscale based on modified couple stress, modified strain gradient theories and surface stress effect. The non-local higher order stress model (new nonlocal method) is used in this article that has been studied by few researchers in other fields and the results from the present study show that the trend of the new nonlocal method and size dependent effect including modified couple stress theory is the same. In this regard, the nonlinear motion equations are derived using a variational principal approach considering essential higher-order non-local terms. The surrounded elastic medium is modeled by Pasternak foundation to increase the stability of system where the fluid flow may cause system instability. Effects of various parameters such as non-local parameter, elastic foundation coefficient, and fluid flow velocity on the stability and dimensionless natural frequency of nanotube are investigated. The results of this research show that the small scale parameter based on higher order stress help to increase the natural frequency which has been approved by other small scale theories such as strain gradient theory, modified couple stress theory and experiments, and vice versa for previous nonlocal method. This study may be useful to measure accurately the vibration characteristics of nanotubes conveying viscous nanoflow and to design nanofluidic devices for detecting blood Glucose.

Tail estimates for stochastic fixed point equations via nonlinear renewal theory

DEFF Research Database (Denmark)

Collamore, Jeffrey F.; Vidyashankar, Anand N.

2013-01-01

estimate P(V>u)~Cu^{-r} as u tends to infinity, and also present a corresponding Lundberg-type upper bound. To this end, we introduce a novel dual change of measure on a random time interval and analyze the path properties, using nonlinear renewal theory, of the Markov chain resulting from the forward...... iteration of the given stochastic fixed point equation. In the process, we establish several new results in the realm of nonlinear renewal theory for these processes. As a consequence of our techniques, we also establish a new characterization of the extremal index. Finally, we provide some extensions...... of our methods to Markov-driven processes....

Geometrical phases from global gauge invariance of nonlinear classical field theories

International Nuclear Information System (INIS)

Garrison, J.C.; Chiao, R.Y.

1988-01-01

We show that the geometrical phases recently discovered in quantum mechanics also occur naturally in the theory of any classical complex multicomponent field satisfying nonlinear equations derived from a Lagrangean with is invariant under gauge transformations of the first kind. Some examples are the paraxial wave equation for nonlinear optics, and Ginzburg-Landau equations for complex order parameters in condensed-matter physics

Density functional theory and evolution algorithm calculations of elastic properties of AlON

Energy Technology Data Exchange (ETDEWEB)

Batyrev, I. G.; Taylor, D. E.; Gazonas, G. A.; McCauley, J. W. [U.S. Army Research Laboratory, Aberdeen Proving Ground, Maryland 21005 (United States)

2014-01-14

Different models for aluminum oxynitride (AlON) were calculated using density functional theory and optimized using an evolutionary algorithm. Evolutionary algorithm and density functional theory (DFT) calculations starting from several models of AlON with different Al or O vacancy locations and different positions for the N atoms relative to the vacancy were carried out. The results show that the constant anion model [McCauley et al., J. Eur. Ceram. Soc. 29(2), 223 (2009)] with a random distribution of N atoms not adjacent to the Al vacancy has the lowest energy configuration. The lowest energy structure is in a reasonable agreement with experimental X-ray diffraction spectra. The optimized structure of a 55 atom unit cell was used to construct 220 and 440 atom models for simulation cells using DFT with a Gaussian basis set. Cubic elastic constant predictions were found to approach the experimentally determined AlON single crystal elastic constants as the model size increased from 55 to 440 atoms. The pressure dependence of the elastic constants found from simulated stress-strain relations were in overall agreement with experimental measurements of polycrystalline and single crystal AlON. Calculated IR intensity and Raman spectra are compared with available experimental data.

Probing mesoscopic crystals with electrons: One-step simultaneous inelastic and elastic scattering theory

Science.gov (United States)

Nazarov, Vladimir U.; Silkin, Vyacheslav M.; Krasovskii, Eugene E.

2017-12-01

Inelastic scattering of the medium-energy (˜10 -100 eV) electrons underlies the method of the high-resolution electron energy-loss spectroscopy (HREELS), which has been successfully used for decades to characterize pure and adsorbate-covered surfaces of solids. With the emergence of graphene and other quasi-two-dimensional (Q2D) crystals, HREELS could be expected to become the major experimental tool to study this class of materials. We, however, identify a critical flaw in the theoretical picture of the HREELS of Q2D crystals in the context of the inelastic scattering only ("energy-loss functions" formalism), in contrast to its justifiable use for bulk solids and surfaces. The shortcoming is the neglect of the elastic scattering, which we show is inseparable from the inelastic one, and which, affecting the spectra dramatically, must be taken into account for the meaningful interpretation of the experiment. With this motivation, using the time-dependent density functional theory for excitations, we build a theory of the simultaneous inelastic and elastic electron scattering at Q2D crystals. We apply this theory to HREELS of graphene, revealing an effect of the strongly coupled excitation of the π +σ plasmon and elastic diffraction resonances. Our results open a path to the theoretically interpretable study of the excitation processes in crystalline mesoscopic materials by means of HREELS, with its supreme resolution on the meV energy scale, which is far beyond the capacity of the now overwhelmingly used EELS in transmission electron microscopy.

A non-linear theory of strong interactions

International Nuclear Information System (INIS)

Skyrme, T.H.R.

1994-01-01

A non-linear theory of mesons, nucleons and hyperons is proposed. The three independent fields of the usual symmetrical pseudo-scalar pion field are replaced by the three directions of a four-component field vector of constant length, conceived in an Euclidean four-dimensional isotopic spin space. This length provides the universal scaling factor, all other constants being dimensionless; the mass of the meson field is generated by a φ 4 term; this destroys the continuous rotation group in the iso-space, leaving a 'cubic' symmetry group. Classification of states by this group introduces quantum numbers corresponding to isotopic spin and to 'strangeness'; one consequences is that, at least in elementary interactions, charge is only conserved module 4. Furthermore, particle states have not a well-defined parity, but parity is effectively conserved for meson-nucleon interactions. A simplified model, using only two dimensions of space and iso-space, is considered further; the non-linear meson field has solutions with particle character, and an indication is given of the way in which the particle field variables might be introduced as collective co-ordinates describing the dynamics of these particular solutions of the meson field equations, suggesting a unified theory based on the meson field alone. (author). 7 refs

de Sitter limit of inflation and nonlinear perturbation theory

DEFF Research Database (Denmark)

R. Jarnhus, Philip; Sloth, Martin Snoager

2007-01-01

We study the fourth order action of the comoving curvature perturbation in an inflationary universe in order to understand more systematically the de Sitter limit in nonlinear cosmological perturbation theory. We derive the action of the curvature perturbation to fourth order in the comoving gaug...

Modeling complicated rheological behaviors in encapsulating shells of lipid-coated microbubbles accounting for nonlinear changes of both shell viscosity and elasticity.

Science.gov (United States)

Li, Qian; Matula, Thomas J; Tu, Juan; Guo, Xiasheng; Zhang, Dong

2013-02-21

It has been accepted that the dynamic responses of ultrasound contrast agent (UCA) microbubbles will be significantly affected by the encapsulating shell properties (e.g., shell elasticity and viscosity). In this work, a new model is proposed to describe the complicated rheological behaviors in an encapsulating shell of UCA microbubbles by applying the nonlinear 'Cross law' to the shell viscous term in the Marmottant model. The proposed new model was verified by fitting the dynamic responses of UCAs measured with either a high-speed optical imaging system or a light scattering system. The comparison results between the measured radius-time curves and the numerical simulations demonstrate that the 'compression-only' behavior of UCAs can be successfully simulated with the new model. Then, the shell elastic and viscous coefficients of SonoVue microbubbles were evaluated based on the new model simulations, and compared to the results obtained from some existing UCA models. The results confirm the capability of the current model for reducing the dependence of bubble shell parameters on the initial bubble radius, which indicates that the current model might be more comprehensive to describe the complex rheological nature (e.g., 'shear-thinning' and 'strain-softening') in encapsulating shells of UCA microbubbles by taking into account the nonlinear changes of both shell elasticity and shell viscosity.

Modeling complicated rheological behaviors in encapsulating shells of lipid-coated microbubbles accounting for nonlinear changes of both shell viscosity and elasticity

International Nuclear Information System (INIS)

Li Qian; Tu Juan; Guo Xiasheng; Zhang Dong; Matula, Thomas J

2013-01-01

It has been accepted that the dynamic responses of ultrasound contrast agent (UCA) microbubbles will be significantly affected by the encapsulating shell properties (e.g., shell elasticity and viscosity). In this work, a new model is proposed to describe the complicated rheological behaviors in an encapsulating shell of UCA microbubbles by applying the nonlinear ‘Cross law’ to the shell viscous term in the Marmottant model. The proposed new model was verified by fitting the dynamic responses of UCAs measured with either a high-speed optical imaging system or a light scattering system. The comparison results between the measured radius–time curves and the numerical simulations demonstrate that the ‘compression-only’ behavior of UCAs can be successfully simulated with the new model. Then, the shell elastic and viscous coefficients of SonoVue microbubbles were evaluated based on the new model simulations, and compared to the results obtained from some existing UCA models. The results confirm the capability of the current model for reducing the dependence of bubble shell parameters on the initial bubble radius, which indicates that the current model might be more comprehensive to describe the complex rheological nature (e.g., ‘shear-thinning’ and ‘strain-softening’) in encapsulating shells of UCA microbubbles by taking into account the nonlinear changes of both shell elasticity and shell viscosity. (paper)

Nonlinear dynamic response of electro-thermo-mechanically loaded piezoelectric cylindrical shell reinforced with BNNTs

International Nuclear Information System (INIS)

Yang, J H; Yang, J; Kitipornchai, S

2012-01-01

This paper presents an investigation on the nonlinear dynamic response of piezoelectric cylindrical shells reinforced with boron nitride nanotubes (BNNTs) under a combined axisymmetric electro-thermo-mechanical loading. By employing the classical Donnell shell theory, the von Kármán–Donnell kinematic relationship, and a piezo-elastic constitutive law including thermal effects, the nonlinear governing equations of motion of the shell are derived through the Reissner variational principle. The finite difference method and a time-integration scheme are used to obtain the nonlinear dynamic response of the BNNT-reinforced piezoelectric shell. A parametric study is conducted, showing the effects of geometrically nonlinear deformation, applied voltage, temperature change, mechanical load, BNNT volume fraction and boundary conditions on the nonlinear dynamic response. (paper)

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)

Response statistics of rotating shaft with non-linear elastic restoring forces by path integration

Science.gov (United States)

Gaidai, Oleg; Naess, Arvid; Dimentberg, Michael

2017-07-01

Extreme statistics of random vibrations is studied for a Jeffcott rotor under uniaxial white noise excitation. Restoring force is modelled as elastic non-linear; comparison is done with linearized restoring force to see the force non-linearity effect on the response statistics. While for the linear model analytical solutions and stability conditions are available, it is not generally the case for non-linear system except for some special cases. The statistics of non-linear case is studied by applying path integration (PI) method, which is based on the Markov property of the coupled dynamic system. The Jeffcott rotor response statistics can be obtained by solving the Fokker-Planck (FP) equation of the 4D dynamic system. An efficient implementation of PI algorithm is applied, namely fast Fourier transform (FFT) is used to simulate dynamic system additive noise. The latter allows significantly reduce computational time, compared to the classical PI. Excitation is modelled as Gaussian white noise, however any kind distributed white noise can be implemented with the same PI technique. Also multidirectional Markov noise can be modelled with PI in the same way as unidirectional. PI is accelerated by using Monte Carlo (MC) estimated joint probability density function (PDF) as initial input. Symmetry of dynamic system was utilized to afford higher mesh resolution. Both internal (rotating) and external damping are included in mechanical model of the rotor. The main advantage of using PI rather than MC is that PI offers high accuracy in the probability distribution tail. The latter is of critical importance for e.g. extreme value statistics, system reliability, and first passage probability.

A programmable nonlinear acoustic metamaterial

Directory of Open Access Journals (Sweden)

Tianzhi Yang

2017-09-01

Full Text Available Acoustic metamaterials with specifically designed lattices can manipulate acoustic/elastic waves in unprecedented ways. Whereas there are many studies that focus on passive linear lattice, with non-reconfigurable structures. In this letter, we present the design, theory and experimental demonstration of an active nonlinear acoustic metamaterial, the dynamic properties of which can be modified instantaneously with reversibility. By incorporating active and nonlinear elements in a single unit cell, a real-time tunability and switchability of the band gap is achieved. In addition, we demonstrate a dynamic “editing” capability for shaping transmission spectra, which can be used to create the desired band gap and resonance. This feature is impossible to achieve in passive metamaterials. These advantages demonstrate the versatility of the proposed device, paving the way toward smart acoustic devices, such as logic elements, diode and transistor.

Nonlinear analysis approximation theory, optimization and applications

CERN Document Server

2014-01-01

Many of our daily-life problems can be written in the form of an optimization problem. Therefore, solution methods are needed to solve such problems. Due to the complexity of the problems, it is not always easy to find the exact solution. However, approximate solutions can be found. The theory of the best approximation is applicable in a variety of problems arising in nonlinear functional analysis and optimization. This book highlights interesting aspects of nonlinear analysis and optimization together with many applications in the areas of physical and social sciences including engineering. It is immensely helpful for young graduates and researchers who are pursuing research in this field, as it provides abundant research resources for researchers and post-doctoral fellows. This will be a valuable addition to the library of anyone who works in the field of applied mathematics, economics and engineering.

Elastic-Plastic Nonlinear Response of a Space Shuttle External Tank Stringer. Part 2; Thermal and Mechanical Loadings

Science.gov (United States)

Knight, Norman F., Jr.; Warren, Jerry E.; Elliott, Kenny B.; Song, Kyongchan; Raju, Ivatury S.

2012-01-01

Elastic-plastic, large-deflection nonlinear thermo-mechanical stress analyses are performed for the Space Shuttle external tank s intertank stringers. Detailed threedimensional finite element models are developed and used to investigate the stringer s elastic-plastic response for different thermal and mechanical loading events from assembly through flight. Assembly strains caused by initial installation on an intertank panel are accounted for in the analyses. Thermal loading due to tanking was determined to be the bounding loading event. The cryogenic shrinkage caused by tanking resulted in a rotation of the intertank chord flange towards the center of the intertank, which in turn loaded the intertank stringer feet. The analyses suggest that the strain levels near the first three fasteners remain sufficiently high that a failure may occur. The analyses also confirmed that the installation of radius blocks on the stringer feet ends results in an increase in the stringer capability.

Inverse operator theory method and its applications in nonlinear physics

International Nuclear Information System (INIS)

Fang Jinqing

1993-01-01

Inverse operator theory method, which has been developed by G. Adomian in recent years, and its applications in nonlinear physics are described systematically. The method can be an unified effective procedure for solution of nonlinear and/or stochastic continuous dynamical systems without usual restrictive assumption. It is realized by Mathematical Mechanization by us. It will have a profound on the modelling of problems of physics, mathematics, engineering, economics, biology, and so on. Some typical examples of the application are given and reviewed

Analysis on Forced Vibration of Thin-Wall Cylindrical Shell with Nonlinear Boundary Condition

Directory of Open Access Journals (Sweden)

Qiansheng Tang

2016-01-01

Full Text Available Forced vibration of thin-wall cylindrical shell under nonlinear boundary condition was discussed in this paper. The nonlinear boundary was modeled as supported clearance in one end of shell and the restraint was assumed as linearly elastic in the radial direction. Based on Sanders’ shell theory, Lagrange equation was utilized to derive the nonlinear governing equations of cylindrical shell. The displacements in three directions were represented by beam functions and trigonometric functions. In the study of nonlinear dynamic responses of thin-wall cylindrical shell with supported clearance under external loads, the Newmark method is used to obtain time history, frequency spectrum plot, phase portraits, Poincare section, bifurcation diagrams, and three-dimensional spectrum plot with different parameters. The effects of external loads, supported clearance, and support stiffness on nonlinear dynamics behaviors of cylindrical shell with nonlinear boundary condition were discussed.

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.

In-Flight Aeroelastic Stability of the Thermal Protection System on the NASA HIAD, Part II: Nonlinear Theory and Extended Aerodynamics

Science.gov (United States)

Goldman, Benjamin D.; Dowell, Earl H.; Scott, Robert C.

