Nonlinear elastic waves in materials
Rushchitsky, Jeremiah J
2014-01-01
The main goal of the book is a coherent treatment of the theory of propagation in materials of nonlinearly elastic waves of displacements, which corresponds to one modern line of development of the nonlinear theory of elastic waves. The book is divided on five basic parts: the necessary information on waves and materials; the necessary information on nonlinear theory of elasticity and elastic materials; analysis of one-dimensional nonlinear elastic waves of displacement – longitudinal, vertically and horizontally polarized transverse plane nonlinear elastic waves of displacement; analysis of one-dimensional nonlinear elastic waves of displacement – cylindrical and torsional nonlinear elastic waves of displacement; analysis of two-dimensional nonlinear elastic waves of displacement – Rayleigh and Love nonlinear elastic surface waves. The book is addressed first of all to people working in solid mechanics – from the students at an advanced undergraduate and graduate level to the scientists, professional...
Probing hysteretic elasticity in weakly nonlinear materials
Energy Technology Data Exchange (ETDEWEB)
Johnson, Paul A [Los Alamos National Laboratory; Haupert, Sylvain [UPMC UNIV PARIS; Renaud, Guillaume [UPMC UNIV PARIS; Riviere, Jacques [UPMC UNIV PARIS; Talmant, Maryline [UPMC UNIV PARIS; Laugier, Pascal [UPMC UNIV PARIS
2010-12-07
Our work is aimed at assessing the elastic and dissipative hysteretic nonlinear parameters' repeatability (precision) using several classes of materials with weak, intermediate and high nonlinear properties. In this contribution, we describe an optimized Nonlinear Resonant Ultrasound Spectroscopy (NRUS) measuring and data processing protocol applied to small samples. The protocol is used to eliminate the effects of environmental condition changes that take place during an experiment, and that may mask the intrinsic elastic nonlinearity. As an example, in our experiments, we identified external temperature fluctuation as a primary source of material resonance frequency and elastic modulus variation. A variation of 0.1 C produced a frequency variation of 0.01 %, which is similar to the expected nonlinear frequency shift for weakly nonlinear materials. In order to eliminate environmental effects, the variation in f{sub 0} (the elastically linear resonance frequency proportional to modulus) is fit with the appropriate function, and that function is used to correct the NRUS calculation of nonlinear parameters. With our correction procedure, we measured relative resonant frequency shifts of 10{sup -5} , which are below 10{sup -4}, often considered the limit to NRUS sensitivity under common experimental conditions. Our results show that the procedure is an alternative to the stringent control of temperature often applied. Applying the approach, we report nonlinear parameters for several materials, some with very small nonclassical nonlinearity. The approach has broad application to NRUS and other Nonlinear Elastic Wave Spectroscopy approaches.
Nonlinear elastic behavior of phantom materials for elastography
Energy Technology Data Exchange (ETDEWEB)
Pavan, Theo Z; Madsen, Ernest L; Frank, Gary R; Hall, Timothy J [Medical Physics Department, University of Wisconsin, Room 1005, Wisconsin Institutes for Medical Research, 1111 Highland Avenue, Madison, WI 53705 (United States); Adilton O Carneiro, Antonio, E-mail: tjhall@wisc.ed [Departamento de Fisica e Matematica, FFCLRP, Universidade de Sao Paulo, Av. Bandeirantes, 3900, Monte Alegre, Ribeirao Preto, Sao Paulo (Brazil)
2010-05-07
The development of phantom materials for elasticity imaging is reported in this paper. These materials were specifically designed to provide nonlinear stress/strain relationship that can be controlled independently of the small strain shear modulus of the material. The materials are mixtures of agar and gelatin gels. Oil droplet dispersions in these materials provide further control of the small strain shear modulus and the nonlinear parameter of the material. Since these materials are mostly water, they are assumed to be incompressible under typical experimental conditions in elasticity imaging. The Veronda-Westman model for strain energy density provided a good fit to all materials used in this study. Materials with a constant gelatin concentration (3.0% dry weight) but varying agar concentration (0.6-2.8% dry weight) demonstrated the same power law relationship between elastic modulus and agar concentration found for pure agar (1.89 {+-} 0.02), consistent with percolation theory, and provided a consistent nonlinearity parameter of 4.5 {+-} 0.3. The insights provided by this study will form the basis for stable elastography phantoms with stiffness and nonlinear stress/strain relationships in the background that differ from those in the target.
Dielectric and Elastic Characterization of Nonlinear Heterogeneous Materials
Directory of Open Access Journals (Sweden)
Stefano Giordano
2009-09-01
Full Text Available This review paper deals with the dielectric and elastic characterization of composite materials constituted by dispersions of nonlinear inclusions embedded in a linear matrix. The dielectric theory deals with pseudo-oriented particles shaped as ellipsoids of revolution: it means that we are dealing with mixtures of inclusions of arbitrary aspect ratio and arbitrary non-random orientational distributions. The analysis ranges from parallel spheroidal inclusions to completely random oriented inclusions. Each ellipsoidal inclusion is made of an isotropic dielectric material described by means of the so-called Kerr nonlinear relation. On the other hand, the nonlinear elastic characterization takes into consideration a dispersion of nonlinear (spherical or cylindrical inhomogeneities. Both phases are considered isotropic (actually it means polycrystalline or amorphous solids. Under the simplifying hypotheses of small deformation for the material body and of small volume fraction of the embedded phase, we describe a theory for obtaining the linear and nonlinear elastic properties (bulk and shear moduli and Landau coefficients of the overall material.
Directory of Open Access Journals (Sweden)
Da-Guang Zhang
2015-10-01
Full Text Available 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.
Energy Technology Data Exchange (ETDEWEB)
Zhang, Da-Guang; Li, Meng-Han; Zhou, Hao-Miao, E-mail: zhouhm@cjlu.edu.cn [College of Information Engineering, China Jiliang University, 310018, Hangzhou (China)
2015-10-15
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.
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.
Directory of Open Access Journals (Sweden)
E. Mardani
2008-01-01
Full Text Available A prismatic beam made of a behaviorally nonlinear material was analyzed under a concentrated load moving with a known velocity on a nonlinear elastic foundation with a reaction the vibration equation of motion was derived using Hamilton principle and Euler Lagrange equation. The amplitude of vibration, circular frequency, bending moment, stress and deflection of the beam can be calculated by the presented solution. Considering the response of the beam, in the sense of its resonance, it was found that there is no critical velocity when the behavior of the beam and foundation material is assumed to be physically nonlinear and there are finite values for the deflection, stress and bending moment of the beam when
Eiras, J N; Vu, Q A; Lott, M; Payá, J; Garnier, V; Payan, C
2016-07-01
This study demonstrates the feasibility of the dynamic acousto-elastic effect of a continuous high frequency wave for investigating the material nonlinearity upon transient vibration. The approach is demonstrated on a concrete sample measuring 15×15×60cm(3). Two ultrasonic transducers (emitter and receiver) are placed at its middle span. A continuous high frequency wave of 500kHz propagates through the material and is modulated with a hammer blow. The position of the hammer blow on the sample is configured to promote the first bending mode of vibration. The use of a continuous wave allows discrete time extraction of the nonlinear behavior by a short-time Fourier transform approach, through the simultaneous comparison of a reference non-modulated signal and an impact-modulated signal. The hammer blow results in phase shifts and variations of signal amplitude between reference and perturbed signals, which are driven by the resonant frequency of the sample. Finally, a comprehensive analysis of the relaxation mechanisms (modulus and attenuation recovery) is conducted to untangle the coupled fast and slow hysteretic effects. Copyright © 2016 Elsevier B.V. All rights reserved.
Teaching nonlinear dynamics through elastic cords
Energy Technology Data Exchange (ETDEWEB)
Chacon, R; Galan, C A; Sanchez-Bajo, F, E-mail: rchacon@unex.e [Departamento de Fisica Aplicada, Escuela de IngenierIas Industriales, Universidad de Extremadura, Apartado Postal 382, E-06071 Badajoz (Spain)
2011-01-15
We experimentally studied the restoring force of a length of stretched elastic cord. A simple analytical expression for the restoring force was found to fit all the experimental results for different elastic materials. Remarkably, this analytical expression depends upon an elastic-cord characteristic parameter which exhibits two limiting values corresponding to two nonlinear springs with different Hooke's elastic constants. Additionally, the simplest model of elastic cord dynamics is capable of exhibiting a great diversity of nonlinear phenomena, including bifurcations and chaos, thus providing a suitable alternative model system for discussing the basic essentials of nonlinear dynamics in the context of intermediate physics courses at university level.
An Approximate Method for Analysis of Solitary Waves in Nonlinear Elastic Materials
Rushchitsky, J. J.; Yurchuk, V. N.
2016-05-01
Two types of solitary elastic waves are considered: a longitudinal plane displacement wave (longitudinal displacements along the abscissa axis of a Cartesian coordinate system) and a radial cylindrical displacement wave (displacements in the radial direction of a cylindrical coordinate system). The basic innovation is the use of nonlinear wave equations similar in form to describe these waves and the use of the same approximate method to analyze these equations. The distortion of the wave profile described by Whittaker (plane wave) or Macdonald (cylindrical wave) functions is described theoretically
Hilbert complexes of nonlinear elasticity
Angoshtari, Arzhang; Yavari, Arash
2016-12-01
We introduce some Hilbert complexes involving second-order tensors on flat compact manifolds with boundary that describe the kinematics and the kinetics of motion in nonlinear elasticity. We then use the general framework of Hilbert complexes to write Hodge-type and Helmholtz-type orthogonal decompositions for second-order tensors. As some applications of these decompositions in nonlinear elasticity, we study the strain compatibility equations of linear and nonlinear elasticity in the presence of Dirichlet boundary conditions and the existence of stress functions on non-contractible bodies. As an application of these Hilbert complexes in computational mechanics, we briefly discuss the derivation of a new class of mixed finite element methods for nonlinear elasticity.
Non-linear elastic deformations
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.
Evaluation of frost damage in cement-based materials by a nonlinear elastic wave technique
Eiras, J. N.; Kundu, T.; Popovics, J. S.; Monzó, J.; Soriano, L.; Payá, J.
2014-03-01
Frost resistance of concrete is a major concern in cold regions. RILEM (International union of laboratories and experts in construction materials, systems and structures) recommendations provide two alternatives for evaluating frost damage by nondestructive evaluation methods for concrete like materials. The first method is based on the ultrasonic pulse velocity measurement, while the second alternative technique is based on the resonant vibration test. In this study, we monitor the frost damage in Portland cement mortar samples with water to cement ratio of 0.5 and aggregate to cement ratio of 3. The samples are completely saturated by water and are frozen for 24 hours at -25°C. The frost damage is monitored after 0, 5, 10, 15 and 20 freezing-thawing cycles by nonlinear impact resonance acoustic spectroscopy (NIRAS). The results obtained are compared with those obtained by resonant vibration tests, the second alternative technique recommended by RILEM. The obtained results show that NIRAS is more sensitive to early stages of damage than the standard resonant vibration tests.
Goyal, Deepak
Textile composites have a wide variety of applications in the aerospace, sports, automobile, marine and medical industries. Due to the availability of a variety of textile architectures and numerous parameters associated with each, optimal design through extensive experimental testing is not practical. Predictive tools are needed to perform virtual experiments of various options. The focus of this research is to develop a better understanding of linear elastic response, plasticity and material damage induced nonlinear behavior and mechanics of load flow in textile composites. Textile composites exhibit multiple scales of complexity. The various textile behaviors are analyzed using a two-scale finite element modeling. A framework to allow use of a wide variety of damage initiation and growth models is proposed. Plasticity induced non-linear behavior of 2x2 braided composites is investigated using a modeling approach based on Hill's yield function for orthotropic materials. The mechanics of load flow in textile composites is demonstrated using special non-standard postprocessing techniques that not only highlight the important details, but also transform the extensive amount of output data into comprehensible modes of behavior. The investigations show that the damage models differ from each other in terms of amount of degradation as well as the properties to be degraded under a particular failure mode. When compared with experimental data, predictions of some models match well for glass/epoxy composite whereas other's match well for carbon/epoxy composites. However, all the models predicted very similar response when damage factors were made similar, which shows that the magnitude of damage factors are very important. Full 3D as well as equivalent tape laminate predictions lie within the range of the experimental data for a wide variety of braided composites with different material systems, which validated the plasticity analysis. Conclusions about the effect of
Nonlinear Materials Characterization Facility
Federal Laboratory Consortium — The Nonlinear Materials Characterization Facility conducts photophysical research and development of nonlinear materials operating in the visible spectrum to protect...
In situ nonlinear elastic behavior of soil observed by DAET
Energy Technology Data Exchange (ETDEWEB)
Larmat, Carene [Los Alamos National Laboratory; Renaud, Guillaume [Eramus Medical Center, Rotterdam, The Netherlands; Rutledge, James T. [EES-17: GEOPHYSICS; Lee, Richard C. [Los Alamos National Laboratory; Guyer, Robert A. [Los Alamos National Laboratory; Johnson, Paul A. [Los Alamos National Laboratory
2012-07-05
The key to safe design of critical facilities (strong ground motion in low velocity materials such as soils). Current approaches are predictions from measurements of the elastic non-linear properties of boreholes samples. Need for in-situ, local and complete determination of non-linear properties of soil, rock in response to high-strain motion.
NONLINEAR ELASTICITY OF BLOOD ARTERIAL DUCT
Institute of Scientific and Technical Information of China (English)
黄孟才; 顾忠; 沈俊; 唐复勇
1991-01-01
The paper deals with nonlinear elasticity of blood arterial duct, in which the artery is modeled to bea locally triclinic, transverse isotropic, incorapressible, axisymmetric and thickwalled tube with large deformations, The nonlinear coustitutive relationship of arterial tissues is based on the theorv of Green and Adkins. A nonlinear strain energy density function is introduced for nonlinear stress-strain relationship of second order, in which the coefficient of each term is expressed by means of a Lame’s constant, The elasticity constants are nqcessary to describe such a uonlinear finite strain etastieity of the second order, These constants are determined by means of the stress-strain increment theory.
Solitary waves on nonlinear elastic rods. I
DEFF Research Database (Denmark)
Sørensen, Mads Peter; Christiansen, Peter Leth; Lomdahl, P. S.
1984-01-01
Acoustic waves on elastic rods with circular cross section are governed by improved Boussinesq equations when transverse motion and nonlinearity in the elastic medium are taken into account. Solitary wave solutions to these equations have been found. The present paper treats the interaction between...
Conditioning-induced elastic nonlinearity in hysteretic media
Gliozzi, A. S.; Scalerandi, M.; Antonaci, P.; Bruno, C. L. E.
2010-08-01
The definition and measurement of the nonlinear elastic properties of a sample is of great importance for a large number of applications, including characterization of material performances and damage detection. However, such measurements are often influenced by spurious effects due to a combination of nonlinearity and nonequilibrium phenomena. We will present experimental data to show how nonlinearity due to small cracks in concrete samples increases as a consequence of conditioning, i.e., after having perturbed them with a constant amplitude excitation. In addition, our experimental data highlight "memory effects," i.e., they show that when the excitation is removed, the elastic modulus does not return instantaneously to the initial value.
CHAOTIC BELT PHENOMENA IN NONLINEAR ELASTIC BEAM
Institute of Scientific and Technical Information of China (English)
张年梅; 杨桂通
2003-01-01
The chaotic motions of axial compressed nonlinear elastic beam subjected totransverse load were studied. The damping force in the system is nonlinear. Consideringmaterial and geometric nonlinearity, nonlinear governing equation of the system wasderived. By use of nonlinear Galerkin method, differential dynamic system was set up.Melnikov method was used to analyze the characters of the system. The results showed thatchaos may occur in the system when the load parameters P0 and f satisfy some conditions.The zone of chaotic motion was belted. The route from subharmonic bifurcation to chaoswas analyzed. The critical conditions that chaos occurs were determined.
Immense elastic nonlinearities at the demixing transition of aqueous PNIPAM solutions
Philipp, Martine; Müller, Ulrich; Aleksandrova, Ralitsa; Sanctuary, Roland; Müller-Buschbaum, P.; Krüger, Jan-Kristian
2013-01-01
Elastic nonlinearities are particularly relevant for soft materials because of their inherently small linear elasticity. Nonlinear elastic properties may even take over the leading role for the transformation at mechanical instabilities accompanying many phase transitions in soft matter. Because of inherent experimental difficulties, only little is known about third order (nonlinear) elastic constants within liquids, gels and polymers. Here we show that a key concept to access thi...
Nonlinear elasticity of alginate gels
Hashemnejad, Seyed Meysam; Kundu, Santanu
Alginate is a naturally occurring anionic polysaccharide extracted from brown algae. Because of biocompatibility, low toxicity, and simple gelation process, alginate gels are used in biomedical and food applications. Here, we report the rheological behavior of ionically crosslinked alginate gels, which are obtained by in situ gelation of alginates with calcium salts, in between two parallel plates of a rheometer. Strain stiffening behavior was captured using large amplitude oscillatory shear (LAOS) experiments. In addition, negative normal stress was observed for these gels, which has not been reported earlier for any polysaccharide networks. The magnitude of negative normal stress increases with applied strain and can exceed that of the shear stress at large strain. Rheological results fitted with a constitutive model that considers both stretching and bending of chains indicate that nonlinearity is likely related to the stretching of the chains between the crosslink junctions. The results provide an improved understanding of the deformation mechanism of ionically crosslinked alginate gel and the results will be important in developing synthetic extracellular matrix (ECM) from these materials.
Correlation between ultrasonic nonlinearity and elastic nonlinearity in heat-treated aluminum alloy
Energy Technology Data Exchange (ETDEWEB)
Kim, Jong Beom; Jhang, Kyung Young [Hanyang University, Seoul (Korea, Republic of)
2017-04-15
The nonlinear ultrasonic technique is a potential nondestructive method to evaluate material degradation, in which the ultrasonic nonlinearity parameter is usually measured. The ultrasonic nonlinearity parameter is defined by the elastic nonlinearity coefficients of the nonlinear Hooke’s equation. Therefore, even though the ultrasonic nonlinearity parameter is not equal to the elastic nonlinearity parameter, they have a close relationship. However, there has been no experimental verification of the relationship between the ultrasonic and elastic nonlinearity parameters. In this study, the relationship is experimentally verified for a heat-treated aluminum alloy. Specimens of the aluminum alloy were heat-treated at 300°C for different periods of time (0, 1, 2, 5, 10, 20, and 50 h). The relative ultrasonic nonlinearity parameter of each specimen was then measured, and the elastic nonlinearity parameter was determined by fitting the stress-strain curve obtained from a tensile test to the 5th-order-polynomial nonlinear Hooke’s equation. The results showed that the variations in these parameters were in good agreement with each other.
Athermal nonlinear elastic constants of amorphous solids.
Karmakar, Smarajit; Lerner, Edan; Procaccia, Itamar
2010-08-01
We derive expressions for the lowest nonlinear elastic constants of amorphous solids in athermal conditions (up to third order), in terms of the interaction potential between the constituent particles. The effect of these constants cannot be disregarded when amorphous solids undergo instabilities such as plastic flow or fracture in the athermal limit; in such situations the elastic response increases enormously, bringing the system much beyond the linear regime. We demonstrate that the existing theory of thermal nonlinear elastic constants converges to our expressions in the limit of zero temperature. We motivate the calculation by discussing two examples in which these nonlinear elastic constants play a crucial role in the context of elastoplasticity of amorphous solids. The first example is the plasticity-induced memory that is typical to amorphous solids (giving rise to the Bauschinger effect). The second example is how to predict the next plastic event from knowledge of the nonlinear elastic constants. Using the results of our calculations we derive a simple differential equation for the lowest eigenvalue of the Hessian matrix in the external strain near mechanical instabilities; this equation predicts how the eigenvalue vanishes at the mechanical instability and the value of the strain where the mechanical instability takes place.
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 ...
Eaton, D F
1991-07-19
The current state of materials development in nonlinear optics is summarized, and the promise of these materials is critically evaluated. Properties and important materials constants of current commercial materials and of new, promising, inorganic and organic molecular and polymeric materials with potential in second- and third-order nonlinear optical applications are presented.
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...
Decoupling Nonclassical Nonlinear Behavior of Elastic Wave Types
Remillieux, Marcel C.; Guyer, Robert A.; Payan, Cédric; Ulrich, T. J.
2016-03-01
In this Letter, the tensorial nature of the nonequilibrium dynamics in nonlinear mesoscopic elastic materials is evidenced via multimode resonance experiments. In these experiments the dynamic response, including the spatial variations of velocities and strains, is carefully monitored while the sample is vibrated in a purely longitudinal or a purely torsional mode. By analogy with the fact that such experiments can decouple the elements of the linear elastic tensor, we demonstrate that the parameters quantifying the nonequilibrium dynamics of the material differ substantially for a compressional wave and for a shear wave. This result could lead to further understanding of the nonlinear mechanical phenomena that arise in natural systems as well as to the design and engineering of nonlinear acoustic metamaterials.
Nonlinear elastic inclusions in isotropic solids
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.
Organic nonlinear optical materials
Umegaki, S.
1987-01-01
Recently, it became clear that organic compounds with delocalized pi electrons show a great nonlinear optical response. Especially, secondary nonlinear optical constants of more than 2 digits were often seen in the molecular level compared to the existing inorganic crystals such as LiNbO3. The crystallization was continuously tried. Organic nonlinear optical crystals have a new future as materials for use in the applied physics such as photomodulation, optical frequency transformation, opto-bistabilization, and phase conjugation optics. Organic nonlinear optical materials, e.g., urea, O2NC6H4NH2, I, II, are reviewed with 50 references.
Non-linear theory of elasticity
Lurie, AI
2012-01-01
This book examines in detail the Theory of Elasticity which is a branch of the mechanics of a deformable solid. Special emphasis is placed on the investigation of the process of deformation within the framework of the generally accepted model of a medium which, in this case, is an elastic body. A comprehensive list of Appendices is included providing a wealth of references for more in depth coverage. The work will provide both a stimulus for future research in this field as well as useful reference material for many years to come.
Nonlinear mechanics of hyper elastic polyurethane furniture foams
Directory of Open Access Journals (Sweden)
Jerzy Smardzewski
2008-07-01
Full Text Available Upholstered furniture intended to provide better sleep and rest, especially furniture for disabled persons, require careful design of elastic spring systems. In the majority of cases, when designing new articles, both furniture designers and manufacturers rely on long-term experience and craftsman’s intuition. On the other hand, the accumulated interdisciplinary knowledge of modern medical laboratories as well as furniture certification offices indicate that it is necessary to carry out investigations related to the mechanical properties of raw materials used to manufacture furniture and to conduct virtual modelling of the phenomena connected with the contact of the human body with the elastic base. The aim of this study was to determine the elastic properties of hyper-plastic polyurethane foams applied in furniture industry, to elaborate mathematical models of these materials on the basis of non-linear Mooney-Rivlin models and to conduct a non-linear numerical analysis of contact strains in a deformed seat made of polyurethane foam. The results of the experiments revealed that the mechanical properties of polyurethanefoams are described properly by the Mooney-Rivlin model. Knowing the mechanical properties of these foams, it is possible to create freely complex furniture elastic systems. The state of strains in the contact of the human body with foam depends on the friction between these bodies. Therefore, in practice, it is advisable to design seatsystems resulting in minimal frictions between the user’s clothes and the furniture seat.
Homogenization method for elastic materials
Directory of Open Access Journals (Sweden)
Seifrt F.
2007-11-01
Full Text Available In the paper we study the homogenization method and its potential for research of some phenomenons connected with periodic elastic materials. This method will be applied on partial differential equations that describe the deformation of a periodic composite material. The next part of the paper will deal with applications of the homogenization method. The importance of the method will be discussed more detailed for the exploration of the so called bandgaps. Bandgap is a phenomenon which may appear during vibrations of some periodically heterogeneous materials. This phenomenon is not only observable during vibrations for the aforementioned materials, but we may also observe similar effects by propagation of electromagnetic waves of heterogeneous dielectric medias.
The elastic pendulum: A nonlinear paradigm
Breitenberger, Ernst; Mueller, Robert D.
1981-06-01
A pendulum with an elastic instead of an inextensible suspension is the simplest realization of an autonomous, conservative, oscillatory system of several degrees of freedom with nonlinear coupling; it can also have an internal 1:2 resonance. A fairly complete study of this system at and near resonance is here undertaken by means of the ''slow-fluctuation'' approximation which consists in developing the x2y-type interaction into a trigonometric polynomial and keeping only the term with the slowest frequency. Extensive computations showed that up to moderately large amplitudes the approximate solutions were virtually as accurate as numerical integrations of the exact equations of motion. The slow-fluctuation equations of motion can be completely integrated by quadratures. Explicit solutions for amplitudes and phases are given in terms of elliptic functions, and can be linked to initial conditions. There exist two branches of purely periodic, harmonic, constant-amplitude motions which are orbitally stable but Liapunov unstable. The pure suspension motion is Liapunov unstable and remains orbitally stable only up to and including a critical amplitude; the standard ''method of variational equations'' leads to a slightly different stability criterion but is shown to be unreliable. In the dynamical neighborhood of the unstable pure suspension mode are motions which convert to it after infinite time. When a motion has an amplitude modulation minimum at or near zero, a phase reversal of the suspension takes place which is shown to be an artefact inherent in the description in terms of amplitudes and phases. In addition there is in the pendulum (but not in the exactly soluble system having the slow-fluctuation Hamiltonian) a fast phase transient which vitiates the slow-fluctuation technique for a few periods around the suspension amplitude minimum; this is the only restriction on the method. An appendix outlines formal isomorphisms between the elastic pendulum and the
Institute of Scientific and Technical Information of China (English)
吴艺
2011-01-01
In order to provide more references for UPFs users and break the application limitation of ANSYS in seismic area for the lack of nonlinear viscous-elastic material model, the nonlinear viucous-elastic material model was developed in ANSYS with UPFs and verified by example, and the procedure of developing material model with UPFs of ANSYS is demonstrated deliberately. Additionally, the problems encountered during this developing and their solutions and technical experiences were presented. Verifying shows that the development of nonlinear viscous-elastic material model with UPFs is successful; the solutions of programming problems and techniques are effective; the nonlinear viscous-elastic material model developed by this paper can extend application of ANSYS in geotechni-cal and structural seismic engineering; the successful UPFs experiences can be referenced by UPFs users.%UPFs是大型通用商业有限元软件ANSYS强大的二次开发工具，为了ANSYS用户在使用UPFs进行二次开发时有更多的参考并弥补ANSYS因无非线性黏弹性本构模型而在抗震工程应用中严重受限的不足,在ANSYS中用UPFs对非线性黏弹性本构模型进行二次开发和算例验证，结合实例详细演示了用ANSYS的UPFs进行本构模型二次开发的具体过程，并对应用UPFs时所碰到的实际问题及解决办法和经验技巧进行了总结。算例验证结果表明，所开发的本构模型可使ANSYS更好地应用于岩土和结构抗震工程当中，开发的技术和经验可供UPFs用户参考。
Extremal Overall Elastic Response of Polycrystalline Materials
DEFF Research Database (Denmark)
Bendsøe, Martin P; Lipton, Robert
1996-01-01
Polycrystalline materials comprised of grains obtained froma single anisotropic material are considered in the frameworkof linear elasticity. No assumptions on the symmetry of thepolycrystal are made. We subject the material to independentexternal strain and stress fields with prescribed mean...
GLOBAL ATTRACTOR FOR THE NONLINEAR STRAIN WAVES IN ELASTIC WAVEGUIDES
Institute of Scientific and Technical Information of China (English)
戴正德; 杜先云
2001-01-01
In this paper the authors consider the initial boundary value problems of the generalized nonlinear strain waves in elastic waveguides and prove the existence of global attractors and thefiniteness of the Hausdorff and the fractal dimensions of the attractors.
Nonlinear surface waves in soft, weakly compressible elastic media.
Zabolotskaya, Evgenia A; Ilinskii, Yurii A; Hamilton, Mark F
2007-04-01
Nonlinear surface waves in soft, weakly compressible elastic media are investigated theoretically, with a focus on propagation in tissue-like media. The model is obtained as a limiting case of the theory developed by Zabolotskaya [J. Acoust. Soc. Am. 91, 2569-2575 (1992)] for nonlinear surface waves in arbitrary isotropic elastic media, and it is consistent with the results obtained by Fu and Devenish [Q. J. Mech. Appl. Math. 49, 65-80 (1996)] for incompressible isotropic elastic media. In particular, the quadratic nonlinearity is found to be independent of the third-order elastic constants of the medium, and it is inversely proportional to the shear modulus. The Gol'dberg number characterizing the degree of waveform distortion due to quadratic nonlinearity is proportional to the square root of the shear modulus and inversely proportional to the shear viscosity. Simulations are presented for propagation in tissue-like media.
Scalerandi, Marco; Agostini, Valentina; Delsanto, Pier Paolo; Van Den Abeele, Koen; Johnson, Paul A
2003-06-01
Recent studies show that a broad category of materials share "nonclassical" nonlinear elastic behavior much different from "classical" (Landau-type) nonlinearity. Manifestations of "nonclassical" nonlinearity include stress-strain hysteresis and discrete memory in quasistatic experiments, and specific dependencies of the harmonic amplitudes with respect to the drive amplitude in dynamic wave experiments, which are remarkably different from those predicted by the classical theory. These materials have in common soft "bond" elements, where the elastic nonlinearity originates, contained in hard matter (e.g., a rock sample). The bond system normally comprises a small fraction of the total material volume, and can be localized (e.g., a crack in a solid) or distributed, as in a rock. In this paper a model is presented in which the soft elements are treated as hysteretic or reversible elastic units connected in a one-dimensional lattice to elastic elements (grains), which make up the hard matrix. Calculations are performed in the framework of the local interaction simulation approach (LISA). Experimental observations are well predicted by the model, which is now ready both for basic investigations about the physical origins of nonlinear elasticity and for applications to material damage diagnostics.
Uniform Stability of Damped Nonlinear Vibrations of an Elastic String
Indian Academy of Sciences (India)
Ganesh C Gorain; Sujit K Bose
2003-11-01
Here we are concerned about uniform stability of damped nonlinear transverse vibrations of an elastic string fixed at its two ends. The vibrations governed by nonlinear integro-differential equation of Kirchoff type, is shown to possess energy uniformly bounded by exponentially decaying function of time. The result is achieved by considering an energy-like Lyapunov functional for the system.
An elastic mechanics model and computation method for geotechnical material
Institute of Scientific and Technical Information of China (English)
Zheng Yingren; Gao Hong; Zheng Lushi
2010-01-01
Internal friction characteristic is one of the basic properties of geotechnical materials and it exists in mechanical elements all the time.However,until now internal friction is only considered in limit analysis and plastic mechanics but not included in elastic theory for rocks and soils.We consider that internal friction exists in both elastic state and plastic state of geotechnical materials,so the mechanical unit of friction material is constituted.Based on study results of soil tests,the paper also proposes that cohesion takes effect first and internal friction works gradually with the increment of deformation.By assuming that the friction coefficient is proportional to the strain,the internal friction is computed.At last,by imitating the linear elastic mechanics,the nonlinear elastic mechanics model of friction material is established,where the shear modulus G is not a constant.The new model and the traditional elastic model are used simultaneously to analyze an elastic foundation.The results indicate that the displacements computed by the new model are less than those from the traditional method,which agrees with the fact and shows that the mechanical units of friction material are suitable for geotechnical material.
Non-linear theory of elasticity and optimal design
Ratner, LW
2003-01-01
In order to select an optimal structure among possible similar structures, one needs to compare the elastic behavior of the structures. A new criterion that describes elastic behavior is the rate of change of deformation. Using this criterion, the safe dimensions of a structure that are required by the stress distributed in a structure can be calculated. The new non-linear theory of elasticity allows one to determine the actual individual limit of elasticity/failure of a structure using a simple non-destructive method of measurement of deformation on the model of a structure while presently it
Fluid flow of incompressible viscous fluid through a non-linear elastic tube
Energy Technology Data Exchange (ETDEWEB)
Lazopoulos, A.; Tsangaris, S. [National Technical University of Athens, Fluids Section, School of Mechanical Engineering, Zografou, Athens (Greece)
2008-11-15
The study of viscous flow in tubes with deformable walls is of specific interest in industry and biomedical technology and in understanding various phenomena in medicine and biology (atherosclerosis, artery replacement by a graft, etc) as well. The present work describes numerically the behavior of a viscous incompressible fluid through a tube with a non-linear elastic membrane insertion. The membrane insertion in the solid tube is composed by non-linear elastic material, following Fung's (Biomechanics: mechanical properties of living tissue, 2nd edn. Springer, New York, 1993) type strain-energy density function. The fluid is described through a Navier-Stokes code coupled with a system of non linear equations, governing the interaction with the membrane deformation. The objective of this work is the study of the deformation of a non-linear elastic membrane insertion interacting with the fluid flow. The case of the linear elastic material of the membrane is also considered. These two cases are compared and the results are evaluated. The advantages of considering membrane nonlinear elastic material are well established. Finally, the case of an axisymmetric elastic tube with variable stiffness along the tube and membrane sections is studied, trying to substitute the solid tube with a membrane of high stiffness, exhibiting more realistic response. (orig.)