2015-01-01

Conical shell theory and a supersonic potential flow aerodynamic theory are used to study the nonlinear pressure buckling and aeroelastic limit cycle behavior of the thermal protection system for NASA's Hypersonic Inflatable Aerodynamic Decelerator. The structural model of the thermal protection system consists of an orthotropic conical shell of the Donnell type, resting on several circumferential elastic supports. Classical Piston Theory is used initially for the aerodynamic pressure, but was found to be insufficient at low supersonic Mach numbers. Transform methods are applied to the convected wave equation for potential flow, and a time-dependent aerodynamic pressure correction factor is obtained. The Lagrangian of the shell system is formulated in terms of the generalized coordinates for all displacements and the Rayleigh-Ritz method is used to derive the governing differential-algebraic equations of motion. Aeroelastic limit cycle oscillations and buckling deformations are calculated in the time domain using a Runge-Kutta method in MATLAB. Three conical shell geometries were considered in the present analysis: a 3-meter diameter 70 deg. cone, a 3.7-meter 70 deg. cone, and a 6-meter diameter 70 deg. cone. The 6-meter configuration was loaded statically and the results were compared with an experimental load test of a 6-meter HIAD. Though agreement between theoretical and experimental strains was poor, the circumferential wrinkling phenomena observed during the experiments was captured by the theory and axial deformations were qualitatively similar in shape. With Piston Theory aerodynamics, the nonlinear flutter dynamic pressures of the 3-meter configuration were in agreement with the values calculated using linear theory, and the limit cycle amplitudes were generally on the order of the shell thickness. The effect of axial tension was studied for this configuration, and increasing tension was found to decrease the limit cycle amplitudes when the circumferential

A novel nonlinear damage resonance intermodulation effect for structural health monitoring

Science.gov (United States)

Ciampa, Francesco; Scarselli, Gennaro; Meo, Michele

2017-04-01

This paper is aimed at developing a theoretical model able to predict the generation of nonlinear elastic effects associated to the interaction of ultrasonic waves with the steady-state nonlinear response of local defect resonance (LDR). The LDR effect is used in nonlinear elastic wave spectroscopy to enhance the excitation of the material damage at its local resonance, thus to dramatically increase the vibrational amplitude of material nonlinear phenomena. The main result of this work is to prove both analytically and experimentally the generation of novel nonlinear elastic wave effects, here named as nonlinear damage resonance intermodulation, which correspond to a nonlinear intermodulation between the driving frequency and the LDR one. Beside this intermodulation effect, other nonlinear elastic wave phenomena such as higher harmonics of the input frequency and superharmonics of LDR frequency were found. The analytical model relies on solving the nonlinear equation of motion governing bending displacement under the assumption of both quadratic and cubic nonlinear defect approximation. Experimental tests on a damaged composite laminate confirmed and validated these predictions and showed that using continuous periodic excitation, the nonlinear structural phenomena associated to LDR could also be featured at locations different from the damage resonance. These findings will provide new opportunities for material damage detection using nonlinear ultrasounds.

Energy-momentum conserving higher-order time integration of nonlinear dynamics of finite elastic fiber-reinforced continua

Science.gov (United States)

Erler, Norbert; Groß, Michael

2015-05-01

Since many years the relevance of fibre-reinforced polymers is steadily increasing in fields of engineering, especially in aircraft and automotive industry. Due to the high strength in fibre direction, but the possibility of lightweight construction, these composites replace more and more traditional materials as metals. Fibre-reinforced polymers are often manufactured from glass or carbon fibres as attachment parts or from steel or nylon cord as force transmission parts. Attachment parts are mostly subjected to small strains, but force transmission parts usually suffer large deformations in at least one direction. Here, a geometrically nonlinear formulation is necessary. Typical examples are helicopter rotor blades, where the fibres have the function to stabilize the structure in order to counteract large centrifugal forces. For long-run analyses of rotor blade deformations, we have to apply numerically stable time integrators for anisotropic materials. This paper presents higher-order accurate and numerically stable time stepping schemes for nonlinear elastic fibre-reinforced continua with anisotropic stress behaviour.

Janus field theories from non-linear BF theories for multiple M2-branes

International Nuclear Information System (INIS)

Ryang, Shijong

2009-01-01

We integrate the nonpropagating B μ gauge field for the non-linear BF Lagrangian describing N M2-branes which includes terms with even number of the totally antisymmetric tensor M IJK in arXiv:0808.2473 and for the two-types of non-linear BF Lagrangians which include terms with odd number of M IJK as well in arXiv:0809:0985. For the former Lagrangian we derive directly the DBI-type Lagrangian expressed by the SU(N) dynamical A μ gauge field with a spacetime dependent coupling constant, while for the low-energy expansions of the latter Lagrangians the B μ integration is iteratively performed. The derived Janus field theory Lagrangians are compared.

Soliton excitations in a class of nonlinear field theory models

International Nuclear Information System (INIS)

Makhan'kov, V.G.; Fedyanin, V.K.

1985-01-01

Investigation results of nonlinear models of the field theory with a lagrangian are described. The theory includes models both with zero stable vacuum epsilon=1 and with condensate epsilon=-1 (of disturbed symmetry). Conditions of existence of particle-like solutions (PLS), stability of these solutions are investigated. Soliton dynamics is studied. PLS formfactors are calculated. Statistical mechanics of solitons is built and their dynamic structure factors are calculated

Elastic thickness determination based on Vening Meinesz-Moritz and flexural theories of isostasy

Science.gov (United States)

Eshagh, Mehdi

2018-06-01

Elastic thickness (Te) is one of mechanical properties of the Earth's lithosphere. The lithosphere is assumed to be a thin elastic shell, which is bended under the topographic, bathymetric and sediment loads on. The flexure of this elastic shell depends on its thickness or Te. Those shells having larger Te flex less. In this paper, a forward computational method is presented based on the Vening Meinesz-Moritz (VMM) and flexural theories of isostasy. Two Moho flexure models are determined using these theories, considering effects of surface and subsurface loads. Different values are selected for Te in the flexural method to see by which one, the closest Moho flexure to that of the VMM is achieved. The effects of topographic/bathymetric, sediments and crustal crystalline masses, and laterally variable upper mantle density, Young's modulus and Poisson's ratio are considered in whole computational process. Our mathematical derivations are based on spherical harmonics, which can be used to estimate Te at any single point, meaning that there is no edge effect in the method. However, the Te map needs to be filtered to remove noise at some points. A median filter with a window size of 5° × 5° and overlap of 4° works well for this purpose. The method is applied to estimate Te over South America using the data of CRUST1.0 and a global gravity model.

A new nonlinear parameter in the developed strain-to-applied strain of the soft tissues and its application in ultrasound elasticity imaging.

Science.gov (United States)

Xu, Jingping; Tripathy, Sakya; Rubin, Jonathan M; Stidham, Ryan W; Johnson, Laura A; Higgins, Peter D R; Kim, Kang

2012-03-01

Strain developed under quasi-static deformation has been mostly used in ultrasound elasticity imaging (UEI) to determine the stiffness change of tissues. However, the strain measure in UEI is often less sensitive to a subtle change of stiffness. This is particularly true for Crohn's disease where we have applied strain imaging to the differentiation of acutely inflamed bowel from chronically fibrotic bowel. In this study, a new nonlinear elastic parameter of the soft tissues is proposed to overcome this limit. The purpose of this study is to evaluate the newly proposed method and demonstrate its feasibility in the UEI. A nonlinear characteristic of soft tissues over a relatively large dynamic range of strain was investigated. A simplified tissue model based on a finite element (FE) analysis was integrated with a laboratory developed ultrasound radio-frequency (RF) signal synthesis program. Two-dimensional speckle tracking was applied to this model to simulate the nonlinear behavior of the strain developed in a target inclusion over the applied average strain to the surrounding tissues. A nonlinear empirical equation was formulated and optimized to best match the developed strain-to-applied strain relation obtained from the FE simulation. The proposed nonlinear equation was applied to in vivo measurements and nonlinear parameters were further empirically optimized. For an animal model, acute and chronic inflammatory bowel disease was induced in Lewis rats with trinitrobenzene sulfonic acid (TNBS)-ethanol treatments. After UEI, histopathology and direct mechanical measurements were performed on the excised tissues. The extracted nonlinear parameter from the developed strain-to-applied strain relation differentiated the three different tissue types with 1.96 ± 0.12 for normal, 1.50 ± 0.09 for the acutely inflamed and 1.03 ± 0.08 for the chronically fibrotic tissue. T-tests determined that the nonlinear parameters between normal, acutely inflamed and fibrotic tissue

Synthesis of robust nonlinear autopilots using differential game theory

Science.gov (United States)

Menon, P. K. A.

1991-01-01

A synthesis technique for handling unmodeled disturbances in nonlinear control law synthesis was advanced using differential game theory. Two types of modeling inaccuracies can be included in the formulation. The first is a bias-type error, while the second is the scale-factor-type error in the control variables. The disturbances were assumed to satisfy an integral inequality constraint. Additionally, it was assumed that they act in such a way as to maximize a quadratic performance index. Expressions for optimal control and worst-case disturbance were then obtained using optimal control theory.

Linear and nonlinear instability theory of a noble gas MHD generator

International Nuclear Information System (INIS)

Mesland, A.J.

1982-01-01

This thesis deals with the stability of the working medium of a seeded noble gas magnetohydrodynamic generator. The aim of the study is to determine the instability mechanism which is most likely to occur in experimental MHD generators and to describe its behaviour with linear and nonlinear theories. In chapter I a general introduction is given. The pertinent macroscopic basic equations are derived in chapter II, viz. the continuity, the momentum and the energy equation for the electrons and the heavy gas particles, consisting of the seed particles and the noble gas atoms. Chapter III deals with the linear plane wave analysis of small disturbances of a homogeneous steady state. The steady state is discussed in chapter IV. The values for the steady state parameters used for the calculations both for the linear analysis as for the nonlinear analysis are made plausible with the experimental values. Based on the results of the linear plane wave theory a nonlinear plane wave model of the electrothermal instability is introduced in chapter V. (Auth.)

Properties of some nonlinear Schroedinger equations motivated through information theory

International Nuclear Information System (INIS)

Yuan, Liew Ding; Parwani, Rajesh R

2009-01-01

We update our understanding of nonlinear Schroedinger equations motivated through information theory. In particular we show that a q-deformation of the basic nonlinear equation leads to a perturbative increase in the energy of a system, thus favouring the simplest q = 1 case. Furthermore the energy minimisation criterion is shown to be equivalent, at leading order, to an uncertainty maximisation argument. The special value η = 1/4 for the interpolation parameter, where leading order energy shifts vanish, implies the preservation of existing supersymmetry in nonlinearised supersymmetric quantum mechanics. Physically, η might be encoding relativistic effects.

On the hyperporous non-linear elasticity model for fusion-relevant pebble beds

International Nuclear Information System (INIS)

Di Maio, P.A.; Giammusso, R.; Vella, G.

2010-01-01

Packed pebble beds are particular granular systems composed of a large amount of small particles, arranged in irregular lattices and surrounded by a gas filling interstitial spaces. Due to their heterogeneous structure, pebble beds have non-linear and strongly coupled thermal and mechanical behaviours whose constitutive models seem limited, being not suitable for fusion-relevant design-oriented applications. Within the framework of the modelling activities promoted for the lithiated ceramics and beryllium pebble beds foreseen in the Helium-Cooled Pebble Bed breeding blanket concept of DEMO, at the Department of Nuclear Engineering of the University of Palermo (DIN) a thermo-mechanical constitutive model has been set-up assuming that pebble beds can be considered as continuous, homogeneous and isotropic media. The present paper deals with the DIN non-linear elasticity constitutive model, based on the assumption that during the reversible straining of a pebble bed its effective logarithmic bulk modulus depends on the equivalent pressure according to a modified power law and its effective Poisson modulus remains constant. In these hypotheses the functional dependence of the effective tangential and secant bed deformation moduli on either the equivalent pressure or the volumetric strain have been derived in a closed analytical form. A procedure has been, then, defined to assess the model parameters for a given pebble bed from its oedometric test results and it has been applied to both polydisperse lithium orthosilicate and single size beryllium pebble beds.

Variational problems arising in classical mechanics and nonlinear elasticity

International Nuclear Information System (INIS)

Spencer, P.

1999-01-01

In this thesis we consider two different classes of variational problems. First, one-dimensional problems arising from classical mechanics where the problem is to determine whether there is a unique function η 0 (x) which minimises the energy functional of the form I(η) = ∫ a b L(x,η(x), η'(x)) dx. We will investigate uniqueness by making a change of dependent and independent variables and showing that for a class of integrands L with a particular kind of scaling invariance the resulting integrand is completely convex. The change of variables arises by applying results from Lie group theory as applied in the study of differential equations and this work is motivated by [60] and [68]. Second, the problem of minimising energy functionals of the form E(u) = ∫ A W(∇u(x)) dx in the case of a nonlinear elastic body occupying an annular region A contains R 2 with u : A-bar → A-bar. This work is motivated by [57] (in particular the example of paragraph 4). We will consider rotationally symmetric deformations satisfying prescribed boundary conditions. We will show the existence of minimisers for stored energy functions of the form W(F) = g-tilde(vertical bar-F-vertical bar, det(F)) in a class of general rotationally symmetric deformations of a compressible annulus and for stored energy functions of the form W(F) = g-bar(vertical bar-F-vertical bar) in a class of rotationally symmetric deformations of an incompressible annulus. We will also show that in each case the minimisers are solutions of the full equilibrium equations. A model problem will be considered where the energy functional is the Dirichlet integral and it will be shown that the rotationally symmetric solution obtained is a minimiser among admissible non-rotationally symmetric deformations. In the case of an incompressible annulus, we will consider the Dirichlet integral as the energy functional and show that the rotationally symmetric equilibrium solutions in this case are weak local minimisers in

A Leonard-Sanders-Budiansky-Koiter-Type Nonlinear Shell Theory with a Hierarchy of Transverse-Shearing Deformations

Science.gov (United States)

Nemeth, Michael P.

2013-01-01

A detailed exposition on a refined nonlinear shell theory suitable for nonlinear buckling analyses of laminated-composite shell structures is presented. This shell theory includes the classical nonlinear shell theory attributed to Leonard, Sanders, Koiter, and Budiansky as an explicit proper subset. This approach is used in order to leverage the exisiting experience base and to make the theory attractive to industry. In addition, the formalism of general tensors is avoided in order to expose the details needed to fully understand and use the theory. The shell theory is based on "small" strains and "moderate" rotations, and no shell-thinness approximations are used. As a result, the strain-displacement relations are exact within the presumptions of "small" strains and "moderate" rotations. The effects of transverse-shearing deformations are included in the theory by using analyst-defined functions to describe the through-the-thickness distributions of transverse-shearing strains. Constitutive equations for laminated-composite shells are derived without using any shell-thinness approximations, and simplified forms and special cases are presented.

Internal resonance of an elastic body levitated above high-Tc superconducting bulks

International Nuclear Information System (INIS)

Kokuzawa, T; Toshihiko, S; Yoshizawa, M

2010-01-01

In high-Tc superconducting magnetic levitation systems, levitated bodies can keep stable levitation with no contact and no control and thus their damping is very small. Thanks to these features, their applications to various apparatus are expected. However, on account of their small damping, the nonlinearity of electromagnetic levitation force can give notable effects upon motion of the levitated bodies. Therefore this nonlinearity must be taken into account to accurately analyze the dynamical behavior of the levitated bodies. Structures of such a levitated body can show elastic deformation if the large electromagnetic force acts on it. Therefore, we need to deal with the model as an elastic body. As mentioned above, nonlinear characteristics easily appear in this elastic vibration on account of the small damping. Especially when the ratio of the natural frequencies of the eigenmodes is integer, internal resonance can occur. This nonlinear resonance is derived from nonlinear interactions among the eigenmodes of the elastic levitated body. This kind of internal resonance of an elastic body appearing in high-Tc superconducting levitation systems has not been studied so far. This research especially deals with internal resonance of a beam supported at both its ends by electromagnetic forces acting on permanent magnets. The governing equation with the nonlinear boundary conditions for the dynamics of a levitated beam has been derived. Numerical results show internal resonance of the 1st mode and the 3rd mode. Experimental results are qualitatively in good agreement with numerical ones.

Nonlinear vibrations analysis of rotating drum-disk coupling structure

Science.gov (United States)

Chaofeng, Li; Boqing, Miao; Qiansheng, Tang; Chenyang, Xi; Bangchun, Wen

2018-04-01

A dynamic model of a coupled rotating drum-disk system with elastic support is developed in this paper. By considering the effects of centrifugal and Coriolis forces as well as rotation-induced hoop stress, the governing differential equation of the drum-disk is derived by Donnell's shell theory. The nonlinear amplitude-frequency characteristics of coupled structure are studied. The results indicate that the natural characteristics of the coupling structure are sensitive to the supporting stiffness of the disk, and the sensitive range is affected by rotating speeds. The circumferential wave numbers can affect the characteristics of the drum-disk structure. If the circumferential wave number n = 1 , the vibration response of the drum keeps a stable value under an unbalanced load of the disk, there is no coupling effect if n ≠ 1 . Under the excitation, the nonlinear hardening characteristics of the forward traveling wave are more evident than that of the backward traveling wave. Moreover, because of the coupling effect of the drum and the disk, the supporting stiffness of the disk has certain effect on the nonlinear characteristics of the forward and backward traveling waves. In addition, small length-radius and thickness-radius ratios have a significant effect on the nonlinear characteristics of the coupled structure, which means nonlinear shell theory should be adopted to design rotating drum's parameter for its specific structural parameters.