Nonlinear acoustics and honeycomb materials
Thompson, D. O.
2012-05-01
The scope of research activity that Bruce Thompson embraced was very large. In this talk three different research topics that the author shared with Bruce are reviewed. They represent Bruce's introduction to NDE and include nonlinear acoustics, nondestructive measurements of adhesive bond strengths in honeycomb panels, and studies of flexural wave dispersion in honeycomb materials. In the first of these, four harmonics of a 30 Mhz finite amplitude wave were measured for both fused silica and aluminum single crystals with varying lengths and amounts of cold work using a capacity microphone with heterodyne receiver with a flat frequency response from 30 to 250 Mhz. The results for fused silica with no dislocation structure could be described by a model due to Fubini, originally developed for gases, that depends upon only the second and third order elastic constants and not the fourth and higher order constants. The same was not true for the aluminum with dislocation structures. These results raised some questions about models for harmonic generation in materials with dislocations. In the second topic, experiments were made to determine the adhesive bond strengths of honeycomb panels using the vibrational response of the panels (Chladni figures). The results showed that both the damping characteristics of panel vibrations as a whole and velocity of propagation of elastic waves that travel along the surface and sample the bondline can be correlated with destructively determined bond strengths. Finally, the phase velocity of flexural waves traveling along a 1-inch honeycomb sandwich panel was determined from 170 Hz to 50 Khz, ranging from 2.2×104 cm/sec at the low end to 1.18×105 cm/sec at 40 Khz. The dispersion arises from the finite thickness of the panel and agreed with the results of continuum models for the honeycomb. Above 40 Khz, this was not the case. The paper concludes with a tribute to Bruce for his many wonderful contributions and lessons beyond his
Miniaci, M.; Gliozzi, A. S.; Morvan, B.; Krushynska, A.; Bosia, F.; Scalerandi, M.; Pugno, N. M.
2017-05-01
The appearance of nonlinear effects in elastic wave propagation is one of the most reliable and sensitive indicators of the onset of material damage. However, these effects are usually very small and can be detected only using cumbersome digital signal processing techniques. Here, we propose and experimentally validate an alternative approach, using the filtering and focusing properties of phononic crystals to naturally select and reflect the higher harmonics generated by nonlinear effects, enabling the realization of time-reversal procedures for nonlinear elastic source detection. The proposed device demonstrates its potential as an efficient, compact, portable, passive apparatus for nonlinear elastic wave sensing and damage detection.
Nonlinear coda wave analysis of hysteretic elastic behavior in strongly scattering media
Ouarabi, M. Ait; Boubenider, F.; Gliozzi, A. S.; Scalerandi, M.
2016-10-01
Strongly scattering elastic media, such as consolidated granular materials, respond to ultrasonic pulse excitations with a long response signal with peculiar properties. The portion of the signal at late times, termed coda, is due to multiple scattering. It contains information about the elastic properties of the material, and it has been proven to be very sensitive to small variations in the modulus. Here we propose a technique based on a nonlinear analysis of the coda of a signal, which might be applied to quantify the nonlinear elastic response in consolidated granular media exhibiting a hysteretic elastic behavior. The method proposed allows for an intrinsic definition of the reference signal which is normally needed for applying coda-based methods.
Fast and slow dynamics in a nonlinear elastic bar excited by longitudinal vibrations
Favrie, Nicolas; Payan, Cédric
2014-01-01
Heterogeneous materials, such as rocks and concrete, have a complex dynamics including hysteresis, nonlinear elasticity and viscoelasticity. It is very sensitive to microstructural changes and damage. The goal of this paper is to propose a physical model describing the longitudinal vibrations of this class of material, and to develop a numerical strategy for solving the evolution equations. The theory relies on the coupling between two processes with radically-different time scales: a fast process at the frequency of the excitation, governed by nonlinear elasticity and viscoelasticity; a slow process, governed by the evolution of defects. The evolution equations are written as a nonlinear hyperbolic system with relaxation. A time-domain numerical scheme is developed, based on a splitting strategy. The numerical simulations show qualitative agreement with the features observed experimentally by Dynamic Acousto-Elastic Testing.
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...... spring-mass chains with non-linear inclusions. The presented analytical and numerical results suggest that the effective material properties can easily be altered by establishing finite amplitude HF standing waves in the non-linear regions of the chain....
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.
NONLINEAR WAVES AND PERIODIC SOLUTION IN FINITE DEFORMATION ELASTIC ROD
Institute of Scientific and Technical Information of China (English)
Liu Zhifang; Zhang Shanyuan
2006-01-01
A nonlinear wave equation of elastic rod taking account of finite deformation, transverse inertia and shearing strain is derived by means of the Hamilton principle in this paper. Nonlinear wave equation and truncated nonlinear wave equation are solved by the Jacobi elliptic sine function expansion and the third kind of Jacobi elliptic function expansion method. The exact periodic solutions of these nonlinear equations are obtained, including the shock wave solution and the solitary wave solution. The necessary condition of exact periodic solutions, shock solution and solitary solution existence is discussed.
Nonlinear elasticity in rocks: A comprehensive three-dimensional description
Lott, Martin; Remillieux, Marcel C.; Garnier, Vincent; Le Bas, Pierre-Yves; Ulrich, T. J.; Payan, Cédric
2017-07-01
We study theoretically and experimentally the mechanisms of nonlinear and nonequilibrium dynamics in geomaterials through dynamic acoustoelasticity testing. In the proposed theoretical formulation, the classical theory of nonlinear elasticity is extended to include the effects of conditioning. This formulation is adapted to the context of dynamic acoustoelasticity testing in which a low-frequency "pump" wave induces a strain field in the sample and modulates the propagation of a high-frequency "probe" wave. Experiments are conducted to validate the formulation in a long thin bar of Berea sandstone. Several configurations of the pump and probe are examined: the pump successively consists of the first longitudinal and first torsional mode of vibration of the sample while the probe is successively based on (pressure) P and (shear) S waves. The theoretical predictions reproduce many features of the elastic response observed experimentally, in particular, the coupling between nonlinear and nonequilibrium dynamics and the three-dimensional effects resulting from the tensorial nature of elasticity.
Theory of nonlinear elastic behavior in rock
Energy Technology Data Exchange (ETDEWEB)
McCall, K.R.
1993-04-01
We study plane wave propagation in an isotropic, homogeneous solid with cubic and quartic anharmonicity. Attenuation is introduced through use of a retarded displacement response. We develop a Green function technique to exhibit the solution for the displacement field as a systematic hierarchy in the nonlinear parameters. This solution is applied to three problems: propagation from monochromatic and broadband sources, and the shape of nonlinear stress curves.
Theory of nonlinear elastic behavior in rock
Energy Technology Data Exchange (ETDEWEB)
McCall, K.R.
1993-01-01
We study plane wave propagation in an isotropic, homogeneous solid with cubic and quartic anharmonicity. Attenuation is introduced through use of a retarded displacement response. We develop a Green function technique to exhibit the solution for the displacement field as a systematic hierarchy in the nonlinear parameters. This solution is applied to three problems: propagation from monochromatic and broadband sources, and the shape of nonlinear stress curves.
Measurement of elastic nonlinearity of soft solid with transient elastography
Catheline, S.; Gennisson, J.-L.; Fink, M.
2003-12-01
Transient elastography is a powerful tool to measure the speed of low-frequency shear waves in soft tissues and thus to determine the second-order elastic modulus μ (or the Young's modulus E). In this paper, it is shown how transient elastography can also achieve the measurement of the nonlinear third-order elastic moduli of an Agar-gelatin-based phantom. This method requires speed measurements of polarized elastic waves measured in a statically stressed isotropic medium. A static uniaxial stress induces a hexagonal anisotropy (transverse isotropy) in solids. In the special case of uniaxially stressed isotropic media, the anisotropy is not caused by linear elastic coefficients but by the third-order nonlinear elastic constants, and the medium recovers its isotropic properties as soon as the uniaxial stress disappears. It has already been shown how transient elastography can measure the elastic (second-order) moduli in a media with transverse isotropy such as muscles. Consequently this method, based on the measurement of the speed variations of a low-frequency (50-Hz) polarized shear strain waves as a function of the applied stress, allows one to measure the Landau moduli A, B, C that completely describe the third-order nonlinearity. The several orders of magnitude found among these three constants can be justified from the theoretical expression of the internal energy.
Measurement of elastic nonlinearity of soft solid with transient elastography.
Catheline, S; Gennisson, J L; Fink, M
2003-12-01
Transient elastography is a powerful tool to measure the speed of low-frequency shear waves in soft tissues and thus to determine the second-order elastic modulus mu (or the Young's modulus E). In this paper, it is shown how transient elastography can also achieve the measurement of the nonlinear third-order elastic moduli of an Agar-gelatin-based phantom. This method requires speed measurements of polarized elastic waves measured in a statically stressed isotropic medium. A static uniaxial stress induces a hexagonal anisotropy (transverse isotropy) in solids. In the special case of uniaxially stressed isotropic media, the anisotropy is not caused by linear elastic coefficients but by the third-order nonlinear elastic constants, and the medium recovers its isotropic properties as soon as the uniaxial stress disappears. It has already been shown how transient elastography can measure the elastic (second-order) moduli in a media with transverse isotropy such as muscles. Consequently this method, based on the measurement of the speed variations of a low-frequency (50-Hz) polarized shear strain waves as a function of the applied stress, allows one to measure the Landau moduli A, B, C that completely describe the third-order nonlinearity. The several orders of magnitude found among these three constants can be justified from the theoretical expression of the internal energy.
Nonlinear Waves in an Inhomogeneous Fluid Filled Elastic Tube
Institute of Scientific and Technical Information of China (English)
DUAN Wen-Shan
2004-01-01
In a thin-walled, homogeneous, straight, long, circular, and incompressible fluid filled elastic tube, small but finite long wavelength nonlinear waves can be describe by a KdV (Korteweg de Vries) equation, while the carrier wave modulations are described by a nonlinear Schrodinger equation (NLSE). However if the elastic tube is slowly inhomogeneous, then it is found, in this paper, that the carrier wave modulations are described by an NLSE-like equation. There are soliton-like solutions for them, but the stability and instability regions for this soliton-like waves will change,depending on what kind of inhomogeneity the tube has.
Nonlinear analysis of flexible plates lying on elastic foundation
Directory of Open Access Journals (Sweden)
Trushin Sergey
2017-01-01
Full Text Available This article describes numerical procedures for analysis of flexible rectangular plates lying on elastic foundation. Computing models are based on the theory of plates with account of transverse shear deformations. The finite difference energy method of discretization is used for reducing the initial continuum problem to finite dimensional problem. Solution procedures for nonlinear problem are based on Newton-Raphson method. This theory of plates and numerical methods have been used for investigation of nonlinear behavior of flexible plates on elastic foundation with different properties.
NONLINEAR RESPONSES OF A FLUID-CONVEYING PIPE EMBEDDED IN NONLINEAR ELASTIC FOUNDATIONS
Institute of Scientific and Technical Information of China (English)
Qin Qian; Lin Wang; Qiao Ni
2008-01-01
The nonlinear responses of planar motions of a fluid-conveying pipe embedded in nonlinear elastic foundations are investigated via the differential quadrature method diseretization (DQMD) of the governing partial differential equation. For the analytical model, the effect of the nonlinear elastic foundation is modeled by a nonlinear restraining force. By using an iterative algorithm, a set of ordinary differential dynamical equations derived from the equation of motion of the system are solved numerically and then the bifurcations are analyzed. The numerical results, in which the existence of chaos is demonstrated, are presented in the form of phase portraits of the oscillations. The intermittency transition to chaos has been found to arise.
Extremal Overall Elastic Response of Polycrystalline Materials
DEFF Research Database (Denmark)
Bendsøe, Martin P; Lipton, Robert
1997-01-01
Polycrystalline materials comprised of grains obtained from a single anisotropic material are considered in the framework of linear elasticity. No assumptions on the symmetry of the polycrystal are made. We subject the material to independent external strain and stress fields with prescribed mean...
A nonlinear constitutive model for magnetostrictive materials
Institute of Scientific and Technical Information of China (English)
Xin'en Liu; Xiaojing Zheng
2005-01-01
A general nonlinear constitutive model is proposed for magnetostrictive materials, based on the important physical fact that a nonlinear part of the elastic strain produced by a pre-stress is related to the magnetic domain rotation or movement and is responsible for the change of the maximum magnetostrictive strain with the pre-stress. To avoid the complicity of determining the tensor function describing the nonlinear elastic strain part, this paper proposes a simplified model by means of linearizing the nonlinear function.For the convenience of engineering applications, the expressions of the 3-D (bulk), 2-D (film) and 1-D (rod) models are, respectively, given for an isotropic material and their applicable ranges are also discussed. By comparison with the experimental data of a Terfenol-D rod, it is found that the proposed model can accurately predict the magnetostrictive strain curves in low, moderate and high magnetic field regions for various compressive pre-stress levels. The numerical simulation further illustrates that, for either magnetostrictive rods or thin films, the proposed model can effectively describe the effects of the pre-stress or residual stress on the magnetization and magnetostrictive strain curves, while none of the known models can capture all of them. Therefore, the proposed model enjoys higher precision and wider applicability than the previous models, especially in the region of the high field.
Scattering of time-harmonic elastic waves by an elastic inclusion with quadratic nonlinearity.
Tang, Guangxin; Jacobs, Laurence J; Qu, Jianmin
2012-04-01
This paper considers the scattering of a plane, time-harmonic wave by an inclusion with heterogeneous nonlinear elastic properties embedded in an otherwise homogeneous linear elastic solid. When the inclusion and the surrounding matrix are both isotropic, the scattered second harmonic fields are obtained in terms of the Green's function of the surrounding medium. It is found that the second harmonic fields depend on two independent acoustic nonlinearity parameters related to the third order elastic constants. Solutions are also obtained when these two acoustic nonlinearity parameters are given as spatially random functions. An inverse procedure is developed to obtain the statistics of these two random functions from the measured forward and backscattered second harmonic fields.
Multiwave nonlinear couplings in elastic structures
Directory of Open Access Journals (Sweden)
2006-01-01
Full Text Available This short contribution considers the essentials of nonlinear wave properties in typical mechanical systems such as an infinite straight bar, a circular ring, and a flat plate. It is found that nonlinear resonance is experienced in all the systems exhibiting continuous and discrete spectra, respectively. Multiwave interactions and the stability of coupled modes with respect to small perturbations are discussed. The emphasis is placed on mechanical phenomena, for example, stress amplification, although some analogies with some nonlinear optical systems are also obvious. The nonlinear resonance coupling in a plate within the Kirchhoff-Love approximation is selected as a two-dimensional example exhibiting a rich range of resonant wave phenomena. This is originally examined by use of Whitham's averaged Lagrangian method. In particular, the existence of three basic resonant triads between longitudinal, shear, and bending modes is shown. Some of these necessarily enter cascade wave processes related to the instability of some mode components of the triad under small perturbations.
Nonlinear elastic behavior of rocks revealed by dynamic acousto-elastic testing
Shokouhi, Parisa; Riviere, Jacques; Guyer, Robert; Johnson, Paul
2017-04-01
Nonlinear elastic behavior of rocks is studied at the laboratory scale with the goal of illuminating observations at the Earth scale, for instance during strong ground motion and earthquake slip processes. A technique called Dynamic Acousto-Elastic Testing (DAET) is used to extract the nonlinear elastic response of disparate rocks (sandstone, granite and soapstone). DAET is the dynamic analogous to standard (quasi-static) acousto-elastic testing. It consists in measuring speed of sound with high-frequency low amplitude pulses (MHz range) across the sample while it is dynamically loaded with a low frequency, large amplitude resonance (kHz range). This particular configuration provides the instantaneous elastic response over a full dynamic cycle and reveals unprecedented details: instantaneous softening, tension/compression asymmetry as well as hysteretic behaviors. The strain-induced modulation of ultrasonic pulse velocities ('fast dynamics') is analyzed to extract nonlinearity parameters. A projection method is used to extract the harmonic content and a careful comparison of the fast dynamics response is made. In order to characterize the rate of elastic recovery ('slow dynamics'), we continue to monitor the ultrasonic wave velocity for about 30 minutes after the low-frequency resonance is turned off. In addition, the frequency, pressure and humidity dependences of the nonlinear parameters are reported for a subset of samples. We find that the nonlinear components can be clustered into two categories, which suggests that two main mechanisms are at play. The first one, related to the second harmonic, is likely related to the opening/closing of microstructural features such as cracks and grain/grain contacts. In contrast, the second mechanism is related to all other nonlinear parameters (transient softening, hysteresis area and higher order harmonics) and may arise from shearing mechanisms at grain interfaces.
A nonlinear theory for elastic plates with application to characterizing paper properties
M. W. Johnson; Thomas J. Urbanik
1984-03-01
A theory of thin plates which is physically as well as kinematically nonlinear is, developed and used to characterize elastic material behavior for arbitrary stretching and bending deformations. It is developed from a few clearly defined assumptions and uses a unique treatment of strain energy. An effective strain concept is introduced to simplify the theory to a...
Vibration Analysis of Timoshenko Beams on a Nonlinear Elastic Foundation
Institute of Scientific and Technical Information of China (English)
MO Yihua; OU Li; ZHONG Hongzhi
2009-01-01
The vibrations of beams on a nonlinear elastic foundation were analyzed considering the effects of transverse shear deformation and the rotational inertia of beams. A weak form quadrature element method (QEM) is used for the vibration analysis. The fundamental frequencies of beams are presented for various slenderness ratios and nonlinear foundation parameters for both slender and short beams. The results for slender beams compare well with finite element results. The analysis shows that the transverse shear de-formation and the nonlinear foundation parameter significantly affect the fundamental frequency of the beams.
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.
PARADOX SOLUTION ON ELASTIC WEDGE DISSIMILAR MATERIALS
Institute of Scientific and Technical Information of China (English)
姚伟岸; 张兵茹
2003-01-01
According to the Hellinger-Reissner variational principle and introducing proper transformation of variables, the problem on elastic wedge dissimilar materials can be led to Hamiltonian system, so the solution of the problem can be got by employing the separation of variables method and symplectic eigenfunction expansion under symplectic space, which consists of original variables and their dual variables. The eigenvalue - 1 is a special one of all symplectic eigenvalue for Hamiltonian system in polar coordinate. In general, the eigenvalue - is a single eigenvalue, and the classical solution of an elastic wedge dissimilar materials subjected to a unit concentrated couple at the vertex is got directly by solving the eigenfunction vector for eigenvalue - 1 . But the eigenvalue - 1 becomes a double eigenvalue when the vertex angles and modulus of the materials satisfy certain definite relationships and the classical solution for the stress distribution becomes infinite at this moment, that is, the paradox should occur. Here the Jordan form eigenfunction vector for eigenvalue - 1 exists, and solution of the paradox on elastic wedge dissimilar materials subjected to a unit concentrated couple at the vertex is obtained directly by solving this special Jordan form eigenfunction. The result shows again that the solutions of the special paradox on elastic wedge in the classical theory of elasticity are just Jordan form solutions in symplectic space under Hamiltonian system.
Elastic reflection based waveform inversion with a nonlinear approach
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.
A nonlinear approach of elastic reflection waveform inversion
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.
Nonlinear optics and organic materials
Energy Technology Data Exchange (ETDEWEB)
Shen, Y.R.
1994-07-01
We shall consider an interesting topic relating nonlinear optics and organic materials: how nonlinear optics can be used to study organic materials. One of the main differences between linear and nonlinear responses of a medium to incoming radiation is in their symmetries. It leads to the possibility that some properties of the medium could be more sensitively probed by nonlinear, rather than linear, optical means, or vise versa. A well-known example is that some vibrational modes of a medium could be Raman-active but infrared-inactive, and would be more readily observed by Raman scattering, which is a two-photon transition process. In this paper, we shall discuss, with the help of three examples, how we can use second harmonic generation (SHG) and sum frequency generation (SFG) to obtain unique information about a material. We shall focus on thin films, surfaces, and interfaces.
Controlling elastic wave with isotropic transformation materials
Chang, Zheng; Hu, Gengkai; Tao, Ran; Wang, Yue
2010-01-01
There are great demands to design functional devices with isotropic materials, however the transformation method usually leads to anisotropic material parameters difficult to be realized in practice. In this letter, we derive the isotropic transformed material parameters in case of elastodynamic under local conformal transformation, they are subsequently used to design a beam bender, a four-beam antenna and an approximate carpet cloak for elastic wave with isotropic materials, the simulation results validate the derived transformed material parameters. The obtained materials are isotropic and greatly simplify subsequent experimental implementation.
Küchler, Sebastian; Meurer, Thomas; Jacobs, Laurence J; Qu, Jianmin
2009-03-01
This study investigates two-dimensional wave propagation in an elastic half-space with quadratic nonlinearity. The problem is formulated as a hyperbolic system of conservation laws, which is solved numerically using a semi-discrete central scheme. These numerical results are then analyzed in the frequency domain to interpret the nonlinear effects, specifically the excitation of higher-order harmonics. To quantify and compare the nonlinearity of different materials, a new parameter is introduced, which is similar to the acoustic nonlinearity parameter beta for one-dimensional longitudinal waves. By using this new parameter, it is found that the nonlinear effects of a material depend on the point of observation in the half-space, both the angle and the distance to the excitation source. Furthermore it is illustrated that the third-order elastic constants have a linear effect on the acoustic nonlinearity of a material.
Nonlinear Forced Vibration Analysis for Thin Rectangular Plate on Nonlinear Elastic Foundation
Directory of Open Access Journals (Sweden)
Zhong Zhengqiang
2013-02-01
Full Text Available Nonlinear forced vibration is analyzed for thin rectangular plate with four free edges on nonlinear elastic foundation. Based on Hamilton variation principle, equations of nonlinear vibration motion for thin rectangular plate under harmonic loads on nonlinear elastic foundation are established. In the case of four free edges, viable expressions of trial functions for this specification are proposed, satisfying all boundary conditions. Then, equations are transformed to a system of nonlinear algebraic equations by using Galerkin method and are solved by using harmonic balance method. In the analysis of numerical computations, the effect on the amplitude-frequency characteristic curve due to change of the structural parameters of plate, parameters of foundation and parameters of excitation force are discussed.
Stress-enhanced Gelation: A Dynamic Nonlinearity of Elasticity
Yao, Norman Y.; Broedersz, Chase P.; Depken, Martin; Becker, Daniel J.; Pollak, Martin R.; MacKintosh, Frederick C.; Weitz, David A.
2013-01-01
A hallmark of biopolymer networks is their sensitivity to stress, reflected by pronounced nonlinear elastic stiffening. Here, we demonstrate a distinct dynamical nonlinearity in biopolymer networks consisting of F-actin cross-linked by α-actinin-4. Applied stress delays the onset of relaxation and flow, markedly enhancing gelation and extending the regime of solid-like behavior to much lower frequencies. We show that this macroscopic network response can be accounted for at the single molecule level by the increased binding affinity of the cross-linker under load, characteristic of catch-bond-like behavior. PMID:23383843
On nonlinear thermo-electro-elasticity.
Mehnert, Markus; Hossain, Mokarram; Steinmann, Paul
2016-06-01
Electro-active polymers (EAPs) for large actuations are nowadays well-known and promising candidates for producing sensors, actuators and generators. In general, polymeric materials are sensitive to differential temperature histories. During experimental characterizations of EAPs under electro-mechanically coupled loads, it is difficult to maintain constant temperature not only because of an external differential temperature history but also because of the changes in internal temperature caused by the application of high electric loads. In this contribution, a thermo-electro-mechanically coupled constitutive framework is proposed based on the total energy approach. Departing from relevant laws of thermodynamics, thermodynamically consistent constitutive equations are formulated. To demonstrate the performance of the proposed thermo-electro-mechanically coupled framework, a frequently used non-homogeneous boundary-value problem, i.e. the extension and inflation of a cylindrical tube, is solved analytically. The results illustrate the influence of various thermo-electro-mechanical couplings.
Whittam, A J
2001-01-01
susceptibility from 26 pm/V (same film without octadecanoic acid) to 40 pm/V. This increase in the second-order susceptibility occurred even though the amount of NLO-active dye was effectively diluted by the addition of the inactive octadecanoic acid. The wavelength of the absorption maximum ranged from 346-440 nm and there was direct correlation between the susceptibilities and the transparency of the films at the harmonic wavelength. Hemicyanine dyes were synthesised, with the general formulae: - (a) C sub 1 sub 8 H sub 3 sub 7 -A sup + -[CH=CH-C sub 6 H sub 4] sub x -N(CH sub 3) sub 2 I (b) C sub 1 sub 8 H sub 3 sub 7 -A sup + -[CH=CH] sub y -C sub 6 H sub 4 -N(CH sub 3) sub 2 I where A sup + is a pyridinium or isoquinolinium acceptor, and x = 1 or 2, and y = 1 or 2. The optically nonlinear dyes were investigated via the Langmuir-Blodgett (LB) technique. The dyes all produced isotherm data, with molecular areas of 22-60 A sup 2 per molecule, which are consistent with the cross-sectional areas of the chromo...
Free-vibration acoustic resonance of a nonlinear elastic bar
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.
Elasticity in Amorphous Solids: Nonlinear or Piecewise Linear?
Dubey, Awadhesh K; Procaccia, Itamar; Shor, Carmel A B Z; Singh, Murari
2016-02-26
Quasistatic strain-controlled measurements of stress versus strain curves in macroscopic amorphous solids result in a nonlinear-looking curve that ends up either in mechanical collapse or in a steady state with fluctuations around a mean stress that remains constant with increasing strain. It is therefore very tempting to fit a nonlinear expansion of the stress in powers of the strain. We argue here that at low temperatures the meaning of such an expansion needs to be reconsidered. We point out the enormous difference between quenched and annealed averages of the stress versus strain curves and propose that a useful description of the mechanical response is given by a stress (or strain) -dependent shear modulus for which a theoretical evaluation exists. The elastic response is piecewise linear rather than nonlinear.
Nonlinear effect of elastic vortexlike motion on the dynamic stress state of solids
Shilko, Evgeny V.; Grinyaev, Yurii V.; Popov, Mikhail V.; Popov, Valentin L.; Psakhie, Sergey G.
2016-05-01
We present a theoretical analysis of the dynamic stress-strain state of regions in a solid body that are involved in a collective elastic vortexlike motion. It is shown that the initiation of elastic vortexlike motion in the material is accompanied by the appearance of dilatancy and equivalent strain, the magnitudes of which are proportional to the square of the ratio of linear velocity on the periphery of the elastic vortex to the velocity of longitudinal elastic waves (P wave). Under conditions of dynamic loading the described dynamic effects are able to initiate inelastic deformation or destruction of the material at loading speeds of a few percent of the P -wave speed. The obtained analytical estimates suggest that dynamic nonlinear strains can make a significant contribution in a number of widely studied nonlinear dynamic phenomena in solids. Among them are the effect of acoustic (dynamic) dilatancy in solids and granular media, which leads to the generation of longitudinal elastic waves by transverse waves [V. Tournat et al., Phys. Rev. Lett. 92, 085502 (2004), 10.1103/PhysRevLett.92.085502] and the formation of an array of intense "hot spots" (reminiscent of shear-induced hydrodynamic instabilities in fluids) in adiabatic shear bands [P. R. Guduru et al., Phys. Rev. E 64, 036128 (2001), 10.1103/PhysRevE.64.036128].
Bauer-Gogonea, S.; Camacho-Gonzalez, F.; Schwödiauer, R.; Ploss, B.; Bauer, S.
2007-09-01
Nonlinearities in ferroelectret polymer foam capacitors arise from voltage-dependent thickness changes. Such thickness changes are caused by the converse piezoelectric and electrostrictive effects in these soft materials. The authors show that the higher harmonics of the current response during application of a sinusoidal voltage to ferroelectret capacitors provide information on the elastic and electromechanical properties of the foam. The authors demonstrate the potential of this versatile measurement technique by investigating the temperature dependence of the piezoelectric response and by monitoring the changes in the elastic and electromechanical properties during inflation of cellular polypropylene.
Nonlinear dispersion effects in elastic plates: numerical modelling and validation
Kijanka, Piotr; Radecki, Rafal; Packo, Pawel; Staszewski, Wieslaw J.; Uhl, Tadeusz; Leamy, Michael J.
2017-04-01
Nonlinear features of elastic wave propagation have attracted significant attention recently. The particular interest herein relates to complex wave-structure interactions, which provide potential new opportunities for feature discovery and identification in a variety of applications. Due to significant complexity associated with wave propagation in nonlinear media, numerical modeling and simulations are employed to facilitate design and development of new measurement, monitoring and characterization systems. However, since very high spatio- temporal accuracy of numerical models is required, it is critical to evaluate their spectral properties and tune discretization parameters for compromise between accuracy and calculation time. Moreover, nonlinearities in structures give rise to various effects that are not present in linear systems, e.g. wave-wave interactions, higher harmonics generation, synchronism and | recently reported | shifts to dispersion characteristics. This paper discusses local computational model based on a new HYBRID approach for wave propagation in nonlinear media. The proposed approach combines advantages of the Local Interaction Simulation Approach (LISA) and Cellular Automata for Elastodynamics (CAFE). The methods are investigated in the context of their accuracy for predicting nonlinear wavefields, in particular shifts to dispersion characteristics for finite amplitude waves and secondary wavefields. The results are validated against Finite Element (FE) calculations for guided waves in copper plate. Critical modes i.e., modes determining accuracy of a model at given excitation frequency - are identified and guidelines for numerical model parameters are proposed.
Hmiel, A.; Winey, J. M.; Gupta, Y. M.; Desjarlais, M. P.
2016-05-01
Accurate theoretical calculations of the nonlinear elastic response of strong solids (e.g., diamond) constitute a fundamental and important scientific need for understanding the response of such materials and for exploring the potential synthesis and design of novel solids. However, without corresponding experimental data, it is difficult to select between predictions from different theoretical methods. Recently the complete set of third-order elastic constants (TOECs) for diamond was determined experimentally, and the validity of various theoretical approaches to calculate the same may now be assessed. We report on the use of density functional theory (DFT) methods to calculate the six third-order elastic constants of diamond. Two different approaches based on homogeneous deformations were used: (1) an energy-strain fitting approach using a prescribed set of deformations, and (2) a longitudinal stress-strain fitting approach using uniaxial compressive strains along the [100], [110], and [111] directions, together with calculated pressure derivatives of the second-order elastic constants. The latter approach provides a direct comparison to the experimental results. The TOECs calculated using the energy-strain approach differ significantly from the measured TOECs. In contrast, calculations using the longitudinal stress-uniaxial strain approach show good agreement with the measured TOECs and match the experimental values significantly better than the TOECs reported in previous theoretical studies. Our results on diamond have demonstrated that, with proper analysis procedures, first-principles calculations can indeed be used to accurately calculate the TOECs of strong solids.
Non-linear waves in heterogeneous elastic rods via homogenization
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.
Soft, elastic, water-repellent materials
Coux, Martin; Clanet, Christophe; Quéré, David
2017-06-01
Small hydrophobic textures at solid surfaces provide water repellency, a situation whose detailed properties critically depend on the geometry of textures. Depending on their size, density, and shape, water slip, rain repellency, or antifogging can be achieved. Here, we discuss how the use of soft, elastic materials allows us to tune reversibly the texture density by stretching or relaxing the materials, which is found to impact water adhesion and rebounds. In addition, solid deformations can also be exploited to largely vary the shape of Wenzel drops, a consequence of the strong pinning of water in this state.
Rayleigh scattering and nonlinear inversion of elastic waves
Energy Technology Data Exchange (ETDEWEB)
Gritto, R.
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 {minus}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{sub p}R = 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.
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.
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.
MACROSCOPIC STRAIN POTENTIALS IN NONLINEAR POROUS MATERIALS
Institute of Scientific and Technical Information of China (English)
刘熠; 黄筑平
2003-01-01
By taking a hollow sphere as a representative volume element (RVE), the macroscopic strain potentials of porous materials with power-law incompressible matrix are studied in this paper.According to the principles of the minimum potential energy in nonlinear elasticity and the variational procedure, static admissible stress fields and kinematic admissible displacement fields are constructed,and hence the upper and the lower bounds of the macroscopic strain potential are obtained. The bounds given in the present paper differ so slightly that they both provide perfect approximations of the exact strain potential of the studied porous materials. It is also found that the upper bound proposed by previous authors is much higher than the present one, and the lower bounds given by Cocks is much lower. Moreover, the present calculation is also compared with the variational lower bound of Ponte Castafneda for statistically isotropic porous materials. Finally, the validity of the hollow spherical RVE for the studied nonlinear porous material is discussed by the difference between the present numerical results and the Cocks bound.