Nonlinear Correction to the Euler Buckling Formula for Compressed Cylinders with Guided-Guided End Conditions

KAUST Repository

De Pascalis, Riccardo

2010-07-22

Euler\\'s celebrated buckling formula gives the critical load N for the buckling of a slender cylindrical column with radius B and length L as N/(π3B2)=(E/4)(B/L)2 where E is Young\\'s modulus. Its derivation relies on the assumptions that linear elasticity applies to this problem, and that the slenderness (B/L) is an infinitesimal quantity. Here we ask the following question: What is the first non-linear correction in the right hand-side of this equation when terms up to (B/L)4 are kept? To answer this question, we specialize the exact solution of incremental non-linear elasticity for the homogeneous compression of a thick compressible cylinder with lubricated ends to the theory of third-order elasticity. In particular, we highlight the way second- and third-order constants-including Poisson\\'s ratio-all appear in the coefficient of (B/L)4. © 2010 Springer Science+Business Media B.V.

Nonlinear Correction to the Euler Buckling Formula for Compressed Cylinders with Guided-Guided End Conditions

KAUST Repository

De Pascalis, Riccardo; Destrade, Michel; Goriely, Alain

2010-01-01

Euler's celebrated buckling formula gives the critical load N for the buckling of a slender cylindrical column with radius B and length L as N/(π3B2)=(E/4)(B/L)2 where E is Young's modulus. Its derivation relies on the assumptions that linear elasticity applies to this problem, and that the slenderness (B/L) is an infinitesimal quantity. Here we ask the following question: What is the first non-linear correction in the right hand-side of this equation when terms up to (B/L)4 are kept? To answer this question, we specialize the exact solution of incremental non-linear elasticity for the homogeneous compression of a thick compressible cylinder with lubricated ends to the theory of third-order elasticity. In particular, we highlight the way second- and third-order constants-including Poisson's ratio-all appear in the coefficient of (B/L)4. © 2010 Springer Science+Business Media B.V.

Nonlinear aeroelastic modelling for wind turbine blades based on blade element momentum theory and geometrically exact beam theory

International Nuclear Information System (INIS)

Wang, Lin; Liu, Xiongwei; Renevier, Nathalie; Stables, Matthew; Hall, George M.

2014-01-01

Due to the increasing size and flexibility of large wind turbine blades, accurate and reliable aeroelastic modelling is playing an important role for the design of large wind turbines. Most existing aeroelastic models are linear models based on assumption of small blade deflections. This assumption is not valid anymore for very flexible blade design because such blades often experience large deflections. In this paper, a novel nonlinear aeroelastic model for large wind turbine blades has been developed by combining BEM (blade element momentum) theory and mixed-form formulation of GEBT (geometrically exact beam theory). The nonlinear aeroelastic model takes account of large blade deflections and thus greatly improves the accuracy of aeroelastic analysis of wind turbine blades. The nonlinear aeroelastic model is implemented in COMSOL Multiphysics and validated with a series of benchmark calculation tests. The results show that good agreement is achieved when compared with experimental data, and its capability of handling large deflections is demonstrated. Finally the nonlinear aeroelastic model is applied to aeroelastic modelling of the parked WindPACT 1.5 MW baseline wind turbine, and reduced flapwise deflection from the nonlinear aeroelastic model is observed compared to the linear aeroelastic code FAST (Fatigue, Aerodynamics, Structures, and Turbulence). - Highlights: • A novel nonlinear aeroelastic model for wind turbine blades is developed. • The model takes account of large blade deflections and geometric nonlinearities. • The model is reliable and efficient for aeroelastic modelling of wind turbine blades. • The accuracy of the model is verified by a series of benchmark calculation tests. • The model provides more realistic aeroelastic modelling than FAST (Fatigue, Aerodynamics, Structures, and Turbulence)

Complexity, Chaos, and Nonlinear Dynamics: A New Perspective on Career Development Theory

Science.gov (United States)

Bloch, Deborah P.

2005-01-01

The author presents a theory of career development drawing on nonlinear dynamics and chaos and complexity theories. Career is presented as a complex adaptive entity, a fractal of the human entity. Characteristics of complex adaptive entities, including (a) autopiesis, or self-regeneration; (b) open exchange; (c) participation in networks; (d)…

Numerical simulation of the interaction between a nonlinear elastic structure and compressible flow by the discontinuous Galerkin method

Czech Academy of Sciences Publication Activity Database

Kosík, Adam; Feistauer, M.; Hadrava, Martin; Horáček, Jaromír

2015-01-01

Roč. 267, September (2015), s. 382-396 ISSN 0096-3003 R&D Projects: GA ČR(CZ) GAP101/11/0207 Institutional support: RVO:61388998 Keywords : discontinuous Galerkin method * nonlinear elasticity * compressible viscous flow * fluid–structure interaction Subject RIV: BI - Acoustics Impact factor: 1.345, year: 2015 http://www.sciencedirect.com/science/article/pii/S0096300315002453/pdfft?md5=02d46bc730e3a7fb8a5008aaab1da786&pid=1-s2.0-S0096300315002453-main.pdf

Comment on the consistency of truncated nonlinear integral equation based theories of freezing

International Nuclear Information System (INIS)

Cerjan, C.; Bagchi, B.; Rice, S.A.

1985-01-01

We report the results of two studies of aspects of the consistency of truncated nonlinear integral equation based theories of freezing: (i) We show that the self-consistent solutions to these nonlinear equations are unfortunately sensitive to the level of truncation. For the hard sphere system, if the Wertheim--Thiele representation of the pair direct correlation function is used, the inclusion of part but not all of the triplet direct correlation function contribution, as has been common, worsens the predictions considerably. We also show that the convergence of the solutions found, with respect to number of reciprocal lattice vectors kept in the Fourier expansion of the crystal singlet density, is slow. These conclusions imply great sensitivity to the quality of the pair direct correlation function employed in the theory. (ii) We show the direct correlation function based and the pair correlation function based theories of freezing can be cast into a form which requires solution of isomorphous nonlinear integral equations. However, in the pair correlation function theory the usual neglect of the influence of inhomogeneity of the density distribution on the pair correlation function is shown to be inconsistent to the lowest order in the change of density on freezing, and to lead to erroneous predictions

Theory-Guided Materials Design of Multi-Phase Ti-Nb Alloys with Bone-Matching Elastic Properties

Directory of Open Access Journals (Sweden)

Jörg Neugebauer

2012-10-01

Full Text Available We present a scale-bridging approach for modeling the integral elasticresponse of polycrystalline composite that is based on a multi-disciplinary combination of(i parameter-free first-principles calculations of thermodynamic phase stability andsingle-crystal elastic stiffness; and (ii homogenization schemes developed forpolycrystalline aggregates and composites. The modeling is used as a theory-guidedbottom-up materials design strategy and applied to Ti-Nb alloys as promising candidatesfor biomedical implant applications. The theoretical results (i show an excellent agreementwith experimental data and (ii reveal a decisive influence of the multi-phase character ofthe polycrystalline composites on their integral elastic properties. The study shows thatthe results based on the density functional theory calculations at the atomistic level canbe directly used for predictions at the macroscopic scale, effectively scale-jumping severalorders of magnitude without using any empirical parameters.

Langevin-elasticity-theory-based description of the tensile properties of double network rubbers

Czech Academy of Sciences Publication Activity Database

Meissner, Bohumil; Matějka, Libor

2003-01-01

Roč. 44, č. 16 (2003), s. 4611-4617 ISSN 0032-3861 R&D Projects: GA ČR GA104/00/1311; GA AV ČR IAA4050008 Institutional research plan: CEZ:AV0Z4050913 Keywords : theory of rubber elasticity * double network rubbers * experimental testing Subject RIV: CD - Macromolecular Chemistry Impact factor: 2.340, year: 2003

Analytic theory of the nonlinear M = 1 tearing mode

International Nuclear Information System (INIS)

Hazeltine, R.D.; Meiss, J.D.; Morrison, P.J.

1985-09-01

Numerical studies show that the m = 1 tearing mode continues to grow exponentially well into the nonlinear regime, in contrast with the slow, ''Rutherford,'' growth of m > 1 modes. We present a single helicity calculation which generalizes that of Rutherford to the case when the constant-psi approximation is invalid. As in that theory, the parallel current becomes an approximate flux function when the island size, W, exceeds the linear tearing layer width. However for the m = 1 mode, W becomes proportional to deltaB, rather than (deltaB)/sup 1/2/ above this critical amplitude. This implies that the convective nonlinearity in Ohm's law, which couples the m = 0 component to the m = 1 component, dominates the resistive diffusion term. The balance between the inductive electric field and this convective nonlinearity results in exponential growth. Assuming the form of the perturbed fields to be like that of the linear mode, we find that the growth occurs at 71% of the linear rate

Static stability analysis of smart magneto-electro-elastic heterogeneous nanoplates embedded in an elastic medium based on a four-variable refined plate theory

Science.gov (United States)

Ebrahimi, Farzad; Barati, Mohammad Reza

2016-10-01

In this article, a nonlocal four-variable refined plate theory is developed to examine the buckling behavior of nanoplates made of magneto-electro-elastic functionally graded (MEE-FG) materials resting on Winkler-Pasternak foundation. Material properties of nanoplate change in spatial coordinate based on power-law distribution. The nonlocal governing equations are deduced by employing the Hamilton principle. For various boundary conditions, the analytical solutions of nonlocal MEE-FG plates for buckling problem will be obtained based on an exact solution approach. Finally, dependency of buckling response of MEE-FG nanoplate on elastic foundation parameters, magnetic potential, external electric voltage, various boundary conditions, small scale parameter, power-law index, plate side-to-thickness ratio and aspect ratio will be figure out. These results can be advantageous for the mechanical analysis and design of intelligent nanoscale structures constructed from magneto-electro-thermo-elastic functionally graded materials.

Ultrashort optical waveguide excitations in uniaxial silica fibers: elastic collision scenarios.

Science.gov (United States)

Kuetche, Victor K; Youssoufa, Saliou; Kofane, Timoleon C

2014-12-01

In this work, we investigate the dynamics of an uniaxial silica fiber under the viewpoint of propagation of ultimately ultrashort optical waveguide channels. As a result, we unveil the existence of three typical kinds of ultrabroadband excitations whose profiles strongly depend upon their angular momenta. Looking forward to surveying their scattering features, we unearth some underlying head-on scenarios of elastic collisions. Accordingly, we address some useful and straightforward applications in nonlinear optics through secured data transmission systems, as well as laser physics and soliton theory with optical soliton dynamics.

The Scalar, Vector and Tensor Fields in Theory of Elasticity and Plasticity

Directory of Open Access Journals (Sweden)

František FOJTÍK

2014-06-01

Full Text Available This article is devoted to an analysis of scalar, vector and tensor fields, which occur in the loaded and deformed bodies. The aim of this article is to clarify and simplify the creation of an understandable idea of some elementary concepts and quantities in field theories, such as, for example equiscalar levels, scalar field gradient, Hamilton operator, divergence, rotation and gradient of vector or tensor and others. Applications of those mathematical terms are shown in simple elasticity and plasticity tasks. We hope that content of our article might help technicians to make their studies of necessary mathematical chapters of vector and tensor analysis and field theories easier.

Nonlinear polarization of ionic liquids: theory, simulations, experiments

Science.gov (United States)

Kornyshev, Alexei

2010-03-01

Room temperature ionic liquids (RTILs) composed of large, often asymmetric, organic cations and simple or complex inorganic or organic anions do not freeze at ambient temperatures. Their rediscovery some 15 years ago is widely accepted as a ``green revolution'' in chemistry, offering an unlimited number of ``designer'' solvents for chemical and photochemical reactions, homogeneous catalysis, lubrication, and solvent-free electrolytes for energy generation and storage. As electrolytes they are non-volatile, some can sustain without decomposition up to 6 times higher voltages than aqueous electrolytes, and many are environmentally friendly. The studies of RTILs and their applications have reached a critical stage. So many of them can be synthesized - about a thousand are known already - their mixtures can further provide ``unlimited'' number of combinations! Thus, establishing some general laws that could direct the best choice of a RTIL for a given application became crucial; guidance is expected from theory and modelling. But for a physical theory, RTILs comprise a peculiar and complex class of media, the description of which lies at the frontier line of condensed matter theoretical physics: dense room temperature ionic plasmas with ``super-strong'' Coulomb correlations, which behave like glasses at short time-scale, but like viscous liquids at long-time scale. This talk will introduce RTILs to physicists and overview the current understanding of the nonlinear response of RTILs to electric field. It will focus on the theory, simulations, and experimental characterisation of the structure and nonlinear capacitance of the electrical double layer at a charged electrode. It will also discuss pros and contras of supercapacitor applications of RTILs.

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.

Pressure dependence of elastic constants in zinc-blende III-N and their influence on the light emission in nitride heterostructures

International Nuclear Information System (INIS)

Lepkowski, S.P.; Majewski, J.A.

2004-01-01

We studied the nonlinear elasticity effects for the case of III-N compounds. Particularly, we determined the pressure dependences of elastic constants, in zinc-blende InN, GaN, and AlN by performing ab initio calculations in the framework of plane-wave pseudopotential implementation of the density-functional theory. We found significant and almost linear increase in C 11 , C 12 with pressure for considered nitrides compounds. Much weaker dependences on pressure was observed for C 44 . We also discussed pressure dependences of two-dimensional Poisson's ratio and elastic anisotropy coefficient. Finally, we showed that the pressure dependence of elastic constants results in significant reduction of the pressure coefficient of the energy emission in cubic InGaN/GaN quantum well and essentially improves the agreement between experimental and theoretical values. (author)

Effects of weak nonlinearity on dispersion relations and frequency band-gaps of periodic structures

DEFF Research Database (Denmark)

Sorokin, Vladislav; Thomsen, Jon Juel

2015-01-01

of these for nonlinear problems is impossible or cumbersome, since Floquet theory is applicable for linear systems only. Thus the nonlinear effects for periodic structures are not yet fully uncovered, while at the same time applica-tions may demand effects of nonlinearity on structural response to be accounted for....... The present work deals with analytically predicting dynamic responses for nonlinear continuous elastic periodic structures. Specifically, the effects of weak nonlinearity on the dispersion re-lation and frequency band-gaps of a periodic Bernoulli-Euler beam performing bending os-cillations are analyzed......The analysis of the behaviour of linear periodic structures can be traced back over 300 years, to Sir Isaac Newton, and still attracts much attention. An essential feature of periodic struc-tures is the presence of frequency band-gaps, i.e. frequency ranges in which waves cannot propagate...

Nonlinear Displacement Discontinuity Model for Generalized Rayleigh Wave in Contact Interface

Energy Technology Data Exchange (ETDEWEB)

Kim, No Hyu; Yang, Seung Yong [Korea University of Technology and Education, Cheonan (Korea, Republic of)

2007-12-15

Imperfectly jointed interface serves as mechanical waveguide for elastic waves and gives rise to two distinct kinds of guided wave propagating along the interface. Contact acoustic nonlinearity (CAN) is known to plays major role in the generation of these interface waves called generalized Rayleigh waves in non-welded interface. Closed crack is modeled as non-welded interface that has nonlinear discontinuity condition in displacement across its boundary. Mathematical analysis of boundary conditions and wave equation is conducted to investigate the dispersive characteristics of the interface waves. Existence of the generalized Rayleigh wave(interface wave) in nonlinear contact interface is verified in theory where the dispersion equation for the interface wave is formulated and analyzed. It reveals that the interface waves have two distinct modes and that the phase velocity of anti-symmetric wave mode is highly dependent on contact conditions represented by linear and nonlinear dimensionless specific stiffness

Nonlinear Displacement Discontinuity Model for Generalized Rayleigh Wave in Contact Interface

International Nuclear Information System (INIS)

Kim, No Hyu; Yang, Seung Yong

2007-01-01

Imperfectly jointed interface serves as mechanical waveguide for elastic waves and gives rise to two distinct kinds of guided wave propagating along the interface. Contact acoustic nonlinearity (CAN) is known to plays major role in the generation of these interface waves called generalized Rayleigh waves in non-welded interface. Closed crack is modeled as non-welded interface that has nonlinear discontinuity condition in displacement across its boundary. Mathematical analysis of boundary conditions and wave equation is conducted to investigate the dispersive characteristics of the interface waves. Existence of the generalized Rayleigh wave(interface wave) in nonlinear contact interface is verified in theory where the dispersion equation for the interface wave is formulated and analyzed. It reveals that the interface waves have two distinct modes and that the phase velocity of anti-symmetric wave mode is highly dependent on contact conditions represented by linear and nonlinear dimensionless specific stiffness

Non-Linear Wave Loads and Ship responses by a time-domain Strip Theory

DEFF Research Database (Denmark)

Xia, Jinzhu; Wang, Zhaohui; Jensen, Jørgen Juncher

1998-01-01

. Based on this time-domain strip theory, an efficient non-linear hyroelastic method of wave- and slamming-induced vertical motions and structural responses of ships is developed, where the structure is represented by the Timoshenko beam theory. Numerical calculations are presented for the S175...