Geometric Structure-Preserving Discretization Schemes for Nonlinear Elasticity
2015-08-13
conditions. 15. SUBJECT TERMS geometric theory for nonlinear elasticity, discrete exterior calculus 16. SECURITY CLASSIFICATION OF: 17. LIMITATION...associated Laplacian. We use the general theory for approximation of Hilbert complexes and the finite element exterior calculus and introduce some stable mixed...Ωk(B)→ Ωk+1(B) be the standard exterior derivative given by (dβ)I0⋯Ik = k ∑ i=0 (−1)iβI0⋯Îi⋯Ik, Ii , where the hat over an index implies the
GEOMETRICAL NONLINEAR WAVES IN FINITE DEFORMATION ELASTIC RODS
Institute of Scientific and Technical Information of China (English)
GUO Jian-gang; ZHOU Li-jun; ZHANG Shan-yuan
2005-01-01
By using Hamilton-type variation principle in non-conservation system, the nonlinear equation of wave motion of a elastic thin rod was derived according to Lagrange description of finite deformation theory. The dissipation caused due to viscous effect and the dispersion introduced by transverse inertia were taken into consideration so that steady traveling wave solution can be obtained. Using multi-scale method the nonlinear equation is reduced to a KdV-Burgers equation which corresponds with saddle-spiral heteroclinic orbit on phase plane. Its solution is called the oscillating-solitary wave or saddle-spiral shock wave.If viscous effect or transverse inertia is neglected, the equation is degraded to classical KdV or Burgers equation. The former implies a propagating solitary wave with homoclinic on phase plane, the latter means shock wave and heteroclinic orbit.
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
New nonlinear optical materials based on ferrofluids
Energy Technology Data Exchange (ETDEWEB)
Huang, J P [Department of Physics, Fudan University, Shanghai 200433 (China); Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz (Germany); Institute of Theoretical Physics, Chinese University of Hong Kong, Shatin, NT, Hong Kong (China); Yu, K W [Department of Physics, Chinese University of Hong Kong, Shatin, NT, Hong Kong (China); Institute of Theoretical Physics, Chinese University of Hong Kong, Shatin, NT, Hong Kong (China)
2006-01-01
We exploit theoretically a new class of magneto-controlled nonlinear optical material based on ferrofluids in which ferromagnetic nanoparticles are coated with a nonmagnetic metallic nonlinear shell. Such an optical material can have anisotropic nonlinear optical properties and a giant enhancement of nonlinearity, as well as an attractive figure of merit.
Duc, Nguyen Dinh; Quan, Tran Quoc
2012-09-01
An analytical investigation into the nonlinear response of thick functionally graded double-curved shallow panels resting on elastic foundations and subjected to thermal and thermomechanical loads is presented. Young's modulus and Poisson's ratio are both graded in the thickness direction according to a simple power-law distribution in terms of volume fractions of constituents. All formulations are based on the classical shell theory with account of geometrical nonlinearity and initial geometrical imperfection in the cases of Pasternak-type elastic foundations. By applying the Galerkin method, explicit relations for the thermal load-deflection curves of simply supported curved panels are found. The effects of material and geometrical properties and foundation stiffness on the buckling and postbuckling load-carrying capacity of the panels in thermal environments are analyzed and discussed.
Dumbbell formation for elastic capsules in nonlinear extensional Stokes flows
Dimitrakopoulos, P.
2017-06-01
Cross-slot and four-roll-mill microdevices are commonly used for particle manipulation and characterization owing to the stagnation-point flow at the device center. Because of the solid boundaries, these devices may generate extensional Stokes flows where the velocity is a nonlinear function of position associated with a decreased pressure at the particle edges and an increased pressure at the particle middle. Our computational investigation shows that in this class of Stokes flows, an elastic capsule made of a strain-hardening membrane develops two distinct steady-state conformations at strong flows, i.e., an elongated weak dumbbell shape with rounded edges at low flow nonlinearity and a laterally extended dumbbell shape at high flow nonlinearity. These effects are more pronounced for the less strain-hardening capsules which develop a flat extended middle where the two sides of the membrane approach each other. The strong stability properties of the strain-hardening capsules (owing to the development of strong membrane tensions) contrast significantly with the behavior of droplets in these nonlinear flows which are unable to achieve highly deformed steady-state dumbbell shapes owing to their constant surface tension.
Lamb Wave Technique for Ultrasonic Nonlinear Characterization in Elastic Plates
Energy Technology Data Exchange (ETDEWEB)
Lee, Tae Hun; Kim, Chung Seok; Jhang, Kyung Young [Hanyang University, Seoul (Korea, Republic of)
2010-10-15
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
Nonlinear mechanics of surface growth for cylindrical and spherical elastic bodies
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.
Scaling Laws for the Response of Nonlinear Elastic Media with Implications for Cell Mechanics
Shokef, Yair; Safran, Samuel A.
2012-04-01
We show how strain stiffening affects the elastic response to internal forces, caused either by material defects and inhomogeneities or by active forces that molecular motors generate in living cells. For a spherical force dipole in a material with a strongly nonlinear strain energy density, strains change sign with distance, indicating that, even around a contractile inclusion or molecular motor, there is radial compression; it is only at a long distance that one recovers the linear response in which the medium is radially stretched. Scaling laws with irrational exponents relate the far-field renormalized strain to the near-field strain applied by the inclusion or active force.
Surface Waves in Almost Incompressible Elastic Materials
Virta, Kristoffer
2013-01-01
A recent study shows that the classical theory concerning accuracy and points per wavelength is not valid for surface waves in almost incompressible elastic materials. The grid size must instead be proportional to $(\\frac{\\mu}{\\lambda})^{(1/p)}$ to achieve a certain accuracy. Here $p$ is the order of accuracy the scheme and $\\mu$ and $\\lambda$ are the Lame parameters. This accuracy requirement becomes very restrictive close to the incompressible limit where $\\frac{\\mu}{\\lambda} \\ll 1$, especially for low order methods. We present results concerning how to choose the number of grid points for 4th, 6th and 8th order summation-by-parts finite difference schemes. The result is applied to Lambs problem in an almost incompressible material.
Graphene - a rather ordinary nonlinear optical material
khurgin, Jacob B
2014-01-01
An analytical expression for the nonlinear refractive index of graphene has been derived and used to obtain the performance metrics of third order nonlinear devices using graphene as a nonlinear medium. None of the metrics is found to be superior to the existing nonlinear optical materials.
Korman, M. S.; Duong, D. V.; Kalsbeck, A. E.
2015-10-01
significant curvature when the soil particle velocity is relatively higher. An oscillator with hysteresis modeled by a distribution of parallel spring elements each with a different threshold slip condition seems to describe fairly linear backbone curve behavior [W. D. Iwan, Transactions of the ASME, J. of Applied Mech., 33,(1966), 893-900], while a single bilinear hysteresis element describes the backbone curvature results in the experiments reported here [T. K. Caughey, Transactions of the ASME, J. of Applied Mech., 27, (1960), 640-643]. When "off target" resonances have a different backbone curvature than "on the mine" backbone curves, then false alarms may be eliminated due to resonances from the natural soil layering. See [R. A. Guyer, J. TenCate, and P. Johnson, "Hysteresis and the Dynamic Elasticity of Consolidated Granular Materials," Phys. Rev. Lett., 82, 16 (1999), 3280-3283] for recent models of nonlinear mesoscopic behavior.
Nonlinear elastic model for compacted clay concrete interface
Institute of Scientific and Technical Information of China (English)
R. R. SHAKIR; Jungao ZHU
2009-01-01
In this paper, a nonlinear elastic model was developed to simulate the behavior of compacted clay concrete interface (CCCI) based on the principle of transition mechanism failure (TMF). A number of simple shear tests were conducted on CCCI to demonstrate different failure mechanisms; i.e., sliding failure and deformation failure. The clay soil used in the test was collected from the "Shuang Jang Kou" earth rockfill dam project. It was found that the behavior of the interface depends on the critical water contents by which two failure mechanisms can be recognized. Mathematical relations were proposed between the shear at failure and water content in addition to the transition mechanism indicator.The mathematical relations were then incorporated into the interface model. The performance of the model is verified with the experimental results. The verification shows that the proposed model is capable of predicting the interface shear stress versus the total shear displacement very well.
Variational principles for nonlinear piezoelectric materials
Energy Technology Data Exchange (ETDEWEB)
Rodriguez-Ramos, R.; Guinovart-Diaz, R. [Universidad de la Habana, Facultad de Matematica y Computacion, Vedado, Habana (Cuba); Pobedria, B.E. [Moscow State University M. V. Lomonosov, Composites Department, Moscow (Russian Federation); Padilla, P. [Universidad Nacional Autonoma de Mexico, Instituto de Investigaciones en Matematicas Aplicadas y en Sistemas (IIMAS), Cd. Universitaria, Mexico D.F. (Mexico); Bravo-Castillero, J. [Universidad de la Habana, Facultad de Matematica y Computacion, Vedado, Habana (Cuba); Campus Estado de Mexico. Division de Arquitectura e Ingenieria, Instituto Tecnologico de Estudios Superiores de Monterrey, Atizapan de Zaragoza, Estado de Mexico (Mexico); Maugin, G.A. [Universite Pierre et Marie Curie. Case 162, UMR 7607 CNRS, Laboratoire de Modelisation en Mecanique, Paris Cedex 05 (France)
2004-12-01
In the present paper, we consider the behavior of nonlinear piezoelectric materials by generalization for this case of the Hashin-Shtrikman variational principles. The new general formulation used here differs from others, because, it gives the possibility to evaluate the upper and lower Hashin-Shtrikman bounds for specific physical nonlinearities of piezoelectric materials. Geometrical nonlinearities are not considered. (orig.)
Modeling of the wave transmission properties of large arteries using nonlinear elastic tubes.
Pythoud, F; Stergiopulos, N; Meister, J J
1994-11-01
We propose a new, simple way of constructing elastic tubes which can be used to model the nonlinear elastic properties of large arteries. The tube models are constructed from a silicon elastomer (Sylgard 184, Dow Corning), which exhibits a nonlinear behavior with increased stiffness at high strains. Tests conducted on different tube models showed that, with the proper choice of geometric parameters, the elastic properties, in terms of area-pressure relation and compliance, can be similar to that of real arteries.
Geometric and material nonlinear analysis of tensegrity structures
Institute of Scientific and Technical Information of China (English)
Hoang Chi Tran; Jaehong Lee
2011-01-01
A numerical method is presented for the large deflection in elastic analysis of tensegrity structures including both geometric and material nonlinearities.The geometric nonlinearity is considered based on both total Lagrangian and updated Lagrangian formulations,while the material nonlinearity is treated through elastoplastic stressstrain relationship.The nonlinear equilibrium equations are solved using an incremental-iterative scheme in conjunction with the modified Newton-Raphson method.A computer program is developed to predict the mechanical responses of tensegrity systems under tensile,compressive and flexural loadings.Numerical results obtained are compared with those reported in the literature to demonstrate the accuracy and efficiency of the proposed program.The flexural behavior of the double layer quadruplex tensegrity grid is sufficiently good for lightweight large-span structural applications.On the other hand,its bending strength capacity is not sensitive to the self-stress level.
Finsler geometry of nonlinear elastic solids with internal structure
Clayton, J. D.
2017-02-01
Concepts from Finsler differential geometry are applied towards a theory of deformable continua with internal structure. The general theory accounts for finite deformation, nonlinear elasticity, and various kinds of structural features in a solid body. The general kinematic structure of the theory includes macroscopic and microscopic displacement fields-i.e., a multiscale representation-whereby the latter are represented mathematically by the director vector of pseudo-Finsler space, not necessarily of unit magnitude. A physically appropriate fundamental (metric) tensor is introduced, leading to affine and nonlinear connections. A deformation gradient tensor is defined via differentiation of the macroscopic motion field, and another metric indicative of strain in the body is a function of this gradient. A total energy functional of strain, referential microscopic coordinates, and horizontal covariant derivatives of the latter is introduced. Variational methods are applied to derive Euler-Lagrange equations and Neumann boundary conditions. The theory is shown to encompass existing continuum physics models such as micromorphic, micropolar, strain gradient, phase field, and conventional nonlinear elasticity models, and it can reduce to such models when certain assumptions on geometry, kinematics, and energy functionals are imposed. The theory is applied to analyze two physical problems in crystalline solids: shear localization/fracture in a two-dimensional body and cavitation in a spherical body. In these examples, a conformal or Weyl-type transformation of the fundamental tensor enables a description of dilatation associated, respectively, with cleavage surface roughness and nucleation of voids or vacancies. For the shear localization problem, the Finsler theory is able to accurately reproduce the surface energy of Griffith's fracture mechanics, and it predicts dilatation-induced toughening as observed in experiments on brittle crystals. For the cavitation problem
Duc, Nguyen Dinh; Quan, Tran Quoc
2013-11-01
The nonlinear response of buckling and posbuckling of imperfect thin functionally graded doubly curved thin shallow shells resting on elastic foundations and subjected to some mechanical loads is investigated analytically. The elastic moduli of materials, Young's modulus, and Poisson ratio are all graded in the shell thickness direction according to a simple power-law in terms of volume fractions of constituents. All formulations are based on the classical theory of shells with account of geometrical nonlinearity, an initial geometrical imperfection, and a Pasternak-type elastic foundation. By employing the Galerkin method, explicit relations for the load-deflection curves of simply supported doubly curved shallow FGM shells are determined. The effects of material and geometrical properties, foundation stiffness, and imperfection of shells on the buckling and postbuckling loadcarrying capacity of spherical and cylindrical shallow FGM shells are analyzed and discussed.
Advances in nonlinear optical materials and devices
Byer, Robert L.
1991-01-01
The recent progress in the application of nonlinear techniques to extend the frequency of laser sources has come from the joint progress in laser sources and in nonlinear materials. A brief summary of the progress in diode pumped solid state lasers is followed by an overview of progress in nonlinear frequency extension by harmonic generation and parametric processes. Improved nonlinear materials including bulk crystals, quasiphasematched interactions, guided wave devices, and quantum well intersubband studies are discussed with the idea of identifying areas of future progress in nonlinear materials and devices.
Analysis of nonlinear elastic behavior in miniature pneumatic artificial muscles
Hocking, Erica G.; Wereley, Norman M.
2013-01-01
Pneumatic artificial muscles (PAMs) are well known for their excellent actuator characteristics, including high specific work, specific power, and power density. Recent research has focused on miniaturizing this pneumatic actuator technology in order to develop PAMs for use in small-scale mechanical systems, such as those found in robotic or aerospace applications. The first step in implementing these miniature PAMs was to design and characterize the actuator. To that end, this study presents the manufacturing process, experimental characterization, and analytical modeling of PAMs with millimeter-scale diameters. A fabrication method was developed to consistently produce low-cost, high performance, miniature PAMs using commercially available materials. The quasi-static behavior of these PAMs was determined through experimentation on a single actuator with an active length of 39.16 mm (1.54 in) and a diameter of 4.13 mm (0.1625 in). Testing revealed the PAM’s full evolution of force with displacement for operating pressures ranging from 207 to 552 kPa (30-80 psi in 10 psi increments), as well as the blocked force and free contraction at each pressure. Three key nonlinear phenomena were observed: nonlinear PAM stiffness, hysteresis of the force versus displacement response for a given pressure, and a pressure deadband. To address the analysis of the nonlinear response of these miniature PAMs, a nonlinear stress versus strain model, a hysteresis model, and a pressure bias are introduced into a previously developed force balance analysis. Parameters of these nonlinear model refinements are identified from the measured force versus displacement data. This improved nonlinear force balance model is shown to capture the full actuation behavior of the miniature PAMs at each operating pressure and reconstruct miniature PAM response with much more accuracy than previously possible.
Cellular Automata Model for Elastic Solid Material
Institute of Scientific and Technical Information of China (English)
DONG Yin-Feng; ZHANG Guang-Cai; XU Ai-Guo; GAN Yan-Biao
2013-01-01
The Cellular Automaton (CA) modeling and simulation of solid dynamics is a long-standing difficult problem.In this paper we present a new two-dimensional CA model for solid dynamics.In this model the solid body is represented by a set of white and black particles alternatively positioned in the x-and y-directions.The force acting on each particle is represented by the linear summation of relative displacements of the nearest-neighboring particles.The key technique in this new model is the construction of eight coefficient matrices.Theoretical and numerical analyses show that the present model can be mathematically described by a conservative system.So,it works for elastic material.In the continuum limit the CA model recovers the well-known Navier equation.The coefficient matrices are related to the shear module and Poisson ratio of the material body.Compared with previous CA model for solid body,this model realizes the natural coupling of deformations in the x-and y-directions.Consequently,the wave phenomena related to the Poisson ratio effects are successfully recovered.This work advances significantly the CA modeling and simulation in the field of computational solid dynamics.
Elastic and thermal expansion asymmetry in dense molecular materials.
Burg, Joseph A; Dauskardt, Reinhold H
2016-09-01
The elastic modulus and coefficient of thermal expansion are fundamental properties of elastically stiff molecular materials and are assumed to be the same (symmetric) under both tension and compression loading. We show that molecular materials can have a marked asymmetric elastic modulus and coefficient of thermal expansion that are inherently related to terminal chemical groups that limit molecular network connectivity. In compression, terminal groups sterically interact to stiffen the network, whereas in tension they interact less and disconnect the network. The existence of asymmetric elastic and thermal expansion behaviour has fundamental implications for computational approaches to molecular materials modelling and practical implications on the thermomechanical strains and associated elastic stresses. We develop a design space to control the degree of elastic asymmetry in molecular materials, a vital step towards understanding their integration into device technologies.
Elastic and thermal expansion asymmetry in dense molecular materials
Burg, Joseph A.; Dauskardt, Reinhold H.
2016-09-01
The elastic modulus and coefficient of thermal expansion are fundamental properties of elastically stiff molecular materials and are assumed to be the same (symmetric) under both tension and compression loading. We show that molecular materials can have a marked asymmetric elastic modulus and coefficient of thermal expansion that are inherently related to terminal chemical groups that limit molecular network connectivity. In compression, terminal groups sterically interact to stiffen the network, whereas in tension they interact less and disconnect the network. The existence of asymmetric elastic and thermal expansion behaviour has fundamental implications for computational approaches to molecular materials modelling and practical implications on the thermomechanical strains and associated elastic stresses. We develop a design space to control the degree of elastic asymmetry in molecular materials, a vital step towards understanding their integration into device technologies.
Ahmadpoor, Fatemeh; Wang, Peng; Huang, Rui; Sharma, Pradeep
2017-10-01
The study of statistical mechanics of thermal fluctuations of graphene-the prototypical two-dimensional material-is rendered rather complicated due to the necessity of accounting for geometric deformation nonlinearity. Unlike fluid membranes such as lipid bilayers, coupling of stretching and flexural modes in solid membranes like graphene leads to a highly anharmonic elastic Hamiltonian. Existing treatments draw heavily on analogies in the high-energy physics literature and are hard to extend or modify in the typical contexts that permeate materials, mechanics and some of the condensed matter physics literature. In this study, using a variational perturbation method, we present a ;mechanics-oriented; treatment of the thermal fluctuations of elastic sheets such as graphene and evaluate their effect on the effective bending stiffness at finite temperatures. In particular, we explore the size, pre-strain and temperature dependency of the out-of-plane fluctuations, and demonstrate how an elastic sheet becomes effectively stiffer at larger sizes. Our derivations provide a transparent approach that can be extended to include multi-field couplings and anisotropy for other 2D materials. To reconcile our analytical results with atomistic considerations, we also perform molecular dynamics simulations on graphene and contrast the obtained results and physical insights with those in the literature.
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.
The 'sixth sense' of ultrasound: probing nonlinear elasticity with acoustic radiation force.
Guzina, Bojan B; Dontsov, Egor V; Urban, Matthew W; Fatemi, Mostafa
2015-05-07
Prompted by a recent finding that the magnitude of the acoustic radiation force (ARF) in isotropic tissue-like solids depends linearly on a particular third-order modulus of elasticity-hereon denoted by C, this study investigates the possibility of estimating C from the amplitude of the ARF-generated shear waves. The featured coefficient of nonlinear elasticity, which captures the incipient nonlinear interaction between the volumetric and deviatoric modes of deformation, has so far received only a limited attention in the context of soft tissues due to the fact that the latter are often approximated as (i) fluid-like when considering ultrasound waves, and (ii) incompressible under static deformations. On establishing the analytical and computational platform for the proposed sensing methodology, the study proceeds with applying the prototype technique toward estimating via ARF the third-order modulus C in a series of tissue-mimicking phantoms. To help validate the concept and its implementation, the germane third-order modulus is independently estimated in each phantom via an established technique known as acoustoelasticity. The C-estimates obtained respectively via acoustoelasticity and the new theory of ARF show a significant degree of consistency. The key features of the new sensing methodology are that: (a) it requires no external deformation of a material other than that produced by the ARF, and (b) it estimates the nonlinear C-modulus locally, over the focal region of an ultrasound beam-where the shear waves are being generated.
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.
Nonlinear dynamic acousto-elasticity measurement by Rayleigh wave in concrete cover evaluation
Vu, Quang Anh; Garnier, Vincent; Payan, Cédric; Chaix, Jean-François; Lott, Martin; Eiras, Jesús N.
2015-10-01
This paper presents local non-destructive evaluation of concrete cover by using surface Rayleigh wave in nonlinear Dynamic Acousto-Elasticity (DAE) measurement. Dynamic non classical nonlinear elastic behavior like modulus decrease under applied stress and slow dynamic process has been observed in many varieties of solid, also in concrete. The measurements conducted in laboratory, consist in qualitative evaluation of concrete thermal damage. Nonlinear elastic parameters especially conditioning offset are analyzed for the cover concrete by Rayleigh wave. The results of DAE method show enhanced sensitivity when compared to velocity measurement. Afterward, this technique broadens measurements to the field.
Nonlinear visco-elastic finite element analysis of different porcelain veneers configuration.
Sorrentino, Roberto; Apicella, Davide; Riccio, Carlo; Gherlone, Enrico; Zarone, Fernando; Aversa, Raffaella; Garcia-Godoy, Franklin; Ferrari, Marco; Apicella, Antonio
2009-11-01
This study is aimed at evaluating the biomechanical behavior of feldspathic versus alumina porcelain veneers. A 3D numerical model of a maxillary central incisor, with the periodontal ligament (PDL) and the alveolar bone was generated. Such model was made up of four main volumes: dentin, enamel, cement layer and veneer. Incisors restored with alumina and feldspathic porcelain veneers were compared with a natural sound tooth (control). Enamel, cementum, cancellous and cortical bone were considered as isotropic elastic materials; on the contrary, the tubular structure of dentin was designed as elastic orthotropic. The nonlinear visco-elatic behavior of the PDL was considered. The veneer volumes were coupled with alumina and feldspathic porcelain mechanical properties. The adhesive layers were modeled in the FE environment using spring elements. A 50N load applied at 60 degrees angle with tooth longitudinal axis was applied and validated. Compressive stresses were concentrated on the external surface of the buccal side of the veneer close to the incisal margin; such phenomenon was more evident in the presence of alumina. Tensile stresses were negligible when compared to compressive ones. Alumina and feldspathic ceramic were characterized by a different biomechanical behavior in terms of elastic deformations and stress distributions. The ultimate strength of both materials was not overcome in the performed analysis.
Design of Organic Nonlinear Optical Materials
1990-06-01
This project deals with a new approach to designing organic nonlinear optical materials for second harmonic generation based on the use of hydrogen...patterns for even simple organic molecules. For organic nonlinear optical materials this dilemma means that even the most promising organic molecule may
Extreme non-linear elasticity and transformation optics
DEFF Research Database (Denmark)
Gersborg, Allan Roulund; Sigmund, Ole
2010-01-01
Transformation optics is a powerful concept for designing novel optical components such as high transmission waveguides and cloaking devices. The selection of specific transformations is a non-unique problem. Here we reveal that transformations which allow for all dielectric and broadband optical...... realizations correspond to minimizers of elastic energy potentials for extreme values of the mechanical Poisson's ratio ν . For TE (Hz) polarized light an incompressible transformation ν = 1/2 is ideal and for TM (E z) polarized light one should use a compressible transformation with negative Poissons's ratio...... ν = -1. For the TM polarization the mechanical analogy corresponds to a modified Liao functional known from the transformation optics literature. Finally, the analogy between ideal transformations and solid mechanical material models automates and broadens the concept of transformation optics...
Elastic properties of superconductors and materials with weakly correlated spins.
Binek, Christian
2017-07-07
It is shown that in the ergodic regime, the temperature dependence of Young's modulus is solely determined by the magnetic properties of a material. For the large class of materials with paramagnetic or diamagnetic response, simple functional forms of the temperature derivative of Young's modulus are derived and compared with experimental data and empirical results. Superconducting materials in the Meissner phase are ideal diamagnets. As such, they display remarkable elastic properties. Constant diamagnetic susceptibility gives rise to a temperature independent elastic modulus for ceramic and single crystalline superconductors alike. The thermodynamic approach established in this report, paves the way to tailor elastic material parameters through the design of magnetic properties.
Elastic constants of Transversely Isotropically Porous (TIP) materials
Energy Technology Data Exchange (ETDEWEB)
Tuchinskii, L.I.; Kalimova, N.L. [Institute of Problems of Materials Science, Kiev (Ukraine)
1994-11-01
The authors derive formulas describing the dependence of the elastic characteristics of multicapillary materials on the capillary porosity. The investigated materials are classified as transversely isotropic, and the anisotropy in their properties is the result of the directionality of the capillary pores. Analysis of the dependences obtained has shown that the elasticity moduli of these materials may be calculated using formulas suggested for reinforced materials, in which the elastic constants of the fibers are assumed to be equal to zero. The authors derive a relation between the Poisson`s ratios and the capillary porosity.
Finite element analysis of 3D elastic-plastic frictional contact problem for Cosserat materials
Zhang, S.; Xie, Z. Q.; Chen, B. S.; Zhang, H. W.
2013-06-01
The objective of this paper is to develop a finite element model for 3D elastic-plastic frictional contact problem of Cosserat materials. Because 3D elastic-plastic frictional contact problems belong to the unspecified boundary problems with nonlinearities in both material and geometric forms, a large number of calculations are needed to obtain numerical results with high accuracy. Based on the parametric variational principle and the corresponding quadratic programming method for numerical simulation of frictional contact problems, a finite element model is developed for 3D elastic-plastic frictional contact analysis of Cosserat materials. The problems are finally reduced to linear complementarity problems (LCP). Numerical examples show the feasibility and importance of the developed model for analyzing the contact problems of structures with materials which have micro-polar characteristics.
Chew, Huck Beng
2013-01-01
Determining the tractions along a surface or interface from measurement data in the far-fields of nonlinear materials is a challenging inverse problem which has significant engineering and nanoscience applications. Previously, a field projection method was established to identify the crack-tip cohesive zone constitutive relations in an isotropic elastic solid (Hong and Kim, 2003. J. Mech. Phys. Solids 51, 1267). In this paper, the field projection method is further generalized to extracting the tractions along interfaces bounded by nonlinear materials, both with and without pre-existing cracks. The new formulation is based on Maxwell-Betti's reciprocal theorem with a reciprocity gap associated with nonlinear materials. We express the unknown normal and shear tractions along the interface in terms of the Fourier series, and use specially constructed analytical auxiliary fields in the reciprocal theorem to extract the unknown Fourier coefficients from far-field data; the reciprocity gap in the formulation is iteratively determined with a set of numerical algorithms. Our detailed numerical experiments demonstrate that this nonlinear field projection method (NFPM) is well-suited for extracting the interfacial tractions from the far-field data of any nonlinear elastic or elasto-plastic material with known constitutive laws. Applications of the NFPM to experiments and atomistic simulations are discussed.
Analysis of Nonlinear Poro-Elastic and Poro-Visco-Elastic Models
Bociu, Lorena; Guidoboni, Giovanna; Sacco, Riccardo; Webster, Justin T.
2016-12-01
We consider the initial and boundary value problem for a system of partial differential equations describing the motion of a fluid-solid mixture under the assumption of full saturation. The ability of the fluid phase to flow within the solid skeleton is described by the permeability tensor, which is assumed here to be a multiple of the identity and to depend nonlinearly on the volumetric solid strain. In particular, we study the problem of the existence of weak solutions in bounded domains, accounting for non-zero volumetric and boundary forcing terms. We investigate the influence of viscoelasticity on the solution functional setting and on the regularity requirements for the forcing terms. The theoretical analysis shows that different time regularity requirements are needed for the volumetric source of linear momentum and the boundary source of traction depending on whether or not viscoelasticity is present. The theoretical results are further investigated via numerical simulations based on a novel dual mixed hybridized finite element discretization. When the data are sufficiently regular, the simulations show that the solutions satisfy the energy estimates predicted by the theoretical analysis. Interestingly, the simulations also show that, in the purely elastic case, the Darcy velocity and the related fluid energy might become unbounded if indeed the data do not enjoy the time regularity required by the theory.
Micromechanical study of elastic moduli of loose granular materials
Kruyt, N.P.; Agnolin, I.; Luding, S.; Rothenburg, L.
2010-01-01
In micromechanics of the elastic behaviour of granular materials, the macro-scale continuum elastic moduli are expressed in terms of micro-scale parameters, such as coordination number (the average number of contacts per particle) and interparticle contact stiffnesses in normal and tangential direct
Pure Azimuthal Shear of an Elastic Dielectric Material
Directory of Open Access Journals (Sweden)
Kuldeep Kumar
2010-03-01
Full Text Available The purpose of this research is to examine the effect of polarization for the problem of pure azimuthal shear of an elastic dielectric material. The present problem is investigated in context of finite deformation theory. In this paper, the author studied the effect of polarization on the stresses for Neoprene rubber and compare the results with elastic material (Mooney-Rivlin material graphically. Twisting of a rigid cylinder in an infinite elastic medium is considered as a special case in this research.
Coupling of elasticity to capillarity in soft aerated materials.
Ducloué, Lucie; Pitois, Olivier; Goyon, Julie; Chateau, Xavier; Ovarlez, Guillaume
2014-07-28
We study the elastic properties of soft solids containing air bubbles. Contrary to standard porous materials, the softness of the matrix allows for a coupling of the matrix elasticity to surface tension forces acting on the bubble surface. Thanks to appropriate experiments on model systems, we demonstrate how the elastic response of the soft porous solid is governed by two dimensionless parameters: the gas volume fraction and a capillary number comparing the elasticity of the matrix with the stiffness of the bubbles. Furthermore, we show that our experimental results are accurately predicted by computations of the shear modulus through a micro-mechanical approach.
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
This paper presents a theoretical model on the normal(head-on) collision between soft-spheres on the basis of elastic loading of the Hertz contact for compression process and a nonlinear plastic unloading for restitution one,in which the parameters all are determined in terms of the material and geometric ones of the spheres,and the behaviors of perfect elastic,inelastic,and perfect plastic collisions appeared in the classical mechanics are fully described once a value of coefficient of restitution is speci...
Semenova, I. V.; Belashov, A. V.; Garbuzov, F. E.; Samsonov, A. M.; Semenov, A. A.
2017-06-01
We demonstrate an alternative approach to determination of the third order elastic moduli of materials based on registration of nonlinear bulk strain waves in three basic structural waveguides (rod, plate and shell) and further calculation of the Murnaghan moduli from the recorded wave parameters via simple algebra. These elastic moduli are available in literature for a limited number of materials and are measured with considerable errors, that evidences a demand in novel approaches to their determination.
Identification of heterogeneous elastic material characteristics by virtual fields method
Sato, Yuya; Arikawa, Shuichi; Yoneyama, Satoru
2015-03-01
In this study, a method for identifying the elastic material characteristics of a heterogeneous material from measured displacements is proposed. The virtual fields method is employed for determining the elastic material characteristics. The solid propellant is considered as heterogeneous materials for the test subject. An equation representing the distribution of the material properties of the solid propellant is obtained by Fick's law, and the distribution is applied to the virtual fields method. The effectiveness of the proposed method is demonstrated by applying to displacement fields obtained using finite element analysis. Results show that the heterogeneous material properties can be obtained by the proposed method.
Pulse wave attenuation measurement by linear and nonlinear methods in nonlinearly elastic tubes.