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

Experimental determination of third-order elastic constants of diamond.

Science.gov (United States)

Lang, J M; Gupta, Y M

2011-03-25

To determine the nonlinear elastic response of diamond, single crystals were shock compressed along the [100], [110], and [111] orientations to 120 GPa peak elastic stresses. Particle velocity histories and elastic wave velocities were measured by using laser interferometry. The measured elastic wave profiles were used, in combination with published acoustic measurements, to determine the complete set of third-order elastic constants. These constants represent the first experimental determination, and several differ significantly from those calculated by using theoretical models.

Imaging theory of nonlinear second harmonic and third harmonic generations in confocal microscopy

Institute of Scientific and Technical Information of China (English)

TANG Zhilie; XING Da; LIU Songhao

2004-01-01

The imaging theory of nonlinear second harmonic generation (SHG) and third harmonic generation (THG) in confocal microscopy is presented in this paper. The nonlinear effect of SHG and THG on the imaging properties of confocal microscopy has been analyzed in detail by the imaging theory. It is proved that the imaging process of SHG and THG in confocal microscopy, which is different from conventional coherent imaging or incoherent imaging, can be divided into two different processes of coherent imaging. The three-dimensional point spread functions (3D-PSF) of SHG and THG confocal microscopy are derived based on the nonlinear principles of SHG and THG. The imaging properties of SHG and THG confocal microscopy are discussed in detail according to its 3D-PSF. It is shown that the resolution of SHG and THG confocal microscopy is higher than that of single-and two-photon confocal microscopy.

Theories of quantum dissipation and nonlinear coupling bath descriptors

Science.gov (United States)

Xu, Rui-Xue; Liu, Yang; Zhang, Hou-Dao; Yan, YiJing

2018-03-01

The quest of an exact and nonperturbative treatment of quantum dissipation in nonlinear coupling environments remains in general an intractable task. In this work, we address the key issues toward the solutions to the lowest nonlinear environment, a harmonic bath coupled both linearly and quadratically with an arbitrary system. To determine the bath coupling descriptors, we propose a physical mapping scheme, together with the prescription reference invariance requirement. We then adopt a recently developed dissipaton equation of motion theory [R. X. Xu et al., Chin. J. Chem. Phys. 30, 395 (2017)], with the underlying statistical quasi-particle ("dissipaton") algebra being extended to the quadratic bath coupling. We report the numerical results on a two-level system dynamics and absorption and emission line shapes.

A Labor Supply Elasticity Accord?

OpenAIRE

Lars Ljungqvist; Thomas J. Sargent

2011-01-01

A dispute about the size of the aggregate labor supply elasticity has been fortified by a contentious aggregation theory used by real business cycle theorists. The replacement of that aggregation theory with one more congenial to microeconomic observations opens possibilities for an accord about the aggregate labor supply elasticity. The new aggregation theory drops features to which empirical microeconomists objected and replaces them with life-cycle choices. Whether the new aggregation theo...

Elastic-plastic dynamic analysis of a reactor building

International Nuclear Information System (INIS)

Umemura, Hajime; Tanaka, Hiroshi.

1976-01-01

The basic characteristics of the dynamic response of a reactor building to severe earthquake ground motion are very important for the evaluation of the safety of nuclear plant systems. A computer program for elastic-plastic dynamic analysis of reactor buildings using lumped mass models is developed. The box and cylindrical walls of boiling water reactor buildings are treated as vertical beams. The nonlinear moment-rotation and shear force-shear deformation relationships of walls are based in part upon the experiments of prototype structures. The geometrical non-linearity of the soil rocking spring due to foundation separation is also considered. The nonlinear equation of motion is expressed in incremental form using tangent stiffness matrices, following the algorithm developed by E.L. Wilson et al. The damping matrix in the equation is formulated as the combination of the energy evaluation method and Penzien-Wilson's approach to accomodate the different characteristics of soil and building damping. The analysis examples and the comparison of elastic and elastic-plastic analysis results are presented. (auth.)

Traveling wave solution of the Reggeon field theory

International Nuclear Information System (INIS)

Peschanski, Robi

2009-01-01

We identify the nonlinear evolution equation in impact-parameter space for the 'Supercritical Pomeron' in Reggeon field theory as a two-dimensional stochastic Fisher-Kolmogorov-Petrovski-Piscounov equation. It exactly preserves unitarity and leads in its radial form to a high-energy traveling wave solution corresponding to a 'universal' behavior of the impact-parameter front profile of the elastic amplitude; its rapidity dependence and form depend only on one parameter, the noise strength, independently of the initial conditions and of the nonlinear terms restoring unitarity. Theoretical predictions are presented for the three typical distinct regimes corresponding to zero, weak, and strong noise.

Nonlinear analysis of 0-3 polarized PLZT microplate based on the new modified couple stress theory

Science.gov (United States)

Wang, Liming; Zheng, Shijie

2018-02-01

In this study, based on the new modified couple stress theory, the size- dependent model for nonlinear bending analysis of a pure 0-3 polarized PLZT plate is developed for the first time. The equilibrium equations are derived from a variational formulation based on the potential energy principle and the new modified couple stress theory. The Galerkin method is adopted to derive the nonlinear algebraic equations from governing differential equations. And then the nonlinear algebraic equations are solved by using Newton-Raphson method. After simplification, the new model includes only a material length scale parameter. In addition, numerical examples are carried out to study the effect of material length scale parameter on the nonlinear bending of a simply supported pure 0-3 polarized PLZT plate subjected to light illumination and uniform distributed load. The results indicate the new model is able to capture the size effect and geometric nonlinearity.

Modeling dynamic acousto-elastic testing experiments: validation and perspectives.

Science.gov (United States)

Gliozzi, A S; Scalerandi, M

2014-10-01

Materials possessing micro-inhomogeneities often display a nonlinear response to mechanical solicitations, which is sensitive to the confining pressure acting on the sample. Dynamic acoustoelastic testing allows measurement of the instantaneous variations in the elastic modulus due to the change of the dynamic pressure induced by a low-frequency wave. This paper shows that a Preisach-Mayergoyz space based hysteretic multi-state elastic model provides an explanation for experimental observations in consolidated granular media and predicts memory and nonlinear effects comparable to those measured in rocks.

Relativistic mean-field theory for unstable nuclei with non-linear σ and ω terms

International Nuclear Information System (INIS)

Sugahara, Y.; Toki, H.

1994-01-01

We search for a new parameter set for the description of stable as well as unstable nuclei in the wide mass range within the relativistic mean-field theory. We include a non-linear ω self-coupling term in addition to the non-linear σ self-coupling terms, the necessity of which is suggested by the relativistic Brueckner-Hartree-Fock (RBHF) theory of nuclear matter. We find two parameter sets, one of which is for nuclei above Z=20 and the other for nuclei below that. The calculated results agree very well with the existing data for finite nuclei. The parameter set for the heavy nuclei provides the equation of state of nuclear matter similar to the one of the RBHF theory. ((orig.))

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

T.I.Tech./K.E.S. Conference on Nonlinear and Convex Analysis in Economic Theory

CERN Document Server

Takahashi, Wataru

1995-01-01

The papers collected in this volume are contributions to T.I.Tech./K.E.S. Conference on Nonlinear and Convex Analysis in Economic Theory, which was held at Keio University, July 2-4, 1993. The conference was organized by Tokyo Institute of Technology (T. I. Tech.) and the Keio Economic Society (K. E. S.) , and supported by Nihon Keizai Shimbun Inc .. A lot of economic problems can be formulated as constrained optimiza­ tions and equilibrations of their solutions. Nonlinear-convex analysis has been supplying economists with indispensable mathematical machineries for these problems arising in economic theory. Conversely, mathematicians working in this discipline of analysis have been stimulated by various mathematical difficulties raised by economic the­ ories. Although our special emphasis was laid upon "nonlinearity" and "con­ vexity" in relation with economic theories, we also incorporated stochastic aspects of financial economics in our project taking account of the remark­ able rapid growth of this dis...

Nonlinear dynamics and control of a vibrating rectangular plate

Science.gov (United States)

Shebalin, J. V.

1983-01-01

The von Karman equations of nonlinear elasticity are solved for the case of a vibrating rectangular plate by meams of a Fourier spectral transform method. The amplification of a particular Fourier mode by nonlinear transfer of energy is demonstrated for this conservative system. The multi-mode system is reduced to a minimal (two mode) system, retaining the qualitative features of the multi-mode system. The effect of a modal control law on the dynamics of this minimal nonlinear elastic system is examined.

Nonlinear Buckling Analysis of Functionally Graded Graphene Reinforced Composite Shallow Arches with Elastic Rotational Constraints under Uniform Radial Load.

Science.gov (United States)

Huang, Yonghui; Yang, Zhicheng; Liu, Airong; Fu, Jiyang

2018-05-28

The buckling behavior of functionally graded graphene platelet-reinforced composite (FG-GPLRC) shallow arches with elastic rotational constraints under uniform radial load is investigated in this paper. The nonlinear equilibrium equation of the FG-GPLRC shallow arch with elastic rotational constraints under uniform radial load is established using the Halpin-Tsai micromechanics model and the principle of virtual work, from which the critical buckling load of FG-GPLRC shallow arches with elastic rotational constraints can be obtained. This paper gives special attention to the effect of the GPL distribution pattern, weight fraction, geometric parameters, and the constraint stiffness on the buckling load. The numerical results show that all of the FG-GPLRC shallow arches with elastic rotational constraints have a higher buckling load-carrying capacity compared to the pure epoxy arch, and arches of the distribution pattern X have the highest buckling load among four distribution patterns. When the GPL weight fraction is constant, the thinner and larger GPL can provide the better reinforcing effect to the FG-GPLRC shallow arch. However, when the value of the aspect ratio is greater than 4, the flakiness ratio is greater than 103, and the effect of GPL's dimensions on the buckling load of the FG-GPLRC shallow arch is less significant. In addition, the buckling model of FG-GPLRC shallow arch with elastic rotational constraints is changed as the GPL distribution patterns or the constraint stiffness changes. It is expected that the method and the results that are presented in this paper will be useful as a reference for the stability design of this type of arch in the future.

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.

Simulation of creep effects in framework of a geometrically nonlinear endochronic theory of inelasticity

Science.gov (United States)

Zabavnikova, T. A.; Kadashevich, Yu. I.; Pomytkin, S. P.

2018-05-01

A geometric non-linear endochronic theory of inelasticity in tensor parametric form is considered. In the framework of this theory, the creep strains are modelled. The effect of various schemes of applying stresses and changing of material properties on the development of creep strains is studied. The constitutive equations of the model are represented by non-linear systems of ordinary differential equations which are solved in MATLAB environment by implicit difference method. Presented results demonstrate a good qualitative agreement of theoretical data and experimental observations including the description of the tertiary creep and pre-fracture of materials.

Nonlinear analysis of RC cylindrical tank and subsoil accounting for a low concrete strength

Directory of Open Access Journals (Sweden)

Lewiński Paweł M.

2017-01-01

Full Text Available The paper discusses deformational and incremental approaches to a nonlinear FE analysis of soil-structure interaction including the description of behaviour of the RC structure and the subsoil under short-term loading. Two kinds of constitutive models for ground and structure were adopted for a nonlinear interaction analysis of the RC cylindrical tank with subsoil. The constitutive laws for concrete and subsoil were developed in compliance with the deformational and flow theories of plasticity. Moreover, a non-linear elastic-brittle-plastic analysis of RC axi-symmetric structures using finite element iterative techniques is presented. The results of the two types of FE analysis of soil-structure interaction are compared taking into account a low concrete strength of tank structure.

Mathematical Modeling of Contact Problems of Elasticity Theory with Unilateral Discrete Contact

Directory of Open Access Journals (Sweden)

I. V. Stankevich

2015-01-01

Full Text Available Development and operation of modern machinery and latest technology require reliable estimates of the strength characteristics of the critical elements of structures and technological equipment under the impact of high-intensity thermomechanical loading, accompanied, as a rule, by complex contact interaction. Mathematical modeling of stress-strain state of such parts and components in the contact area, based on adequate mathematical models, modern numerical methods and efficient algorithms that implement the direct determination of displacement fields, strains and stresses, is the main tool that allows fast acquisition of data required for the calculations of strength and durability. The paper considers an algorithm for constructing the numerical solution of the contact problem of elasticity theory in relation to the body, which has an obvious one-sided discrete contact interaction with an elastic half-space. The proposed algorithm is specially designed to have a correction of the tangential forces at discrete contact points, allowing us to achieve sufficiently accurate implementation of the adopted law of friction. The algorithm is embedded in a general finite element technology, with which the application code is generated. Numerical study of discrete unilateral contact interaction of an elastic plate and a rigid half-space showed a high efficiency of the developed algorithm and the application code that implements it.

The preparation problem in nonlinear extensions of quantum theory

OpenAIRE

Cavalcanti, Eric G.; Menicucci, Nicolas C.; Pienaar, Jacques L.

2012-01-01

Nonlinear modifications to the laws of quantum mechanics have been proposed as a possible way to consistently describe information processing in the presence of closed timelike curves. These have recently generated controversy due to possible exotic information-theoretic effects, including breaking quantum cryptography and radically speeding up both classical and quantum computers. The physical interpretation of such theories, however, is still unclear. We consider a large class of operationa...

Lectures in nonlinear mechanics and chaos theory

CERN Document Server

Stetz, Albert W

2016-01-01

This elegant book presents a rigorous introduction to the theory of nonlinear mechanics and chaos. It turns out that many simple mechanical systems suffer from a peculiar malady. They are deterministic in the sense that their motion can be described with partial differential equations, but these equations have no proper solutions and the behavior they describe can be wildly unpredictable. This is implicit in Newtonian physics, and although it was analyzed in the pioneering work of Poincaré in the 19th century, its full significance has only been realized since the advent of modern computing. This book follows this development in the context of classical mechanics as it is usually taught in most graduate programs in physics. It starts with the seminal work of Laplace, Hamilton, and Liouville in the early 19th century and shows how their formulation of mechanics inevitably leads to systems that cannot be 'solved' in the usual sense of the word. It then discusses perturbation theory which, rather than providing...

Elasticity Theory Solution of the Problem on Plane Bending of a Narrow Layered Cantilever Beam by Loads at Its Free End

Science.gov (United States)

Goryk, A. V.; Koval'chuk, S. B.

2018-05-01

An exact elasticity theory solution for the problem on plane bending of a narrow layered composite cantilever beam by tangential and normal loads distributed on its free end is presented. Components of the stress-strain state are found for the whole layers package by directly integrating differential equations of the plane elasticity theory problem by using an analytic representation of piecewise constant functions of the mechanical characteristics of layer materials. The continuous solution obtained is realized for a four-layer beam with account of kinematic boundary conditions simulating the rigid fixation of its one end. The solution obtained allows one to predict the strength and stiffness of composite cantilever beams and to construct applied analytical solutions for various problems on the elastic bending of layered beams.

A general sensitivity theory for simulations of nonlinear systems

International Nuclear Information System (INIS)

Kenton, M.A.

1981-01-01

A general sensitivity theory is developed for nonlinear lumped-parameter system simulations. The point-of-departure is general perturbation theory, which has long been used for linear systems in nuclear engineering and reactor physics. The theory allows the sensitivity of particular figures-of-merit of the system behavior to be calculated with respect to any parameter.An explicit procedure is derived for applying the theory to physical systems undergoing sudden events (e.g., reactor scrams, tank ruptures). A related problem, treating figures-of-merit defined as functions of extremal values of system variables occurring at sudden events, is handled by the same procedure. The general calculational scheme for applying the theory to numerical codes is discussed. It is shown that codes which use pre-packaged implicit integration subroutines can be augmented to include sensitivity theory: a companion set of subroutines to solve the sensitivity problem is listed. This combined system analysis code is applied to a simple model for loss of post-accident heat removal in a liquid metal-cooled fast breeder reactor. The uses of the theory for answering more general sensitivity questions are discussed. One application of the theory is to systematically determine whether specific physical processes in a model contribute significantly to the figures-of-merit. Another application of the theory is for selecting parameter values which enable a model to match experimentally observed behavior

Nonlinear responses of chiral fluids from kinetic theory

Science.gov (United States)

Hidaka, Yoshimasa; Pu, Shi; Yang, Di-Lun

2018-01-01

The second-order nonlinear responses of inviscid chiral fluids near local equilibrium are investigated by applying the chiral kinetic theory (CKT) incorporating side-jump effects. It is shown that the local equilibrium distribution function can be nontrivially introduced in a comoving frame with respect to the fluid velocity when the quantum corrections in collisions are involved. For the study of anomalous transport, contributions from both quantum corrections in anomalous hydrodynamic equations of motion and those from the CKT and Wigner functions are considered under the relaxation-time (RT) approximation, which result in anomalous charge Hall currents propagating along the cross product of the background electric field and the temperature (or chemical-potential) gradient and of the temperature and chemical-potential gradients. On the other hand, the nonlinear quantum correction on the charge density vanishes in the classical RT approximation, which in fact satisfies the matching condition given by the anomalous equation obtained from the CKT.

Nonlocal continuum analysis of a nonlinear uniaxial elastic lattice system under non-uniform axial load

Science.gov (United States)

Hérisson, Benjamin; Challamel, Noël; Picandet, Vincent; Perrot, Arnaud

2016-09-01

The static behavior of the Fermi-Pasta-Ulam (FPU) axial chain under distributed loading is examined. The FPU system examined in the paper is a nonlinear elastic lattice with linear and quadratic spring interaction. A dimensionless parameter controls the possible loss of convexity of the associated quadratic and cubic energy. Exact analytical solutions based on Hurwitz zeta functions are developed in presence of linear static loading. It is shown that this nonlinear lattice possesses scale effects and possible localization properties in the absence of energy convexity. A continuous approach is then developed to capture the main phenomena observed regarding the discrete axial problem. The associated continuum is built from a continualization procedure that is mainly based on the asymptotic expansion of the difference operators involved in the lattice problem. This associated continuum is an enriched gradient-based or nonlocal axial medium. A Taylor-based and a rational differential method are both considered in the continualization procedures to approximate the FPU lattice response. The Padé approximant used in the continualization procedure fits the response of the discrete system efficiently, even in the vicinity of the limit load when the non-convex FPU energy is examined. It is concluded that the FPU lattice system behaves as a nonlocal axial system in dynamic but also static loading.

Stochastic analysis of laminated composite plates on elastic foundation: The cases of post-buckling behavior and nonlinear free vibration

International Nuclear Information System (INIS)

Singh, B.N.; Lal, Achchhe

2010-01-01

This study deals with the stochastic post-buckling and nonlinear free vibration analysis of a laminated composite plate resting on a two parameters Pasternak foundation with Winkler cubic nonlinearity having uncertain system properties. The system properties are modeled as basic random variables. A C 0 nonlinear finite element formulation of the random problem based on higher-order shear deformation theory in the von Karman sense is presented. A direct iterative method in conjunction with a stochastic nonlinear finite element method proposed earlier by the authors is extended to analyze the effect of uncertainty in system properties on the post-buckling and nonlinear free vibration of the composite plates having Winler type of geometric nonlinearity. Mean as well as standard deviation of the responses have been obtained for various combinations of geometric parameters, foundation parameters, stacking sequences and boundary conditions and compared with those available in the literature and Monte Carlo simulation.

Elastic scattering of protons at the nucleus 6He in the Glauber multiple scattering theory

International Nuclear Information System (INIS)

Prmantayeva, B.A.; Temerbayev, A.A.; Tleulessova, I.K.; Ibrayeva, E.T.

2011-01-01

Calculation is submitted for the differential cross sections of elastic p 6 He-scattering at energies of 70 and 700 MeV/nucleon within the framework of the Glauber theory of multiple diffraction scattering. We used the three-particle wave functions: α-n-n with realistic intercluster potentials. The sensitivity of elastic scattering to the proton-nuclear interaction and the structure of nuclei had been investigated. It is shown that the contribution of small components of the wave function as well as the multiplicity of the scattering operator Ω should be considered to describe a cross-section in broad angular range . A comparison with available experimental data was made. (author)

Ductile fracture evaluation of ductile cast iron and forged steel by nonlinear-fracture-mechanics. Pt. 1. Tensile test by large scaled test pieces with surface crack

International Nuclear Information System (INIS)

Kosaki, Akio; Ajima, Tatsuro; Inohara, Yasuto

1999-01-01

The ductile fracture tests of Ductile Cast Iron and Forged Steel under a tensile stress condition were conducted using large-scaled flat test specimens with a surface crack and were evaluated by the J-integral values, in order to propose an evaluation method of initiation of ductile fracture of a cask body with crack by nonlinear-fracture-mechanics. Following results were obtained. 1) 1 -strain relations of Ductile Cast Iron and Forged Steel under the tensile stress condition were obtained, which is necessary for the development of J-integral design curves for evaluating the initiation of ductile fracture of the cask body. 2) In case of Ductile Cast Iron, the experimental J-integral values obtained from strain-gauges showed a good agreement with the linear-elastic-theory by Raju and Newman at room temperature, in both elastic and plastic regions. But, at 70degC in plastic region, the experimental i-integral values showed middle values between those predicted by the linear-elastic-theory and by the non- linear-elastic- theory (based on the fully plastic solution by Yagawa et al.). 3) In case of Forged Steel at both -25degC and room temperature, the experimental i-integral values obtained from strain-gauges showed a good agreement with those predicted by the linear-elastic-theory by Raju and Newman, in the elastic region. In the plastic region, however, the experimental i-integral values fell apart from the curve predicted by the linear-elastic-theory by Raju and Newman, and also approached to those by the non-linear-elastic-theory with increasing strain.(author)

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.

Lie Symmetries and Solitons in Nonlinear Systems with Spatially Inhomogeneous Nonlinearities

International Nuclear Information System (INIS)

Belmonte-Beitia, Juan; Perez-Garcia, Victor M.; Vekslerchik, Vadym; Torres, Pedro J.

2007-01-01

Using Lie group theory and canonical transformations, we construct explicit solutions of nonlinear Schroedinger equations with spatially inhomogeneous nonlinearities. We present the general theory, use it to show that localized nonlinearities can support bound states with an arbitrary number solitons, and discuss other applications of interest to the field of nonlinear matter waves

Nonlinear Dynamic Response of an Unbalanced Flexible Rotor Supported by Elastic Bearings Lubricated with Piezo-Viscous Polar Fluids

Directory of Open Access Journals (Sweden)

Mustapha Lahmar

2015-04-01

Full Text Available On the basis of the V. K. Stokes micro-continuum theory, the effects of couple stresses on the nonlinear dynamic response of the unbalanced Jeffcott’s flexible rotor supported by layered hydrodynamic journal bearings is presented in this paper. A nonlinear transient modified Reynolds’ equation is derived and discretized by the finite element method to obtain the fluid-film pressure field as well as the film thickness by means of the implicit Euler method. The nonlinear orbits of the rotor center are determined by solving the nonlinear differential equations of motion with the explicit Euler’s scheme taking into account the flexibility of rotor. According to the obtained results, the combined effects of couple stresses due to the presence of polymer additives in lubricant and the pressure dependent viscosity on the nonlinear dynamic response of the rotor-bearing system are significant and cannot be ignored or overlooked. As expected, these effects are more noticeable for polymers characterized by higher length molecular chains.

Nonlinear response of dense colloidal suspensions under oscillatory shear: mode-coupling theory and Fourier transform rheology experiments.

Science.gov (United States)

Brader, J M; Siebenbürger, M; Ballauff, M; Reinheimer, K; Wilhelm, M; Frey, S J; Weysser, F; Fuchs, M

2010-12-01

Using a combination of theory, experiment, and simulation we investigate the nonlinear response of dense colloidal suspensions to large amplitude oscillatory shear flow. The time-dependent stress response is calculated using a recently developed schematic mode-coupling-type theory describing colloidal suspensions under externally applied flow. For finite strain amplitudes the theory generates a nonlinear response, characterized by significant higher harmonic contributions. An important feature of the theory is the prediction of an ideal glass transition at sufficiently strong coupling, which is accompanied by the discontinuous appearance of a dynamic yield stress. For the oscillatory shear flow under consideration we find that the yield stress plays an important role in determining the nonlinearity of the time-dependent stress response. Our theoretical findings are strongly supported by both large amplitude oscillatory experiments (with Fourier transform rheology analysis) on suspensions of thermosensitive core-shell particles dispersed in water and Brownian dynamics simulations performed on a two-dimensional binary hard-disk mixture. In particular, theory predicts nontrivial values of the exponents governing the final decay of the storage and loss moduli as a function of strain amplitude which are in good agreement with both simulation and experiment. A consistent set of parameters in the presented schematic model achieves to jointly describe linear moduli, nonlinear flow curves, and large amplitude oscillatory spectroscopy.

Development of ultrasound transducer diffractive field theory for nonlinear propagation-based imaging

Science.gov (United States)

Kharin, Nikolay A.

2000-04-01

In nonlinear ultrasound imaging the images are formed using the second harmonic energy generated due to the nonlinear nature of finite amplitude propagation. This propagation can be modeled using the KZK wave equation. This paper presents further development of nonlinear diffractive field theory based on the KZK equation and its solution by means of the slowly changing profile method for moderate nonlinearity. The analytical expression for amplitudes and phases of sum frequency wave are obtained in addition to the second harmonic wave. Also, the analytical expression for the relative curvature of the wave fronts of fundamental and second harmonic signals are derived. The media with different nonlinear properties and absorption coefficients were investigated to characterize the diffractive field of the transducer at medical frequencies. All expressions demonstrate good agreement with experimental results. The expressions are novel and provide an easy way for prediction of amplitude and phase structure of nonlinearly distorted field of a transducer. The sum frequency signal technique could be implemented as well as second harmonic technique to improve the quality of biomedical images. The results obtained are of importance for medical diagnostic ultrasound equipment design.

On residual stresses and homeostasis: an elastic theory of functional adaptation in living matter.

Science.gov (United States)

Ciarletta, P; Destrade, M; Gower, A L

2016-04-26

Living matter can functionally adapt to external physical factors by developing internal tensions, easily revealed by cutting experiments. Nonetheless, residual stresses intrinsically have a complex spatial distribution, and destructive techniques cannot be used to identify a natural stress-free configuration. This work proposes a novel elastic theory of pre-stressed materials. Imposing physical compatibility and symmetry arguments, we define a new class of free energies explicitly depending on the internal stresses. This theory is finally applied to the study of arterial remodelling, proving its potential for the non-destructive determination of the residual tensions within biological materials.

A normal form approach to the theory of nonlinear betatronic motion

International Nuclear Information System (INIS)

Bazzani, A.; Todesco, E.; Turchetti, G.; Servizi, G.

1994-01-01

The betatronic motion of a particle in a circular accelerator is analysed using the transfer map description of the magnetic lattice. In the linear case the transfer matrix approach is shown to be equivalent to the Courant-Snyder theory: In the normal coordinates' representation the transfer matrix is a pure rotation. When the nonlinear effects due to the multipolar components of the magnetic field are taken into account, a similar procedure is used: a nonlinear change of coordinates provides a normal form representation of the map, which exhibits explicit symmetry properties depending on the absence or presence of resonance relations among the linear tunes. The use of normal forms is illustrated in the simplest but significant model of a cell with a sextupolar nonlinearity which is described by the quadratic Henon map. After recalling the basic theoretical results in Hamiltonian dynamics, we show how the normal forms describe the different topological structures of phase space such as KAM tori, chains of islands and chaotic regions; a critical comparison with the usual perturbation theory for Hamilton equations is given. The normal form theory is applied to compute the tune shift and deformation of the orbits for the lattices of the SPS and LHC accelerators, and scaling laws are obtained. Finally, the correction procedure of the multipolar errors of the LHC, based on the analytic minimization of the tune shift computed via the normal forms, is described and the results for a model of the LHC are presented. This application, relevant for the lattice design, focuses on the advantages of normal forms with respect to tracking when parametric dependences have to be explored. (orig.)

Rotation, inversion and perversion in anisotropic elastic cylindrical tubes and membranes

KAUST Repository

Goriely, A.; Tabor, M.

2013-01-01

Cylindrical tubes and membranes are universal structural elements found in biology and engineering over a wide range of scales.Working in the framework of nonlinear elasticity, we consider the possible deformations of elastic cylindrical shells

Nonlinear dynamics between linear and impact limits

CERN Document Server

Pilipchuk, Valery N; Wriggers, Peter

2010-01-01

This book examines nonlinear dynamic analyses based on the existence of strongly nonlinear but simple counterparts to the linear models and tools. Discusses possible application to periodic elastic structures with non-smooth or discontinuous characteristics.

Spline-Interpolation Solution of One Elasticity Theory Problem

CERN Document Server

Shirakova, Elena A

2011-01-01

The book presents methods of approximate solution of the basic problem of elasticity for special types of solids. Engineers can apply the approximate methods (Finite Element Method, Boundary Element Method) to solve the problems but the application of these methods may not be correct for solids with the certain singularities or asymmetrical boundary conditions. The book is recommended for researchers and professionals working on elasticity modeling. It explains methods of solving elasticity problems for special solids. Approximate methods (Finite Element Method, Boundary Element Method) have b

Nonlinear electroelasticity: material properties, continuum theory and applications.

Science.gov (United States)

Dorfmann, Luis; Ogden, Ray W

2017-08-01

In the last few years, it has been recognized that the large deformation capacity of elastomeric materials that are sensitive to electric fields can be harnessed for use in transducer devices such as actuators and sensors. This has led to the reassessment of the mathematical theory that is needed for the description of the electromechanical (in particular, electroelastic) interactions for purposes of material characterization and prediction. After a review of the key experiments concerned with determining the nature of the electromechanical interactions and a discussion of the range of applications to devices, we provide a short account of the history of developments in the nonlinear theory. This is followed by a succinct modern treatment of electroelastic theory, including the governing equations and constitutive laws needed for both material characterization and the analysis of general electroelastic coupling problems. For illustration, the theory is then applied to two simple representative boundary-value problems that are relevant to the geometries of activation devices; in particular, (a) a rectangular plate and (b) a circular cylindrical tube, in each case with compliant electrodes on the major surfaces and a potential difference between them. In (a), an electric field is generated normal to the major surfaces and in (b), a radial electric field is present. This is followed by a short section in which other problems addressed on the basis of the general theory are described briefly.

Nonlinear electroelasticity: material properties, continuum theory and applications

Science.gov (United States)

Dorfmann, Luis; Ogden, Ray W.

2017-08-01

In the last few years, it has been recognized that the large deformation capacity of elastomeric materials that are sensitive to electric fields can be harnessed for use in transducer devices such as actuators and sensors. This has led to the reassessment of the mathematical theory that is needed for the description of the electromechanical (in particular, electroelastic) interactions for purposes of material characterization and prediction. After a review of the key experiments concerned with determining the nature of the electromechanical interactions and a discussion of the range of applications to devices, we provide a short account of the history of developments in the nonlinear theory. This is followed by a succinct modern treatment of electroelastic theory, including the governing equations and constitutive laws needed for both material characterization and the analysis of general electroelastic coupling problems. For illustration, the theory is then applied to two simple representative boundary-value problems that are relevant to the geometries of activation devices; in particular, (a) a rectangular plate and (b) a circular cylindrical tube, in each case with compliant electrodes on the major surfaces and a potential difference between them. In (a), an electric field is generated normal to the major surfaces and in (b), a radial electric field is present. This is followed by a short section in which other problems addressed on the basis of the general theory are described briefly.

Nonlinear theory for the parametric instability with comparable electron and ion temperatures

International Nuclear Information System (INIS)

Oberman, C.

1972-01-01

The basic linear theory of the parametric instability driven by a pump E 0 sin ω 0 t oscillating near the electron plasma frequency is reviewed. An expression is derived for the temporal nonlinear development of the fluctuation spectrum of the excited waves. For plasma with comparable electron and ion temperatures nonlinear Landau damping of electron plasma waves on ions provides the dominant nonlinearity. The steady state solutions are examined both analytically and numerically in the limit when the spontaneous emission term is small. The characteristics of the plasma wave spectrum agrees well with the general features of ionospheric observations. The enhanced dissipation rate of the pump due to the presence of the fluctuations agrees with laboratory observations. (U.S.)

Universality of Nonclassical Nonlinearity Applications to Non-Destructive Evaluations and Ultrasonic

CERN Document Server

Delsanto, Pier Paolo

2006-01-01

This book comes as a result of the research work developed in the framework of two international projects: the European Science Foundation supported program NATEMIS (Nonlinear Acoustic Techniques for Micro-Scale Damage Diagnostics) and a Los Alamos-based international network. The main topics of both the programs and the book cover the phenomenology, theory and applications of Nonclassical Nonlinearity (NCNL). NCNL techniques have been found in recent years to be extremely powerful (up to 1000 times more than the corresponding linear techniques) in a wide range of applications, including Material Characterization, Ultrasonics, Geophysics and Maintenance and Restoration of artifacts. These techniques are being adopted as the main inspection and research tool in another European program: AERONEWS (Health monitoring of aircraft by nonlinear elastic wave propagation). In the future, the proposed Universality of NCNL is expected to extend the range of applications to numerous other fields and scientific discipline...

Estimating the price elasticity of expenditure for prescription drugs in the presence of non-linear price schedules: an illustration from Quebec, Canada.