Bertram, C D; Pythoud, F; Stergiopulos, N; Meister, J J
1999-04-01
Reasons for the continuing difficulty in making definitive measurements of pulse wave attenuation in elastic tubes and arteries in the presence of reflections are sought. The measurement techniques available were re-examined in elastic tubes mimicking the arterial compliance nonlinearity, under conditions of strong reflection. The pulse was of physiological shape, and two different pulse amplitudes in the physiological range were used. Measurements of pressure, flow-rate and diameter pulsation allowed the deployment of four of the classical linear methods of analysis. In addition, a method of separating the forward- and backward-travelling waves that does not require linearising assumptions was used, and the attenuation in the forward and reverse directions was calculated from the resulting waveforms. Overall, the results obtained here suggest that a fully satisfactory way of measuring arterial attenuation has yet to be devised. The classical linear methods all provided comparable attenuation estimates in terms of average value and degree of scatter across frequency. Increased scatter was generally found at the higher pulse amplitude. When the forward waveforms from the separation were similarly compared in terms of frequency components, the average value at energetic harmonics was similar to both the value indicated by the linear methods and the values predicted from linear theory on the basis of estimated viscous and viscoelastic parameter data. The backward waveforms indicated a physically unreasonable result, attributed as the expression for this technique of the same difficulties that normally manifest in scatter. Data in the literature suggesting that one of the classical methods, the three-point, systematically over-estimates attenuation were not supported, but it was confirmed that this method becomes prone to negative attenuation estimates at low harmonics as pulse amplitude increases. Although the goal of definitive attenuation measurement remains elusive
Modulational instability in periodic quadratic nonlinear materials
DEFF Research Database (Denmark)
Corney, Joel Frederick; Bang, Ole
2001-01-01
We investigate the modulational instability of plane waves in quadratic nonlinear materials with linear and nonlinear quasi-phase-matching gratings. Exact Floquet calculations, confirmed by numerical simulations, show that the periodicity can drastically alter the gain spectrum but never complete...
On the vibrations of a simply supported square plate on a weakly nonlinear elastic foundation
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 a
A thermodynamic approach to nonlinear ultrasonics for material state awareness and prognosis
Chillara, Vamshi Krishna
2016-01-01
We develop a thermodynamic framework for modeling nonlinear ultrasonic damage sensing and prognosis in materials undergoing progressive damage. The framework is based on the internal variable approach and relies on the construction of a pseudo-elastic strain energy function that captures the energetics associated with the damage progression. The pseudo-elastic strain energy function is composed of two energy functions - one that describes how a material stores energy in an elastic fashion and the other describes how material dissipates energy or stores it in an inelastic fashion. Experimental motivation for the choice of the above two functionals is discussed and some specific choices pertaining to damage progression during fatigue and creep are presented. The thermodynamic framework is employed to model the nonlinear response of material undergoing stress relaxation and creep-like degradation. For each of the above cases, evolution of the nonlinearity parameter with damage as well as with macroscopic measura...
Magneto-elastic oscillator: Modeling and analysis with nonlinear magnetic interaction
Kumar, K. Aravind; Ali, Shaikh Faruque; Arockiarajan, A.
2017-04-01
The magneto-elastically buckled beam is a classic example of a nonlinear oscillator that exhibits chaotic motions. This system serves as a model to analyze the motion of elastic structures in magnetic fields. The system follows a sixth order magneto-elastic potential and may have up to five static equilibrium positions. However, often the non-dimensional Duffing equation is used to approximate the system, with the coefficients being derived from experiments. In few other instances, numerical methods are used to evaluate the magnetic field values. These field values are then used to approximate the nonlinear magnetic restoring force. In this manuscript, we derive analytical closed form expressions for the magneto-elastic potential and the nonlinear restoring forces in the system. Such an analytical formulation would facilitate tracing the effect of change in a parameter, such as the magnet dimension, on the dynamics of the system. The model is derived assuming a single mode approximation, taking into account the effect of linear elastic and nonlinear magnetic forces. The developed model is then numerically simulated to show that it is accurate in capturing the system dynamics and bifurcation of equilibrium positions. The model is validated through experiments based on forced vibrations of the magneto-elastic oscillator. To gather further insights about the magneto-elastic oscillator, a parametric study has been conducted based on the field strength of the magnets and the distance between the magnets and the results are reported.
Frequency, pressure, and strain dependence of nonlinear elasticity in Berea Sandstone
Rivière, Jacques; Pimienta, Lucas; Scuderi, Marco; Candela, Thibault; Shokouhi, Parisa; Fortin, Jérôme; Schubnel, Alexandre; Marone, Chris; Johnson, Paul A.
2016-04-01
Acoustoelasticity measurements in a sample of room dry Berea sandstone are conducted at various loading frequencies to explore the transition between the quasi-static (f→0) and dynamic (few kilohertz) nonlinear elastic response. We carry out these measurements at multiple confining pressures and perform a multivariate regression analysis to quantify the dependence of the harmonic content on strain amplitude, frequency, and pressure. The modulus softening (equivalent to the harmonic at 0f) increases by a factor 2-3 over 3 orders of magnitude increase in frequency. Harmonics at 2f, 4f, and 6f exhibit similar behaviors. In contrast, the harmonic at 1f appears frequency independent. This result corroborates previous studies showing that the nonlinear elasticity of rocks can be described with a minimum of two physical mechanisms. This study provides quantitative data that describes the rate dependency of nonlinear elasticity. These findings can be used to improve theories relating the macroscopic elastic response to microstructural features.
Elasticity of transversely isotropic materials%"Elasticity of Transversely Isotropic Materials"一书评介
Institute of Scientific and Technical Information of China (English)
王敏中
2006-01-01
@@ 浙江大学土木系丁皓江教授和陈伟球教授及澳大利亚悉尼大学航空、机械与机电工程学院章亮炽教授的专著"Elasticity of Transversely Isotropic Materials"(ISBN:1-4020-4033-4),2006年由Springer公司出版,该书是加拿大著名力学家G.M.L.Gladwell 教授主编的丛书"Solid Mechanics and its Applications"的第126本,是我国大陆学者第一次在该丛书框架下出版专著.
2015-04-01
of dislocations in anisotropic crystals, Int. J. Eng. Sci. 5, 171–190 (1967). [92] A. Yavari and A. Goriely, Riemann -Cartan geometry of nonlinear...distributed point defects, Proc. R. Soc. Lond. A 468, 3902–3922 (2012). [94] A. Yavari and A. Goriely, Riemann -Cartan geometry of nonlinear disclination...ARL-RP-0522 ● APR 2015 US Army Research Laboratory Defects in Nonlinear Elastic Crystals: Differential Geometry , Finite
Development of Organic Nonlinear Optical Materials
1992-10-22
10 SOVRCE Of FUNO#NG NUM#E*S DM J .j PROGRAM PR0jECT TA5. ~ *0. I1I TITLE &Vila* So.Ivety ClaUMC400NJ Development of Organic NonLinear Optical Materials (U...0102-LF-014-6603 UNCLASSIFIED (U) AFOSR Contract: F4962040-C 0097 FINAL REPORT Development of Organic Nonlinear Optical Materials by J. Sounnk IL
The ‘sixth sense’ of ultrasound: probing nonlinear elasticity with acoustic radiation force
Guzina, Bojan B.; Dontsov, Egor V.; Urban, Matthew W.; Fatemi, Mostafa
2015-05-01
Prompted by a recent finding that the magnitude of the acoustic radiation force (ARF) in isotropic tissue-like solids depends linearly on a particular third-order modulus of elasticity—hereon denoted by C, this study investigates the possibility of estimating C from the amplitude of the ARF-generated shear waves. The featured coefficient of nonlinear elasticity, which captures the incipient nonlinear interaction between the volumetric and deviatoric modes of deformation, has so far received only a limited attention in the context of soft tissues due to the fact that the latter are often approximated as (i) fluid-like when considering ultrasound waves, and (ii) incompressible under static deformations. On establishing the analytical and computational platform for the proposed sensing methodology, the study proceeds with applying the prototype technique toward estimating via ARF the third-order modulus C in a series of tissue-mimicking phantoms. To help validate the concept and its implementation, the germane third-order modulus is independently estimated in each phantom via an established technique known as acoustoelasticity. The C-estimates obtained respectively via acoustoelasticity and the new theory of ARF show a significant degree of consistency. The key features of the new sensing methodology are that: (a) it requires no external deformation of a material other than that produced by the ARF, and (b) it estimates the nonlinear C-modulus locally, over the focal region of an ultrasound beam—where the shear waves are being generated.
Nonlinear material behaviour of spider silk yields robust webs.
Cranford, Steven W; Tarakanova, Anna; Pugno, Nicola M; Buehler, Markus J
2012-02-01
Natural materials are renowned for exquisite designs that optimize function, as illustrated by the elasticity of blood vessels, the toughness of bone and the protection offered by nacre. Particularly intriguing are spider silks, with studies having explored properties ranging from their protein sequence to the geometry of a web. This material system, highly adapted to meet a spider's many needs, has superior mechanical properties. In spite of much research into the molecular design underpinning the outstanding performance of silk fibres, and into the mechanical characteristics of web-like structures, it remains unknown how the mechanical characteristics of spider silk contribute to the integrity and performance of a spider web. Here we report web deformation experiments and simulations that identify the nonlinear response of silk threads to stress--involving softening at a yield point and substantial stiffening at large strain until failure--as being crucial to localize load-induced deformation and resulting in mechanically robust spider webs. Control simulations confirmed that a nonlinear stress response results in superior resistance to structural defects in the web compared to linear elastic or elastic-plastic (softening) material behaviour. We also show that under distributed loads, such as those exerted by wind, the stiff behaviour of silk under small deformation, before the yield point, is essential in maintaining the web's structural integrity. The superior performance of silk in webs is therefore not due merely to its exceptional ultimate strength and strain, but arises from the nonlinear response of silk threads to strain and their geometrical arrangement in a web.
Mesoscale Engineering of Nanocomposite Nonlinear Optical Materials
Energy Technology Data Exchange (ETDEWEB)
Afonso, C.N.; Feldman, L.C.; Gonella, F.; Haglund, R.F.; Luepke, G.; Magruder, R.H.; Mazzoldi, P.; Osborne, D.H.; Solis, J.; Zuhr, R.A.
1999-11-01
Complex nonlinear optical materials comprising elemental, compound or alloy quantum dots embedded in appropriate dielectric or semiconducting hosts may be suitable for deployment in photonic devices. Ion implantation, ion exchange followed by ion implantation, and pulsed laser deposition have ail been used to synthesize these materials. However, the correlation between the parameters of energetic-beam synthesis and the nonlinear optical properties is still very rudimentary when one starts to ask what is happening at nanoscale dimensions. Systems integration of complex nonlinear optical materials requires that the mesoscale materials science be well understood within the context of device structures. We discuss the effects of beam energy and energy density on quantum-dot size and spatial distribution, thermal conductivity, quantum-dot composition, crystallinity and defects - and, in turn, on the third-order optical susceptibility of the composite material. Examples from recent work in our laboratories are used to illustrate these effects.
Effective elastic moduli and interface effects of nano- crystalline materials
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
Many properties of nanocrystalline materials are associated with interface effects. Based on their microstructural features, the influence of interfaces on the effective elastic property of nanocrystalline materials is investigated. First, the Mori-Tanaka method is employed to determine the overall effective elastic moduli by considering a nanocrystalline material as a binary composite solid consisting of a crystal or inclusion phase with regular lattice connected by an amorphous-like interface or matrix phase. The effects of strain gradients are then examined on the effective elastic property by using the strain gradient theory to analyze a representative unit cell. Two interface mechanisms are elucidated that influence the effective stiffness and other mechanical properties of materials. One is the softening effect due to the distorted atomic structures and the increased atomic spacings in interface regions, and the other is the baffling effect due to the existence of boundary layers near interfaces.
Hassan, M A; Hamdi, M; Noma, A
2012-01-01
The mechanical behavior of the heart muscle tissues is the central problem in finite element simulation of the heart contraction, excitation propagation and development of an artificial heart. Nonlinear elastic and viscoelastic passive material properties of the left ventricular papillary muscle of a guinea pig heart were determined based on in-vitro precise uniaxial and relaxation tests. The nonlinear elastic behavior was modeled by a hypoelastic model and different hyperelastic strain energy functions such as Ogden and Mooney-Rivlin. Nonlinear least square fitting and constrained optimization were conducted under MATLAB and MSC.MARC in order to obtain the model material parameters. The experimental tensile data was used to get the nonlinear elastic mechanical behavior of the heart muscle. However, stress relaxation data was used to determine the relaxation behavior as well as viscosity of the tissues. Viscohyperelastic behavior was constructed by a multiplicative decomposition of a standard Ogden strain energy function, W, for instantaneous deformation and a relaxation function, R(t), in a Prony series form. The study reveals that hypoelastic and hyperelastic (Ogden) models fit the tissue mechanical behaviors well and can be safely used for heart mechanics simulation. Since the characteristic relaxation time (900 s) of heart muscle tissues is very large compared with the actual time of heart beating cycle (800 ms), the effect of viscosity can be reasonably ignored. The amount and type of experimental data has a strong effect on the Ogden parameters. The in vitro passive mechanical properties are good initial values to start running the biosimulation codes for heart mechanics. However, an optimization algorithm is developed, based on clinical intact heart measurements, to estimate and re-correct the material parameters in order to get the in vivo mechanical properties, needed for very accurate bio-simulation and for the development of new materials for the
Laser and nonlinear optical materials
Energy Technology Data Exchange (ETDEWEB)
De Shazer, L.G.
1986-01-01
This book contains 21 papers. Some of the titles are: Frequency conversion materials from a device perspective; Recent developments in area; Recent developments in barium borate; Growth of laser crystals at Airtron; Crystal growth and the future of solid state lasers; Faraday rotator materials for laser systems; and Mechanical properties of single crystal ceramics.
Material-Point Method Analysis of Bending in Elastic Beams
DEFF Research Database (Denmark)
Andersen, Søren Mikkel; Andersen, Lars
2007-01-01
The aim of this paper is to test different types of spatial interpolation for the material-point method. The interpolations include quadratic elements and cubic splines. A brief introduction to the material-point method is given. Simple liner-elastic problems are tested, including the classical...
Propagation law of impact elastic wave based on specific materials
Directory of Open Access Journals (Sweden)
Chunmin CHEN
2017-02-01
Full Text Available In order to explore the propagation law of the impact elastic wave on the platform, the experimental platform is built by using the specific isotropic materials and anisotropic materials. The glass cloth epoxy laminated plate is used for anisotropic material, and an organic glass plate is used for isotropic material. The PVDF sensors adhered on the specific materials are utilized to collect data, and the elastic wave propagation law of different thick plates and laminated plates under impact conditions is analyzed. The Experimental results show that in anisotropic material, transverse wave propagation speed along the fiber arrangement direction is the fastest, while longitudinal wave propagation speed is the slowest. The longitudinal wave propagation speed in anisotropic laminates is much slower than that in the laminated thick plates. In the test channel arranged along a particular angle away from the central region of the material, transverse wave propagation speed is larger. Based on the experimental results, this paper proposes a material combination mode which is advantageous to elastic wave propagation and diffusion in shock-isolating materials. It is proposed to design a composite material with high acoustic velocity by adding regularly arranged fibrous materials. The overall design of the barrier material is a layered structure and a certain number of 90°zigzag structure.
Aftershocks and Omori's law in a modified Carlson-Langer model with nonlinear visco-elasticity
Sakaguchi, Hidetsugu
2015-01-01
A modified Carlson-Langer model for earthquakes is proposed, which includes nonlinear visco-elasticity. Several aftershocks are generated after the main shock owing to the damping of the additional visco-elastic force. Both the Gutenberg-Richter law and Omori's law are reproduced in a numerical simulation of the modified Carlson-Langer model on a critical percolation cluster of a square lattice.
Nonlinear Vibration of an Elastically Restrained Tapered Beam
DEFF Research Database (Denmark)
Karimpour, S; Ganji, S.S; Barari, Amin;
2012-01-01
This paper presents the analytical simulation of an elastically restrained tapered cantilever beam using the energy balance method (EBM) and the iteration perturbation method (IPM). To assess the accuracy of solutions, we compare the results with the harmonic balance method (HBM). The obtained re...
A Model for Compression-Weakening Materials and the Elastic Fields due to Contractile Cells
Rosakis, Phoebus; Ravichandran, Guruswami
2014-01-01
We construct a homogeneous, nonlinear elastic constitutive law, that models aspects of the mechanical behavior of inhomogeneous fibrin networks. Fibers in such networks buckle when in compression. We model this as a loss of stiffness in compression in the stress-strain relations of the homogeneous constitutive model. Problems that model a contracting biological cell in a finite matrix are solved. It is found that matrix displacements and stresses induced by cell contraction decay slower (with distance from the cell) in a compression weakening material, than linear elasticity would predict. This points toward a mechanism for long-range cell mechanosensing. In contrast, an expanding cell would induce displacements that decay faster than in a linear elastic matrix.