Science.gov (United States)

Contoyannis, Paul; Hurley, Jeremiah; Grootendorst, Paul; Jeon, Sung-Hee; Tamblyn, Robyn

2005-09-01

The price elasticity of demand for prescription drugs is a crucial parameter of interest in designing pharmaceutical benefit plans. Estimating the elasticity using micro-data, however, is challenging because insurance coverage that includes deductibles, co-insurance provisions and maximum expenditure limits create a non-linear price schedule, making price endogenous (a function of drug consumption). In this paper we exploit an exogenous change in cost-sharing within the Quebec (Canada) public Pharmacare program to estimate the price elasticity of expenditure for drugs using IV methods. This approach corrects for the endogeneity of price and incorporates the concept of a 'rational' consumer who factors into consumption decisions the price they expect to face at the margin given their expected needs. The IV method is adapted from an approach developed in the public finance literature used to estimate income responses to changes in tax schedules. The instrument is based on the price an individual would face under the new cost-sharing policy if their consumption remained at the pre-policy level. Our preferred specification leads to expenditure elasticities that are in the low range of previous estimates (between -0.12 and -0.16). Naïve OLS estimates are between 1 and 4 times these magnitudes. (c) 2005 John Wiley & Sons, Ltd.

Enhancing Thermoelectric Performance Using Nonlinear Transport Effects

Science.gov (United States)

Jiang, Jian-Hua; Imry, Yoseph

2017-06-01

We study nonlinear transport effects on the maximum efficiency and power for both inelastic and elastic thermoelectric generators. The former device refers to phonon-assisted hopping in double quantum dots, while the latter device is represented by elastic tunneling through a single quantum dot. We find that nonlinear thermoelectric transport can lead to enhanced efficiency and power for both types of devices. A comprehensive survey of various quantum-dot energy, temperature, and parasitic heat conduction reveals that the nonlinear transport-induced improvements of the maximum efficiency and power are overall much more significant for inelastic devices than for elastic devices, even for temperature biases as small as Th=1.2 Tc (Th and Tc are the temperatures of the hot and cold reservoirs, respectively). The underlying mechanism is revealed as due to the fact that, unlike the Fermi distribution, the Bose distribution is not bounded when the temperature bias increases. A large flux density of absorbed phonons leads to a great enhancement of the electrical current, output power, and energy efficiency, dominating over the concurrent increase of the parasitic heat current. Our study reveals that nonlinear transport effects can be a useful tool for improving thermoelectric performance.

On Interactions of Oscillation Modes for a Weakly Non-Linear Undamped Elastic Beam with AN External Force

Science.gov (United States)

BOERTJENS, G. J.; VAN HORSSEN, W. T.

2000-08-01

In this paper an initial-boundary value problem for the vertical displacement of a weakly non-linear elastic beam with an harmonic excitation in the horizontal direction at the ends of the beam is studied. The initial-boundary value problem can be regarded as a simple model describing oscillations of flexible structures like suspension bridges or iced overhead transmission lines. Using a two-time-scales perturbation method an approximation of the solution of the initial-boundary value problem is constructed. Interactions between different oscillation modes of the beam are studied. It is shown that for certain external excitations, depending on the phase of an oscillation mode, the amplitude of specific oscillation modes changes.

Vibration analysis of orthotropic circular and elliptical nano-plates embedded in elastic medium based on nonlocal Mindlin plate theory and using Galerkin method

International Nuclear Information System (INIS)

Anjomshoa, Amin; Tahani, Masoud

2016-01-01

In the present study a continuum model based on the nonlocal elasticity theory is developed for free vibration analysis of embedded ortho tropic thick circular and elliptical nano-plates rested on an elastic foundation. The elastic foundation is considered to behave like a Pasternak type of foundations. Governing equations for vibrating nano-plate are derived according to the Mindlin plate theory in which the effects of shear deformations of nano-plate are also included. The Galerkin method is then employed to obtain the size dependent natural frequencies of nano-plate. The solution procedure considers the entire nano-plate as a single super-continuum element. Effect of nonlocal parameter, lengths of nano-plate, aspect ratio, mode number, material properties, thickness and foundation on circular frequencies are investigated. It is seen that the nonlocal frequencies of the nano-plate are smaller in comparison to those from the classical theory and this is more pronounced for small lengths and higher vibration modes. It is also found that as the aspect ratio increases or the nanoplate becomes more elliptical, the small scale effect on natural frequencies increases. Further, it is observed that the elastic foundation decreases the influence of nonlocal parameter on the results. Since the effect of shear deformations plays an important role in vibration analysis and design of nano-plates, by predicting smaller values for fundamental frequencies, the study of these nano-structures using thick plate theories such as Mindlin plate theory is essential.

Modeling elastic anisotropy in strained heteroepitaxy.

Science.gov (United States)

Dixit, Gopal Krishna; Ranganathan, Madhav

2017-09-20

Using a continuum evolution equation, we model the growth and evolution of quantum dots in the heteroepitaxial Ge on Si(0 0 1) system in a molecular beam epitaxy unit. We formulate our model in terms of evolution due to deposition, and due to surface diffusion which is governed by a free energy. This free energy has contributions from surface energy, curvature, wetting effects and elastic energy due to lattice mismatch between the film and the substrate. In addition to anisotropy due to surface energy which favors facet formation, we also incorporate elastic anisotropy due to an underlying crystal lattice. The complicated elastic problem of the film-substrate system subjected to boundary conditions at the free surface, interface and the bulk substrate is solved by perturbation analysis using a small slope approximation. This permits an analysis of effects at different orders in the slope and sheds new light on the observed behavior. Linear stability analysis shows the early evolution of the instability towards dot formation. The elastic anisotropy causes a change in the alignment of dots in the linear regime, whereas the surface energy anisotropy changes the dot shapes at the nonlinear regime. Numerical simulation of the full nonlinear equations shows the evolution of the surface morphology. In particular, we show, for parameters of the [Formula: see text] [Formula: see text] on Si(0 0 1), the surface energy anisotropy dominates the shapes of the quantum dots, whereas their alignment is influenced by the elastic energy anisotropy. The anisotropy in elasticity causes a further elongation of the islands whose coarsening is interrupted due to [Formula: see text] facets on the surface.

Modeling elastic anisotropy in strained heteroepitaxy

Science.gov (United States)

Krishna Dixit, Gopal; Ranganathan, Madhav

2017-09-01

Using a continuum evolution equation, we model the growth and evolution of quantum dots in the heteroepitaxial Ge on Si(0 0 1) system in a molecular beam epitaxy unit. We formulate our model in terms of evolution due to deposition, and due to surface diffusion which is governed by a free energy. This free energy has contributions from surface energy, curvature, wetting effects and elastic energy due to lattice mismatch between the film and the substrate. In addition to anisotropy due to surface energy which favors facet formation, we also incorporate elastic anisotropy due to an underlying crystal lattice. The complicated elastic problem of the film-substrate system subjected to boundary conditions at the free surface, interface and the bulk substrate is solved by perturbation analysis using a small slope approximation. This permits an analysis of effects at different orders in the slope and sheds new light on the observed behavior. Linear stability analysis shows the early evolution of the instability towards dot formation. The elastic anisotropy causes a change in the alignment of dots in the linear regime, whereas the surface energy anisotropy changes the dot shapes at the nonlinear regime. Numerical simulation of the full nonlinear equations shows the evolution of the surface morphology. In particular, we show, for parameters of the Ge0.25 Si0.75 on Si(0 0 1), the surface energy anisotropy dominates the shapes of the quantum dots, whereas their alignment is influenced by the elastic energy anisotropy. The anisotropy in elasticity causes a further elongation of the islands whose coarsening is interrupted due to facets on the surface.

Nonlinear mean field theory for nuclear matter and surface properties

International Nuclear Information System (INIS)

Boguta, J.; Moszkowski, S.A.

1983-01-01

Nuclear matter properties are studied in a nonlinear relativistic mean field theory. We determine the parameters of the model from bulk properties of symmetric nuclear matter and a reasonable value of the effective mass. In this work, we stress the nonrelativistic limit of the theory which is essentially equivalent to a Skyrme hamiltonian, and we show that most of the results can be obtained, to a good approximation, analytically. The strength of the required parameters is determined from the binding energy and density of nuclear matter and the effective nucleon mass. For realistic values of the parameters, the nonrelativistic approximation turns out to be quite satisfactory. Using reasonable values of the parameters, we can account for other key properties of nuclei, such as the spin-orbit coupling, surface energy, and diffuseness of the nuclear surface. Also the energy dependence of the nucleon-nucleus optical model is accounted for reasonably well except near the Fermi surface. It is found, in agreement with empirical results, that the Landau parameter F 0 is quite small in normal nuclear matter. Both density dependence and momentum dependence of the NN interaction, but especially the former, are important for nuclear saturation. The required scalar and vector coupling constants agree fairly well with those obtained from analyses of NN scattering phase shifts with one-boson-exchange models. The mean field theory provides a semiquantitative justification for the weak Skyrme interaction in odd states. The strength of the required nonlinear term is roughly consistent with that derived using a new version of the chiral mean field theory in which the vector mass as well as the nucleon mass is generated by the sigma-field. (orig.)

Nonlinear closure relations theory for transport processes in nonequilibrium systems

International Nuclear Information System (INIS)

Sonnino, Giorgio

2009-01-01

A decade ago, a macroscopic theory for closure relations has been proposed for systems out of Onsager's region. This theory is referred to as the thermodynamic field theory (TFT). The aim of this work was to determine the nonlinear flux-force relations that respect the thermodynamic theorems for systems far from equilibrium. We propose a formulation of the TFT where one of the basic restrictions, namely, the closed-form solution for the skew-symmetric piece of the transport coefficients, has been removed. In addition, the general covariance principle is replaced by the De Donder-Prigogine thermodynamic covariance principle (TCP). The introduction of TCP requires the application of an appropriate mathematical formalism, which is referred to as the entropy-covariant formalism. By geometrical arguments, we prove the validity of the Glansdorff-Prigogine universal criterion of evolution. A new set of closure equations determining the nonlinear corrections to the linear ('Onsager') transport coefficients is also derived. The geometry of the thermodynamic space is non-Riemannian. However, it tends to be Riemannian for high values of the entropy production. In this limit, we recover the transport equations found by the old theory. Applications of our approach to transport in magnetically confined plasmas, materials submitted to temperature, and electric potential gradients or to unimolecular triangular chemical reactions can be found at references cited herein. Transport processes in tokamak plasmas are of particular interest. In this case, even in the absence of turbulence, the state of the plasma remains close to (but, it is not in) a state of local equilibrium. This prevents the transport relations from being linear.

Quantum theory from a nonlinear perspective Riccati equations in fundamental physics

CERN Document Server

Schuch, Dieter

2018-01-01

This book provides a unique survey displaying the power of Riccati equations to describe reversible and irreversible processes in physics and, in particular, quantum physics. Quantum mechanics is supposedly linear, invariant under time-reversal, conserving energy and, in contrast to classical theories, essentially based on the use of complex quantities. However, on a macroscopic level, processes apparently obey nonlinear irreversible evolution equations and dissipate energy. The Riccati equation, a nonlinear equation that can be linearized, has the potential to link these two worlds when applied to complex quantities. The nonlinearity can provide information about the phase-amplitude correlations of the complex quantities that cannot be obtained from the linearized form. As revealed in this wide ranging treatment, Riccati equations can also be found in many diverse fields of physics from Bose-Einstein-condensates to cosmology. The book will appeal to graduate students and theoretical physicists interested in ...

On the non-linear scale of cosmological perturbation theory

Energy Technology Data Exchange (ETDEWEB)

Blas, Diego [European Organization for Nuclear Research (CERN), Geneva (Switzerland); Garny, Mathias; Konstandin, Thomas [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

2013-04-15

We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.

On the non-linear scale of cosmological perturbation theory

International Nuclear Information System (INIS)

Blas, Diego; Garny, Mathias; Konstandin, Thomas

2013-04-01

We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.

On the non-linear scale of cosmological perturbation theory

CERN Document Server

Blas, Diego; Konstandin, Thomas

2013-01-01

We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.

Lectures on nonlinear evolution equations initial value problems

CERN Document Server

Racke, Reinhard

2015-01-01

This book mainly serves as an elementary, self-contained introduction to several important aspects of the theory of global solutions to initial value problems for nonlinear evolution equations. The book employs the classical method of continuation of local solutions with the help of a priori estimates obtained for small data. The existence and uniqueness of small, smooth solutions that are defined for all values of the time parameter are investigated. Moreover, the asymptotic behavior of the solutions is described as time tends to infinity. The methods for nonlinear wave equations are discussed in detail. Other examples include the equations of elasticity, heat equations, the equations of thermoelasticity, Schrödinger equations, Klein-Gordon equations, Maxwell equations and plate equations. To emphasize the importance of studying the conditions under which small data problems offer global solutions, some blow-up results are briefly described. Moreover, the prospects for corresponding initial-boundary value p...

Theory of nonlinear acoustic forces acting on fluids and particles in microsystems

DEFF Research Database (Denmark)

Karlsen, Jonas Tobias

fundamentally new capabilities in chemical, biomedical, or clinical studies of single cells and bioparticles. This thesis, entitled Theory of nonlinear acoustic forces acting on fluids and particles in microsystems, advances the fundamental understanding of acoustofluidics by addressing the origin...... of the nonlinear acoustic forces acting on fluids and particles. Classical results in nonlinear acoustics for the non-dissipative acoustic radiation force acting on a particle or an interface, as well as the dissipative acoustic force densities driving acoustic streaming, are derived and discussed in terms...... in the continuous fluid parameters of density and compressibility, e.g., due to a solute concentration field, the thesis presents novel analytical results on the acoustic force density acting on inhomogeneous fluids in acoustic fields. This inhomogeneity-induced acoustic force density is non-dissipative in origin...

Estimation of parameters of constant elasticity of substitution production functional model

Science.gov (United States)

Mahaboob, B.; Venkateswarlu, B.; Sankar, J. Ravi

2017-11-01

Nonlinear model building has become an increasing important powerful tool in mathematical economics. In recent years the popularity of applications of nonlinear models has dramatically been rising up. Several researchers in econometrics are very often interested in the inferential aspects of nonlinear regression models [6]. The present research study gives a distinct method of estimation of more complicated and highly nonlinear model viz Constant Elasticity of Substitution (CES) production functional model. Henningen et.al [5] proposed three solutions to avoid serious problems when estimating CES functions in 2012 and they are i) removing discontinuities by using the limits of the CES function and its derivative. ii) Circumventing large rounding errors by local linear approximations iii) Handling ill-behaved objective functions by a multi-dimensional grid search. Joel Chongeh et.al [7] discussed the estimation of the impact of capital and labour inputs to the gris output agri-food products using constant elasticity of substitution production function in Tanzanian context. Pol Antras [8] presented new estimates of the elasticity of substitution between capital and labour using data from the private sector of the U.S. economy for the period 1948-1998.

Strength of materials and theory of elasticity in 19th century Italy a brief account of the history of mechanics of solids and structures

CERN Document Server

Capecchi, Danilo

2015-01-01

This book examines the theoretical foundations underpinning the field of strength of materials/theory of elasticity, beginning from the origins of the modern theory of elasticity. While the focus is on the advances made within Italy during the nineteenth century, these achievements are framed within the overall European context. The vital contributions of Italian mathematicians, mathematical physicists, and engineers in respect of the theory of elasticity, continuum mechanics, structural mechanics, the principle of least work, and graphical methods in engineering are carefully explained and discussed. The book represents a work of historical research that primarily comprises original contributions and summaries of work published in journals. It is directed at those graduates in engineering, but also in architecture, who wish to achieve a more global and critical view of the discipline and will also be invaluable for all scholars of the history of mechanics.

Elastic and elastic-plastic behaviour of a piping system during blowdown - Comparison of measurement and calculation

International Nuclear Information System (INIS)

Petruschke, W.; Strunk, G.

1987-01-01

The investigations according to the system identification show that the piping model using beam theory and flexibility factors according to the Karman theory are adequate for evaluating natural frequencies, mode shapes, static displacements and stresses. The same accuracy can be seen by comparing the piping response due to blowdown within the elastic range. The simplified elastic-plastic analysis in general overestimates the maximum amplitudes while the frequency content is not simulated very well. For practical purposes, it can be an adequate tool in many cases. The elastic-plastic analysis is the most expensive procedure but gives also the best results. The use of beam elements with multilinear moment-curvature relationships results in a good approximation for the global behaviour (displacements). The strains according to this theory only include the beam deformation modes

The nonlinear theory of slow-wave electron cyclotron masers with inclusion of the beam velocity spread

International Nuclear Information System (INIS)

Kong, Ling-Bao; Wang, Hong-Yu; Hou, Zhi-Ling; Jin, Hai-Bo; Du, Chao-Hai

2013-01-01

The nonlinear theory of slow-wave electron cyclotron masers (ECM) with an initially straight electron beam is developed. The evolution equation of the nonlinear beam electron energy is derived. The numerical studies of the slow-wave ECM efficiency with inclusion of Gaussian beam velocity spread are presented. It is shown that the velocity spread reduces the interaction efficiency. -- Highlights: •The theory of slow-wave electron cyclotron masers is considered. •The calculation of efficiency under the resonance condition is presented. •The efficiency under Gaussian velocity spreads has been obtained

The nonlinear theory of slow-wave electron cyclotron masers with inclusion of the beam velocity spread

Energy Technology Data Exchange (ETDEWEB)

Kong, Ling-Bao, E-mail: konglingbao@gmail.com [School of Science, Beijing University of Chemical Technology, Beijing 100029 (China); Beijing Key Laboratory of Environmentally Harmful Chemicals Assessment, Beijing University of Chemical Technology, Beijing 100029 (China); Wang, Hong-Yu [School of Physics, Anshan Normal University, Anshan 114005 (China); Hou, Zhi-Ling, E-mail: houzl@mail.buct.edu.cn [School of Science, Beijing University of Chemical Technology, Beijing 100029 (China); Beijing Key Laboratory of Environmentally Harmful Chemicals Assessment, Beijing University of Chemical Technology, Beijing 100029 (China); Jin, Hai-Bo [School of Materials Science and Engineering, Beijing Institute of Technology, Beijing 100081 (China); Du, Chao-Hai [Institute of Electronics, Chinese Academy of Sciences, Beijing 100190 (China)

2013-12-15

The nonlinear theory of slow-wave electron cyclotron masers (ECM) with an initially straight electron beam is developed. The evolution equation of the nonlinear beam electron energy is derived. The numerical studies of the slow-wave ECM efficiency with inclusion of Gaussian beam velocity spread are presented. It is shown that the velocity spread reduces the interaction efficiency. -- Highlights: •The theory of slow-wave electron cyclotron masers is considered. •The calculation of efficiency under the resonance condition is presented. •The efficiency under Gaussian velocity spreads has been obtained.

Analysis of elastic-plastic dynamic response of reinforced concrete frame structure

International Nuclear Information System (INIS)

Li Zhongcheng

2009-01-01

Based on a set of data from seismic response test on an R/C frame, a force-based R/C beam fibre model with non-linear material properties and bond-slip effects are presented firstly in this paper, and then the applications to the tested R/C frame are presented to illustrate the model characteristics and to show the accuracy of seismic analysis including consideration of non-linear factors. It can be concluded that the elastic-plastic analysis is a potential step toward the accurate modelling for the dynamic analyses of R/C structures. Especially for the seismic safety re-evaluation of the existing NPPs, the elastic-plastic methodology with consideration of different non-linearities should be involved. (author)

Free vibration analysis of a multiple rotating nano-beams system based on the Eringen nonlocal elasticity theory

Energy Technology Data Exchange (ETDEWEB)

Ghafarian, M.; Ariaei, A., E-mail: ariaei@eng.ui.ac.ir [Department of Mechanical Engineering, Faculty of Engineering, University of Isfahan, Isfahan (Iran, Islamic Republic of)

2016-08-07

The free vibration analysis of a multiple rotating nanobeams' system applying the nonlocal Eringen elasticity theory is presented. Multiple nanobeams' systems are of great importance in nano-optomechanical applications. At nanoscale, the nonlocal effects become non-negligible. According to the nonlocal Euler-Bernoulli beam theory, the governing partial differential equations are derived by incorporating the nonlocal scale effects. Assuming a structure of n parallel nanobeams, the vibration of the system is described by a coupled set of n partial differential equations. The method involves a change of variables to uncouple the equations and the differential transform method as an efficient mathematical technique to solve the nonlocal governing differential equations. Then a number of parametric studies are conducted to assess the effect of the nonlocal scaling parameter, rotational speed, boundary conditions, hub radius, and the stiffness coefficients of the elastic interlayer media on the vibration behavior of the coupled rotating multiple-carbon-nanotube-beam system. It is revealed that the bending vibration of the system is significantly influenced by the rotational speed, elastic mediums, and the nonlocal scaling parameters. This model is validated by comparing the results with those available in the literature. The natural frequencies are in a reasonably good agreement with the reported results.

Rigorous theory of molecular orientational nonlinear optics

International Nuclear Information System (INIS)

Kwak, Chong Hoon; Kim, Gun Yeup

2015-01-01

Classical statistical mechanics of the molecular optics theory proposed by Buckingham [A. D. Buckingham and J. A. Pople, Proc. Phys. Soc. A 68, 905 (1955)] has been extended to describe the field induced molecular orientational polarization effects on nonlinear optics. In this paper, we present the generalized molecular orientational nonlinear optical processes (MONLO) through the calculation of the classical orientational averaging using the Boltzmann type time-averaged orientational interaction energy in the randomly oriented molecular system under the influence of applied electric fields. The focal points of the calculation are (1) the derivation of rigorous tensorial components of the effective molecular hyperpolarizabilities, (2) the molecular orientational polarizations and the electronic polarizations including the well-known third-order dc polarization, dc electric field induced Kerr effect (dc Kerr effect), optical Kerr effect (OKE), dc electric field induced second harmonic generation (EFISH), degenerate four wave mixing (DFWM) and third harmonic generation (THG). We also present some of the new predictive MONLO processes. For second-order MONLO, second-order optical rectification (SOR), Pockels effect and difference frequency generation (DFG) are described in terms of the anisotropic coefficients of first hyperpolarizability. And, for third-order MONLO, third-order optical rectification (TOR), dc electric field induced difference frequency generation (EFIDFG) and pump-probe transmission are presented

Using nonlinearity and spatiotemporal property modulation to control effective structural properties: dynamic rods

DEFF Research Database (Denmark)

Thomsen, Jon Juel; Blekhman, Iliya I.

2007-01-01

What are the effective properties of a generally nonlinear material or structure, whose local properties are modulated in both space and time? It has been suggested to use spatiotemporal modulation of structural properties to create materials and structures with adjustable effective properties......, and to call these dynamic materials or spatiotemporal composites. Also, according to theoretical predictions, structural nonlinearity enhances the possibilities of achieving specific effective properties. For example, with an elastic rod having cubical elastic nonlinearities, it seems possible to control......, and exemplified. Then simple approximate analytical expressions are derived for the effective wave speed and natural frequencies for one-dimensional wave propagation in a nonlinear elastic rod, where the spatiotemporal modulation is imposed as a high-frequency standing wave, supposed to be given. Finally the more...

Stochastic Finite Element Analysis of Non-Linear Structures Modelled by Plasticity Theory

DEFF Research Database (Denmark)

Frier, Christian; Sørensen, John Dalsgaard

2003-01-01

A Finite Element Reliability Method (FERM) is introduced to perform reliability analyses on two-dimensional structures in plane stress, modeled by non-linear plasticity theory. FERM is a coupling between the First Order Reliability Method (FORM) and the Finite Element Method (FEM). FERM can be us...

Beams on nonlinear elastic foundation

International Nuclear Information System (INIS)

Lukkassen, Dag; Meidell, Annette

2014-01-01

In order to determination vertical deflections and rail bending moments the Winkler model (1867) is often used. This linear model neglects several conditions. For example, by using experimental results, it has been observed that there is a substantial increase in the maximum rail deflection and rail bending moment when considering the nonlinearity of the track support system. A deeper mathematical analysis of the models is necessary in order to obtain better methods for more accurate numerical solutions in the determination of deflections and rail bending moments. This paper is intended to be a small step in this direction

Nonlinear scattering from a plasma column. I - Theory. II Special cases

Science.gov (United States)

Crawford, F. W.; Harker, K. J.

1983-01-01

The scattered signal excited by nonlinear mixing of two plane waves normally incident on an infinitely long column of plasma is investigated. A general solution is obtained for the polarization in which the electric field vectors of the waves are perpendicular to the column axis and the column is assumed to be radically inhomogeneous. This general theory is then applied to the special cases of the inhomogeneous column in the long-wavelength limit, and the homogeneous column both for the general case and in the long-wavelength limit. It is determined that dipole and quadrupole components should predominate in the polar radiation pattern for the long-wavelength case. The special case of second harmonic generation due to a single incident wave is analyzed in detail. Nonlinear scattering coefficients are computed, and the corresponding polar radiation patterns are determined. The findings of this study are employed to evaluate the feasibility of observing nonlinear scattering from meteor trails.

bessel functions for axisymmetric elasticity problems of the elastic

African Journals Online (AJOL)

HOD

2, 3DEPARTMENT OF CIVIL ENGINEERING, UNIVERSITY OF NIGERIA, NSUKKA. ENUGU STATE. ... theory of elasticity and in the case of vertical applied loads, was first ... partial differential equations in bodies having cylindrical symmetry.

Analytical Solutions to Nonlinear Conservative Oscillator with Fifth-Order Nonlinearity

DEFF Research Database (Denmark)

Sfahania, M. G.; Ganji, S. S.; Barari, Amin

2010-01-01

This paper describes analytical and numerical methods to analyze the steady state periodic response of an oscillator with symmetric elastic and inertia nonlinearity. A new implementation of the homotopy perturbation method (HPM) and an ancient Chinese method called the max-min approach are presen...

Considering "Nonlinearity" Across the Continuum in Medical Education Assessment: Supporting Theory, Practice, and Future Research Directions.

Science.gov (United States)

Durning, Steven J; Lubarsky, Stuart; Torre, Dario; Dory, Valérie; Holmboe, Eric

2015-01-01

The purpose of this article is to propose new approaches to assessment that are grounded in educational theory and the concept of "nonlinearity." The new approaches take into account related phenomena such as "uncertainty," "ambiguity," and "chaos." To illustrate these approaches, we will use the example of assessment of clinical reasoning, although the principles we outline may apply equally well to assessment of other constructs in medical education. Theoretical perspectives include a discussion of script theory, assimilation theory, self-regulated learning theory, and situated cognition. Assessment examples to include script concordance testing, concept maps, self-regulated learning microanalytic technique, and work-based assessment, which parallel the above-stated theories, respectively, are also highlighted. We conclude with some practical suggestions for approaching nonlinearity. © 2015 The Alliance for Continuing Education in the Health Professions, the Society for Academic Continuing Medical Education, and the Council on Continuing Medical Education, Association for Hospital Medical Education.

Non-linear quenching of current fluctuations in a self-exciting homopolar dynamo, proved by feedback system theory

Science.gov (United States)

de Paor, A. M.

Hide (Nonlinear Processes in Geophysics, 1998) has produced a new mathematical model of a self-exciting homopolar dynamo driving a series- wound motor, as a continuing contribution to the theory of the geomagnetic field. By a process of exact perturbation analysis, followed by combination and partial solution of differential equations, the complete nonlinear quenching of current fluctuations reported by Hide in the case that a parameter ɛ has the value 1 is proved via the Popov theorem from feedback system stability theory.

On the evaluation of elastic follow-up of a high temperature discontinuous structure

International Nuclear Information System (INIS)

Lee, J. M.; Kim, J. B.; Lee, H. Y.; Lee, J. H.

2003-01-01

While high temperature structures of LMR experience inelastic deformation such as plasticity and creep due to high temperature operating temperature of 530∼550 .deg. C, geometric nonlinear structures may undergo elastic follow-up behavior due to the interaction between stiff region and weak region. Thus, careful consideration should be given to the design and analysis of high temperature geometric nonlinear structure. In this study, the elastic follow-up behavior of geometric nonlinear structure has been investigated and the current status of design method implemented in the ASME-NH, Japanese BDS, French RCC-MR, and UK R-5 codes to consider elastic follow-up behavior has been reviewed. It has been shown that the ratio of the stiff region and the weak region and the type of loading affect the elastic follow-up behavior greatly from the detailed inelastic analyses of two bar model and L-shaped structure subjected to various loading situation. The applicability and the conservatism of simplified analysis methods implemented among various design codes need to be studied further

Density functional theory investigation of elastic properties and martensitic transformation of Ti-Ta alloys

Energy Technology Data Exchange (ETDEWEB)

Chakraborty, Tanmoy; Rogal, Jutta; Drautz, Ralf [Interdisciplinary Centre for Advanced Materials Simulation, Ruhr- Universitaet Bochum (Germany)

2016-07-01

Ti-Ta alloys are considered as promising materials for high temperature shape memory alloys as well as biomedical applications. The properties of these alloys have been shown to be strongly composition dependent. The temperature for the martensitic transformation between the high temperature cubic austenite and the low temperature orthorhombic martensite decreases linearly with increasing Ta content. Likewise, the elastic properties show clear trends with changing composition. We use density functional theory to investigate the involved phases in Ti-Ta where the disordered phases are treated by special quasi-random structures. To compare the stability of the involved phases as a function of temperature we calculate free energies using the quasi-harmonic Debye model. The obtained trends in the stability are consistent with experimentally measured transformation temperatures. Furthermore, we determine elastic properties which are in good agreement with experimentally observed trends.

Introduction to linear elasticity

CERN Document Server

Gould, Phillip L

2013-01-01

Introduction to Linear Elasticity, 3rd Edition, provides an applications-oriented grounding in the tensor-based theory of elasticity for students in mechanical, civil, aeronautical, and biomedical engineering, as well as materials and earth science. The book is distinct from the traditional text aimed at graduate students in solid mechanics by introducing the subject at a level appropriate for advanced undergraduate and beginning graduate students. The author's presentation allows students to apply the basic notions of stress analysis and move on to advanced work in continuum mechanics, plasticity, plate and shell theory, composite materials, viscoelasticity and finite method analysis. This book also:  Emphasizes tensor-based approach while still distilling down to explicit notation Provides introduction to theory of plates, theory of shells, wave propagation, viscoelasticity and plasticity accessible to advanced undergraduate students Appropriate for courses following emerging trend of teaching solid mechan...

A neuroeconomic theory of rational addiction and nonlinear time-perception.

Science.gov (United States)

Takahashi, Taiki

2011-01-01

Neuroeconomic conditions for "rational addiction" (Becker & Murphy 1988) have been unknown. This paper derived the conditions for "rational addiction" by utilizing a nonlinear time-perception theory of "hyperbolic" discounting, which is mathematically equivalent to the q-exponential intertemporal choice model based on Tsallis' statistics. It is shown that (i) Arrow-Pratt measure for temporal cognition corresponds to the degree of irrationality (i.e., Prelec's "decreasing impatience" parameter of temporal discounting) and (ii) rationality in addicts is controlled by a nondimensionalization parameter of the logarithmic time-perception function. Furthermore, the present theory illustrates the possibility that addictive drugs increase impulsivity via dopaminergic neuroadaptation without increasing irrationality. Future directions in the application of the model to studies in neuroeconomics are discussed.

φq-field theory for portfolio optimization: “fat tails” and nonlinear correlations

Science.gov (United States)

Sornette, D.; Simonetti, P.; Andersen, J. V.

2000-08-01

Physics and finance are both fundamentally based on the theory of random walks (and their generalizations to higher dimensions) and on the collective behavior of large numbers of correlated variables. The archetype examplifying this situation in finance is the portfolio optimization problem in which one desires to diversify on a set of possibly dependent assets to optimize the return and minimize the risks. The standard mean-variance solution introduced by Markovitz and its subsequent developments is basically a mean-field Gaussian solution. It has severe limitations for practical applications due to the strongly non-Gaussian structure of distributions and the nonlinear dependence between assets. Here, we present in details a general analytical characterization of the distribution of returns for a portfolio constituted of assets whose returns are described by an arbitrary joint multivariate distribution. In this goal, we introduce a non-linear transformation that maps the returns onto Gaussian variables whose covariance matrix provides a new measure of dependence between the non-normal returns, generalizing the covariance matrix into a nonlinear covariance matrix. This nonlinear covariance matrix is chiseled to the specific fat tail structure of the underlying marginal distributions, thus ensuring stability and good conditioning. The portfolio distribution is then obtained as the solution of a mapping to a so-called φq field theory in particle physics, of which we offer an extensive treatment using Feynman diagrammatic techniques and large deviation theory, that we illustrate in details for multivariate Weibull distributions. The interaction (non-mean field) structure in this field theory is a direct consequence of the non-Gaussian nature of the distribution of asset price returns. We find that minimizing the portfolio variance (i.e. the relatively “small” risks) may often increase the large risks, as measured by higher normalized cumulants. Extensive

THE CONTROL VARIATIONAL METHOD FOR ELASTIC CONTACT PROBLEMS

Directory of Open Access Journals (Sweden)

Mircea Sofonea

2010-07-01

Full Text Available We consider a multivalued equation of the form Ay + F(y = fin a real Hilbert space, where A is a linear operator and F represents the (Clarke subdifferential of some function. We prove existence and uniqueness results of the solution by using the control variational method. The main idea in this method is to minimize the energy functional associated to the nonlinear equation by arguments of optimal control theory. Then we consider a general mathematical model describing the contact between a linearly elastic body and an obstacle which leads to a variational formulation as above, for the displacement field. We apply the abstract existence and uniqueness results to prove the unique weak solvability of the corresponding contact problem. Finally, we present examples of contact and friction laws for which our results work.

Second quantization of classical nonlinear relativistic field theory. Pt. 2

International Nuclear Information System (INIS)

Balaban, T.

1976-01-01

The construction of a relativistic interacting local quantum field is given in two steps: first the classical nonlinear relativistic field theory is written down in terms of Poisson brackets, with initial conditions as canonical variables: next a representation of Poisson bracket Lie algebra by means of linear operators in the topological vector space is given and an explicit form of a local interacting relativistic quantum field PHI is obtained. (orig./BJ) [de

Lamb Wave Technique for Ultrasonic Nonlinear Characterization in Elastic Plates

International Nuclear Information System (INIS)

Lee, Tae Hun; Kim, Chung Seok; Jhang, Kyung Young

2010-01-01

Since the acoustic nonlinearity is sensitive to the minute variation of material properties, the nonlinear ultrasonic technique(NUT) has been considered as a promising method to evaluate the material degradation or fatigue. However, there are certain limitations to apply the conventional NUT using the bulk wave to thin plates. In case of plates, the use of Lamb wave can be considered, however, the propagation characteristics of Lamb wave are completely different with the bulk wave, and thus the separate study for the nonlinearity of Lamb wave is required. For this work, this paper analyzed first the conditions of mode pair suitable for the practical application as well as for the cumulative propagation of quadratic harmonic frequency and summarized the result in for conditions: phase matching, non-zero power flux, group velocity matching, and non-zero out-of-plane displacement. Experimental results in aluminum plates showed that the amplitude of the secondary Lamb wave and nonlinear parameter grew up with increasing propagation distance at the mode pair satisfying the above all conditions and that the ration of nonlinear parameters measured in Al6061-T6 and Al1100-H15 was closed to the ratio of the absolute nonlinear parameters

Non-linear quenching of current fluctuations in a self-exciting homopolar dynamo, proved by feedback system theory

Directory of Open Access Journals (Sweden)

A. M. de Paor

1998-01-01

Full Text Available Hide (Nonlinear Processes in Geophysics, 1998 has produced a new mathematical model of a self-exciting homopolar dynamo driving a series- wound motor, as a continuing contribution to the theory of the geomagnetic field. By a process of exact perturbation analysis, followed by combination and partial solution of differential equations, the complete nonlinear quenching of current fluctuations reported by Hide in the case that a parameter ε has the value 1 is proved via the Popov theorem from feedback system stability theory.

The effect of gas and fluid flows on nonlinear lateral vibrations of rotating drill strings

Science.gov (United States)

Khajiyeva, Lelya; Kudaibergenov, Askar; Kudaibergenov, Askat

2018-06-01

In this work we develop nonlinear mathematical models describing coupled lateral vibrations of a rotating drill string under the effect of external supersonic gas and internal fluid flows. An axial compressive load and a torque also affect the drill string. The mathematical models are derived by the use of Novozhilov's nonlinear theory of elasticity with implementation of Hamilton's variation principle. Expressions for the gas flow pressure are determined according to the piston theory. The fluid flow is considered as added mass inside the curved tube of the drill string. Using an algorithm developed in the Mathematica computation program on the basis of the Galerkin approach and the stiffness switching method the numerical solution of the obtained approximate differential equations is found. Influences of the external loads, drill string angular speed of rotation, parameters of the gas and fluid flows on the drill string vibrations are shown.

Nonlinear interaction analysis of RC cylindrical tank with subsoil by adopting two kinds of constitutive models for ground and structure

Science.gov (United States)

Lewiński, Paweł M.; Dudziak, Sławomir

2018-01-01

In the paper, two kinds of constitutive models for ground and structure were adopted for the nonlinear interaction analysis of the RC cylindrical tank with subsoil. The paper discusses deformational and incremental approaches to a nonlinear FE analysis of soil-structure interaction including the description of behaviour of the RC structure and the subsoil under short-term loading. Moreover, a non-linear elastic-brittle-plastic analysis of RC axisymmetric structures using finite element iterative techniques is presented. The constitutive laws for concrete and subsoil are developed in compliance with the deformational and plastic flow theories of plasticity. Two examples of an FE analysis of soil-structure interaction were performed and the results were analysed.

Nonlinear free vibration of piezoelectric nanobeams incorporating surface effects

International Nuclear Information System (INIS)

Hosseini-Hashemi, Shahrokh; Nahas, Iman; Fakher, Mahmood; Nazemnezhad, Reza

2014-01-01

In this study, the nonlinear free vibration of piezoelectric nanobeams incorporating surface effects (surface elasticity, surface tension, and surface density) is studied. The governing equation of the piezoelectric nanobeam is derived within the framework of Euler–Bernoulli beam theory with the von Kármán geometric nonlinearity. In order to satisfy the balance conditions between the nanobeam bulk and its surfaces, the component of the bulk stress, σ zz , is assumed to vary linearly through the nanobeam thickness. An exact solution is obtained for the natural frequencies of a simply supported piezoelectric nanobeam in terms of the Jacobi elliptic functions using the free vibration mode shape of the corresponding linear problem. Then, the influences of the surface effects and the piezoelectric field on the nonlinear free vibration of nanobeams made of aluminum and silicon with positive and negative surface elasticity, respectively, have been studied for various properties of the piezoelectric field, various nanobeam sizes and amplitude ratios. It is observed that if the Young’s modulus of a nanobeam is lower, the effect of the piezoelectric field on the frequency ratios (FRs) of the nanobeam will be greater. In addition, it is seen that by increasing the nanobeam length so that the nanobeam cross section is set to be constant, the surface effects and the piezoelectric field with negative voltage values increases the FRs, whereas it is the other way around when the nanobeam cross section is assumed to be dependent on the length of the nanobeam. (paper)

Extrinsic contribution to the non-linearity in a PZT disc

Energy Technology Data Exchange (ETDEWEB)

Perez, Rafel [Departament de Fisica Aplicada, Universitat Politecnica de Catalunya, Jordi Girona 1-3, Campus Nord, 08034 Barcelona (Spain); Albareda, Alfons [Departament de Fisica Aplicada, Universitat Politecnica de Catalunya, Jordi Girona 1-3, Campus Nord, 08034 Barcelona (Spain); Garcia, Jose E [Departament de Fisica Aplicada, Universitat Politecnica de Catalunya, Jordi Girona 1-3, Campus Nord, 08034 Barcelona (Spain); Tiana, Jordi [Departament de Fisica Aplicada, Universitat Politecnica de Catalunya, Jordi Girona 1-3, Campus Nord, 08034 Barcelona (Spain); Ringgaard, Erling [Ferroperm Piezoceramics A/S, Hejreskovvej 18, DK-3490 Kvistgaard (Denmark); Wolny, Wanda W [Ferroperm Piezoceramics A/S, Hejreskovvej 18, DK-3490 Kvistgaard (Denmark)

2004-10-07

Non-linear increases in elastic, piezoelectric (direct and reverse) and dielectric coefficients have been measured under a high electrical field or under high mechanical stress. The permittivity and reverse piezoelectric coefficient can be measured by applying a high voltage at a low frequency, while the elastic compliance and direct piezoelectric coefficient can be measured at the first radial resonance frequency in order to apply a high stress. The non-linear behaviour has been analysed at the radial resonance of a disc. In all the materials tested, the results show that there is a close relation between the non-linear increments of the different coefficients. An empirical model has been proposed in order to describe and understand these relations. It is assumed that either the strain or the electrical displacement is produced by intrinsic and extrinsic processes, but only the latter, which consist mainly in the motion of domain walls, contribute to the non-linearity. The model enables us to find the domain wall contribution to elastic, piezoelectric and dielectric non-linearities, and allows us to compare the amplitudes of the fields and stresses that produce the same displacement of domain walls.

An Accurate Study on Capacitive Microphone with Circular Diaphragm Using a Higher Order Elasticity Theory

Directory of Open Access Journals (Sweden)

Shakiba Dowlati

Full Text Available Abstract This study has been undertaken to investigate the mechanical behavior of the capacitive microphone with clamped circular diaphragm using modified couple stress theory in comparison to the classical one. Presence of the length scale parameter in modified couple stress theory provides the means to evaluate the size effect on the microphone mechanical behavior. Investigating Pull-in phenomenon and dynamic behavior of the microphone are the matters provided due to the application of a step DC voltage. Also the effects of different air damping coefficients on dynamic pull-in voltage and pull-in time have been studied. The output level or sensitivity of the microphone has been studied by investigating the frequency response in term of magnitude for different length scale parameters to figure out how the length scale parameter affects on the sensitivity of the capacitive microphone. To achieve these ends, the nonlinear differential equation of the circular diaphragm has been extracted using Kirchhoff thin plate theory. Then, a Step-by-Step Linearization Method (SSLM has been used to escape from the nonlinearity of the differential equation. Afterwards, Galerkin-based reduced-order model has been applied to solve the obtained equation.

Strain tensor selection and the elastic theory of incompatible thin sheets.

Science.gov (United States)

Oshri, Oz; Diamant, Haim

2017-05-01

The existing theory of incompatible elastic sheets uses the deviation of the surface metric from a reference metric to define the strain tensor [Efrati et al., J. Mech. Phys. Solids 57, 762 (2009)JMPSA80022-509610.1016/j.jmps.2008.12.004]. For a class of simple axisymmetric problems we examine an alternative formulation, defining the strain based on deviations of distances (rather than distances squared) from their rest values. While the two formulations converge in the limit of small slopes and in the limit of an incompressible sheet, for other cases they are found not to be equivalent. The alternative formulation offers several features which are absent in the existing theory. (a) In the case of planar deformations of flat incompatible sheets, it yields linear, exactly solvable, equations of equilibrium. (b) When reduced to uniaxial (one-dimensional) deformations, it coincides with the theory of extensible elastica; in particular, for a uniaxially bent sheet it yields an unstrained cylindrical configuration. (c) It gives a simple criterion determining whether an isometric immersion of an incompatible sheet is at mechanical equilibrium with respect to normal forces. For a reference metric of constant positive Gaussian curvature, a spherical cap is found to satisfy this criterion except in an arbitrarily narrow boundary layer.

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...

Positron interactions with water–total elastic, total inelastic, and elastic differential cross section measurements

International Nuclear Information System (INIS)

Tattersall, Wade; Chiari, Luca; Machacek, J. R.; Anderson, Emma; Sullivan, James P.; White, Ron D.; Brunger, M. J.; Buckman, Stephen J.; Garcia, Gustavo; Blanco, Francisco

2014-01-01

Utilising a high-resolution, trap-based positron beam, we have measured both elastic and inelastic scattering of positrons from water vapour. The measurements comprise differential elastic, total elastic, and total inelastic (not including positronium formation) absolute cross sections. The energy range investigated is from 1 eV to 60 eV. Comparison with theory is made with both R-Matrix and distorted wave calculations, and with our own application of the Independent Atom Model for positron interactions

Nonlinear stochastic dynamics of mesoscopic homogeneous biochemical reaction systems—an analytical theory

International Nuclear Information System (INIS)

Qian, Hong

2011-01-01

The nonlinear dynamics of biochemical reactions in a small-sized system on the order of a cell are stochastic. Assuming spatial homogeneity, the populations of n molecular species follow a multi-dimensional birth-and-death process on Z n . We introduce the Delbrück–Gillespie process, a continuous-time Markov jump process, whose Kolmogorov forward equation has been known as the chemical master equation, and whose stochastic trajectories can be computed via the Gillespie algorithm. Using simple models, we illustrate that a system of nonlinear ordinary differential equations on R n emerges in the infinite system size limit. For finite system size, transitions among multiple attractors of the nonlinear dynamical system are rare events with exponentially long transit times. There is a separation of time scales between the deterministic ODEs and the stochastic Markov jumps between attractors. No diffusion process can provide a global representation that is accurate on both short and long time scales for the nonlinear, stochastic population dynamics. On the short time scale and near deterministic stable fixed points, Ornstein–Uhlenbeck Gaussian processes give linear stochastic dynamics that exhibit time-irreversible circular motion for open, driven chemical systems. Extending this individual stochastic behaviour-based nonlinear population theory of molecular species to other biological systems is discussed. (invited article)

Transient waves in visco-elastic media

CERN Document Server

Ricker, Norman

1977-01-01

Developments in Solid Earth Geophysics 10: Transient Waves in Visco-Elastic Media deals with the propagation of transient elastic disturbances in visco-elastic media. More specifically, it explores the visco-elastic behavior of a medium, whether gaseous, liquid, or solid, for very-small-amplitude disturbances. This volume provides a historical overview of the theory of the propagation of elastic waves in solid bodies, along with seismic prospecting and the nature of seismograms. It also discusses the seismic experiments, the behavior of waves propagated in accordance with the Stokes wave

Method of asymptotic expansions and qualitative analysis of finite-dimensional models in the nonlinear field theory

International Nuclear Information System (INIS)

Eleonskij, V.M.; Kulagin, N.E.; Novozhilova, N.S.; Silin, V.P.

1984-01-01

The reasons which prevent the existence of periodic in time and self-localised in space solutions of the nonlinear wave equation u=F (u) are determined by the methods of qualitative theory of dynamical systems. The correspondence between the qualitative behaviour of special (separatrix) trajectories in the phase space and asymptotic solutions of the nonlinear wave equation is analysed

Nonlinear Dynamic Phenomena in Mechanics

CERN Document Server

Warminski, Jerzy; Cartmell, Matthew P

2012-01-01

Nonlinear phenomena should play a crucial role in the design and control of engineering systems and structures as they can drastically change the prevailing dynamical responses. This book covers theoretical and applications-based problems of nonlinear dynamics concerned with both discrete and continuous systems of interest in civil and mechanical engineering. They include pendulum-like systems, slender footbridges, shape memory alloys, sagged elastic cables and non-smooth problems. Pendulums can be used as a dynamic absorber mounted in high buildings, bridges or chimneys. Geometrical nonlinear

Application of H∞ control theory to power control of a nonlinear reactor model

International Nuclear Information System (INIS)

Suzuki, Katsuo; Shimazaki, Junya; Shinohara, Yoshikuni

1993-01-01

The H∞ control theory is applied to the compensator design of a nonlinear nuclear reactor model, and the results are compared with standard linear quadratic Gaussian (LQG) control. The reactor model is assumed to be provided with a control rod drive system having the compensation of rod position feedback. The nonlinearity of the reactor model exerts a great influence on the stability of the control system, and hence, it is desirable for a power control system of a nuclear reactor to achieve robust stability and to improve the sensitivity of the feedback control system. A computer simulation based on a power control system synthesized by LQG control was performed revealing that the control system has some stationary offset and less stability. Therefore, here, attention is given to the development of a methodology for robust control that can withstand exogenous disturbances and nonlinearity in view of system parameter changes. The developed methodology adopts H∞ control theory in the feedback system and shows interesting features of robustness. The results of the computer simulation indicate that the feedback control system constructed by the developed H∞ compensator possesses sufficient robustness of control on the stability and disturbance attenuation, which are essential for the safe operation of a nuclear reactor

Non-linear wave loads and ship responses by a time-domain strip theory

DEFF Research Database (Denmark)

Xia, Jinzhu; Wang, Zhaohui; Jensen, Jørgen Juncher

1998-01-01

. Based on this time-domain strip theory, an efficient non-linear hydroelastic method of wave- and slamming-induced vertical motions and structural responses of ships is developed, where the structure is represented as a Timoshenko beam. Numerical calculations are presented for the S175 Containership...

Microstructure, elastic deformation behavior and mechanical properties of biomedical β-type titanium alloy thin-tube used for stents.

Science.gov (United States)

Tian, Yuxing; Yu, Zhentao; Ong, Chun Yee Aaron; Kent, Damon; Wang, Gui

2015-05-01

Cold-deformability and mechanical compatibility of the biomedical β-type titanium alloy are the foremost considerations for their application in stents, because the lower ductility restricts the cold-forming of thin-tube and unsatisfactory mechanical performance causes a failed tissue repair. In this paper, β-type titanium alloy (Ti-25Nb-3Zr-3Mo-2Sn, wt%) thin-tube fabricated by routine cold rolling is reported for the first time, and its elastic behavior and mechanical properties are discussed for the various microstructures. The as cold-rolled tube exhibits nonlinear elastic behavior with large recoverable strain of 2.3%. After annealing and aging, a nonlinear elasticity, considered as the intermediate stage between "double yielding" and normal linear elasticity, is attributable to a moderate precipitation of α phase. Quantitive relationships are established between volume fraction of α phase (Vα) and elastic modulus, strength as well as maximal recoverable strain (εmax-R), where the εmax-R of above 2.0% corresponds to the Vα range of 3-10%. It is considered that the "mechanical" stabilization of the (α+β) microstructure is a possible elastic mechanism for explaining the nonlinear elastic behavior. Copyright © 2015 Elsevier Ltd. All rights reserved.

Charges in nonlinear higher-spin theory

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