A model for compression-weakening materials and the elastic fields due to contractile cells
Rosakis, Phoebus; Notbohm, Jacob; Ravichandran, Guruswami
2015-12-01
We construct a homogeneous, nonlinear elastic constitutive law that models aspects of the mechanical behavior of inhomogeneous fibrin networks. Fibers in such networks buckle when in compression. We model this as a loss of stiffness in compression in the stress-strain relations of the homogeneous constitutive model. Problems that model a contracting biological cell in a finite matrix are solved. It is found that matrix displacements and stresses induced by cell contraction decay slower (with distance from the cell) in a compression weakening material than linear elasticity would predict. This points toward a mechanism for long-range cell mechanosensing. In contrast, an expanding cell would induce displacements that decay faster than in a linear elastic matrix.
Elastic therapeutic tape: do they have the same material properties?
Boonkerd, Chuanpis; Limroongreungrat, Weerawat
2016-01-01
[Purpose] Elastic therapeutic tape has been widely used for rehabilitation and treatment of sports injuries. Tapes with different elastic properties serve different treatment purposes with inappropriate tension reducing tape effectiveness. Many tapes are available in the market, but studies on tape properties are limited. The aim of this study was to examine the material properties of elastic therapeutic tape. [Subjects and Methods] Brands of elastic therapeutic tape included KinesioTex®, ATex, Mueller, 3M, and ThaiTape. The Material Testing System Insight® 1 Electromechanical Testing Systems was used to apply a tensile force on elastic therapeutic tape. Ten specimens of each brand were tested. Stress, load, and Young’s modulus at 25%, 50%, 75%, 100%, and maximum point were collected. One-way analysis of variance with post hoc testing was used to analyze tape parameters. [Results] Maximum elongation and Young’s modulus at all percentages were significantly different between brands. There were no differences in maximum load and maximum stress. [Conclusion] Mechanical properties are different for commercial elastic therapeutic tapes. Physiotherapists and other clinicians should be aware of mechanical tape properties to correctly apply kinesio tape. PMID:27190472
Elastic therapeutic tape: do they have the same material properties?
Boonkerd, Chuanpis; Limroongreungrat, Weerawat
2016-04-01
[Purpose] Elastic therapeutic tape has been widely used for rehabilitation and treatment of sports injuries. Tapes with different elastic properties serve different treatment purposes with inappropriate tension reducing tape effectiveness. Many tapes are available in the market, but studies on tape properties are limited. The aim of this study was to examine the material properties of elastic therapeutic tape. [Subjects and Methods] Brands of elastic therapeutic tape included KinesioTex(®), ATex, Mueller, 3M, and ThaiTape. The Material Testing System Insight(®) 1 Electromechanical Testing Systems was used to apply a tensile force on elastic therapeutic tape. Ten specimens of each brand were tested. Stress, load, and Young's modulus at 25%, 50%, 75%, 100%, and maximum point were collected. One-way analysis of variance with post hoc testing was used to analyze tape parameters. [Results] Maximum elongation and Young's modulus at all percentages were significantly different between brands. There were no differences in maximum load and maximum stress. [Conclusion] Mechanical properties are different for commercial elastic therapeutic tapes. Physiotherapists and other clinicians should be aware of mechanical tape properties to correctly apply kinesio tape.
GENERAL EXPRESSIONS OF CONSTITUTIVE EQUATIONS FOR ISOTROPIC ELASTIC DAMAGED MATERIALS
Institute of Scientific and Technical Information of China (English)
唐雪松; 蒋持平; 郑健龙
2001-01-01
The general expressions of constitutive equations for isotropic elastic damaged materials were derived directly from the basic law of irreversible thermodynamics. The limitations of the classical damage constitutive equation based on the well-known strain equivalence hypothesis were overcome. The relationships between the two elastic isotropic damage models(i. e. single and double scalar damage models)were revealed. When a single scalar damage variable defined according to the microscopic geometry of a damaged material is used to describle the isotropic damage state, the constitutive equations contain two "damage effect functions", which describe the different influences of damage on the two independent elastic constants. The classical damage constitutive equation based on the strain equivalence hypothesis is only the first-order approximation of the general expression.It may be unduly simplified and may fail to describe satisfactorily the damage phenomena of practical materials.
Design of materials with prescribed nonlinear properties
DEFF Research Database (Denmark)
Wang, Fengwen; Sigmund, Ole; Jensen, Jakob Søndergaard
2014-01-01
We systematically design materials using topology optimization to achieve prescribed nonlinear properties under finite deformation. Instead of a formal homogenization procedure, a numerical experiment is proposed to evaluate the material performance in longitudinal and transverse tensile tests un....... The numerical examples illustrate optimized materials with rubber-like behavior and also optimized materials with extreme strain-independent Poisson's ratio for axial strain intervals of εi ∈ [0.00,0.30]. © 2014 Elsevier Ltd. All rights reserved....... under finite deformation, i.e. stress-strain relations and Poisson's ratio. By minimizing errors between actual and prescribed properties, materials are tailored to achieve the target. Both two dimensional (2D) truss-based and continuum materials are designed with various prescribed nonlinear properties...
ElNady, Khaled; Goda, Ibrahim; Ganghoffer, Jean-François
2016-09-01
The asymptotic homogenization technique is presently developed in the framework of geometrical nonlinearities to derive the large strains effective elastic response of network materials viewed as repetitive beam networks. This works extends the small strains homogenization method developed with special emphasis on textile structures in Goda et al. (J Mech Phys Solids 61(12):2537-2565, 2013). A systematic methodology is established, allowing the prediction of the overall mechanical properties of these structures in the nonlinear regime, reflecting the influence of the geometrical and mechanical micro-parameters of the network structure on the overall response of the chosen equivalent continuum. Internal scale effects of the initially discrete structure are captured by the consideration of a micropolar effective continuum model. Applications to the large strain response of 3D hexagonal lattices and dry textiles exemplify the powerfulness of the proposed method. The effective mechanical responses obtained for different loadings are validated by FE simulations performed over a representative unit cell.
Directory of Open Access Journals (Sweden)
K. R. McCall
1996-01-01
Full Text Available The velocity of sound in rock is a strong function of pressure, indicating that wave propagation in rocks is very nonlinear. The quasistatic elastic properties of rocks axe hysteretic, possessing discrete memory. In this paper a new theory is developed, placing all of these properties (nonlinearity, hysteresis, and memory on equal footing. The starting point of the new theory is closer to a microscopic description of a rock than the starting point of the traditional five-constant theory of nonlinear elasticity. However, this starting point (the number density Ï? of generic mechanical elements in an abstract space is deliberately independent of a specific microscopic model. No prejudice is imposed as to the mechanism causing nonlinear response in the microscopic mechanical elements. The new theory (1 relates suitable stress-strain measurements to the number density Ï? and (2 uses the number density Ï? to find the behaviour of nonlinear elastic waves. Thus the new theory provides for the synthesis of the full spectrum of elastic behaviours of a rock. Early development of the new theory is sketched in this contribution.
Elastic properties of superconductors and materials with weakly correlated spins
Binek, Christian
2017-01-01
It is shown that in the ergodic regime, the temperature dependence of Young?s modulus is solely determined by the magnetic properties of a material. For the large class of materials with paramagnetic or diamagnetic response, simple functional forms of the temperature derivative of Young?s modulus are derived and compared with experimental data and empirical results. Superconducting materials in the Meissner phase are ideal diamagnets. As such, they display remarkable elastic properties. Const...
Nonlinear Dynamics of Structures with Material Degradation
Soltani, P.; Wagg, D. J.; Pinna, C.; Whear, R.; Briody, C.
2016-09-01
Structures usually experience deterioration during their working life. Oxidation, corrosion, UV exposure, and thermo-mechanical fatigue are some of the most well-known mechanisms that cause degradation. The phenomenon gradually changes structural properties and dynamic behaviour over their lifetime, and can be more problematic and challenging in the presence of nonlinearity. In this paper, we study how the dynamic behaviour of a nonlinear system changes as the thermal environment causes certain parameters to vary. To this end, a nonlinear lumped mass modal model is considered and defined under harmonic external force. Temperature dependent material functions, formulated from empirical test data, are added into the model. Using these functions, bifurcation parameters are defined and the corresponding nonlinear responses are observed by numerical continuation. A comparison between the results gives a preliminary insight into how temperature induced properties affects the dynamic response and highlights changes in stability conditions of the structure.
MODELING OF NONLINEAR DEFORMATION AND BUCKLING OF ELASTIC INHOMOGENEOUS SHELLS
Directory of Open Access Journals (Sweden)
Bazhenov V.A.
2014-06-01
Full Text Available The paper outlines the fundamentals of the method of solving static problems of geometrically nonlinear deformation, buckling, and postbuckling behavior of thin thermoelastic inhomogeneous shells with complex-shaped mid-surface, geometrical features throughout the thickness, and multilayer structure under complex thermomechanical loading. The method is based on the geometrically nonlinear equations of three-dimensional thermoelasticity and the moment finiteelement scheme. The method is justified numerically. Comparing solutions with those obtained by other authors and by software LIRA and SCAD is conducted.
Energy Technology Data Exchange (ETDEWEB)
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.
Energy Technology Data Exchange (ETDEWEB)
Johnson, P.A.; McCall, K.R.; Meegan, G.D. Jr.
1993-06-01
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.
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.
Generalization of strain-gradient theory to finite elastic deformation for isotropic materials
Beheshti, Alireza
2017-03-01
This paper concerns finite deformation in the strain-gradient continuum. In order to take account of the geometric nonlinearity, the original strain-gradient theory which is based on the infinitesimal strain tensor is rewritten given the Green-Lagrange strain tensor. Following introducing the generalized isotropic Saint Venant-Kirchhoff material model for the strain-gradient elasticity, the boundary value problem is investigated in not only the material configuration but also the spatial configuration building upon the principle of virtual work for a three-dimensional solid. By presenting one example, the convergence of the strain-gradient and classical theories is studied.
Nonlinear elastic response in solid helium: critical velocity or strain?
Day, James; Syshchenko, Oleksandr; Beamish, John
2010-02-19
Torsional oscillator experiments show evidence of mass decoupling in solid 4He. This decoupling is amplitude dependent, suggesting a critical velocity for supersolidity. We observe similar behavior in the elastic shear modulus. By measuring the shear modulus over a wide frequency range, we can distinguish between an amplitude dependence which depends on velocity and one which depends on some other parameter such as displacement. In contrast with the torsional oscillator behavior, the modulus depends on the magnitude of stress, not velocity. We interpret our results in terms of the motion of dislocations which are weakly pinned by 3He impurities but which break away when large stresses are applied.
Possible second-order nonlinear interactions of plane waves in an elastic solid
Korneev, V.A.; Demcenko, A.
2014-01-01
There exist ten possible nonlinear elastic wave interactions for an isotropic solid described by three constants of the third order. All other possible interactions out of 54 combinations (triplets) of interacting and resulting waves are prohibited, because of restrictions of various kinds. The cons
Statistics of the Elastic Behavior of Granular Materials
Kruyt, Nicolaas P.; Rothenburg, L.
2001-01-01
The elastic behaviour of isotropic assemblies of granular materials consisting of two-dimensional, bonded and non-rotating particles is studied from the micromechanical viewpoint. Discrete element simulations have been performed of assemblies of 50,000 particles with various coordination numbers
Statistics of the elastic behaviour of granular materials
Kruyt, N.P.; Rothenburg, L.
2001-01-01
The elastic behaviour of isotropic assemblies of granular materials consisting of two-dimensional, bonded and non-rotating particles is studied from the micromechanical viewpoint. Discrete element simulations have been performed of assemblies of 50,000 particles with various coordination numbers (av
Material-point Method Analysis of Bending in Elastic Beams
DEFF Research Database (Denmark)
Andersen, Søren Mikkel; Andersen, Lars
The aim of this paper is to test different types of spatial interpolation for the materialpoint method. The interpolations include quadratic elements and cubic splines. A brief introduction to the material-point method is given. Simple liner-elastic problems are tested, including the classical...
Fracture Mechanics of an Elastic Softening Material like Concrete
Reinhardt, H.W.
1984-01-01
Concrete is modelled as a linear elastic softening material and introduced into fracture mechanics. A discrete crack is considered with softening zones at the crack tips. Following the approach of Dugdale/Barenblatt, closing stresses are applied to the crack faces in the softening zone. The stresses
Directory of Open Access Journals (Sweden)
Shi Jing
2014-01-01
Full Text Available The solving processes of the homogeneous balance method, Jacobi elliptic function expansion method, fixed point method, and modified mapping method are introduced in this paper. By using four different methods, the exact solutions of nonlinear wave equation of a finite deformation elastic circular rod, Boussinesq equations and dispersive long wave equations are studied. In the discussion, the more physical specifications of these nonlinear equations, have been identified and the results indicated that these methods (especially the fixed point method can be used to solve other similar nonlinear wave equations.
Singh, S. N.
1982-03-01
Using the invariance principle of LaSalle (1962) sufficient conditions for the existence of linear and nonlinear control laws for local and global asymptotic stability of nonlinear Hamiltonian systems are derived. An instability theorem is also presented which identifies the control laws from the given class which cannot achieve asymptotic stability. Some of the stability results are based on certain results for the univalence of nonlinear maps. A similar approach for the stabilization of bilinear systems which include nonconservative systems in elasticity is used and a necessary and sufficient condition for stabilization is obtained. An application to attitude control of a gyrostat Satellite is presented.
Breakdown of nonlinear elasticity in stress-controlled thermal amorphous solids
Dailidonis, Vladimir; Ilyin, Valery; Procaccia, Itamar; Shor, Carmel A. B. Z.
2017-03-01
In recent work it was clarified that amorphous solids under strain control do not possess nonlinear elastic theory in the sense that the shear modulus exists but nonlinear moduli exhibit sample-to-sample fluctuations that grow without bound with the system size. More relevant, however, for experiments are the conditions of stress control. In the present Rapid Communication we show that also under stress control the shear modulus exists, but higher-order moduli show unbounded sample-to-sample fluctuation. The unavoidable consequence is that the characterization of stress-strain curves in experiments should be done with a stress-dependent shear modulus rather than with nonlinear expansions.
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.
A conservation law formulation of nonlinear elasticity in general relativity
Gundlach, Carsten; Erickson, Stephanie J
2011-01-01
We present a practical framework for ideal hyperelasticity in numerical relativity. For this purpose, we recast the formalism of Carter and Quintana as a set of Eulerian conservation laws in an arbitrary 3+1 split of spacetime. The resulting equations are presented as an extension of the standard Valencia formalism for a perfect fluid, with additional terms in the stress-energy tensor, plus a set of kinematic conservation laws that evolve a configuration gradient. We prove that the equations can be made symmetric hyperbolic by suitable constraint additions, at least in a neighbourhood of the unsheared state. We discuss the Newtonian limit of our formalism and its relation to a second formalism also used in Newtonian elasticity. We validate our framework by numerically solving a set of Riemann problems in Minkowski spacetime, as well as Newtonian ones from the literature.
Directory of Open Access Journals (Sweden)
Rasolofosaon P.
2006-12-01
non-linéarité sous fort confinement, et qui pourraient engendrer un signal résultant d'une interaction onde-onde . Tempérant ce pessimisme, il faut noter qu'un éventuel signal d'interaction non linéaire présenterait l'avantage, quant à sa détection, d'être dans une bande de fréquence différente de celle des ondes utilisées pour l'engendrer. Bien que nous n'ayons pas connaissance d'essais d'application actuels, les perspectives paraissent plus encourageantes dans le domaine du génie civil ou minier. C'est dans le domaine diagraphique, où des distances de propagation sont très faibles, que des applications semblent possibles à moyen terme. Si l'on en juge par le dépôt très récent de plusieurs brevets, les compagnies de logging poursuivraient des recherches dans cette voie. A general and important characteristic of rocks is their elastically nonlinear behavior resulting in significant effects on wave propagation. The nonlinear response of rock is a direct consequence of the compliant nature of rock : the macro-and micro-structure of the material (microcracks, grain-to-grain contacts, etc. . As a result, the material modulus varies as a function of the applied pressure. Interest has grown significantly in the last several years, as illustrated by the increasing number of publications regarding this topic. Here we present a summary of the fundamentals of theory and of experimental observations characteristic of rock, and we address possible applications in geophysics. Two disciplines regarding the nonlinear elasticity of rock have been developed over recent years in tandem :- Acoustoelasticity where wave propagation in statically, prestressed materials is studied. Here one relates the variation in applied pressure to the elastic wavespeed in order to extract the nonlinear coefficients. This area of study includes the topic of stress-induced anisotropy. - Acoustic nonlinearity where we are interested in the temporary and local variation in the elastic
A new constitutive theory for fiber-reinforced incompressible nonlinearly elastic solids
Horgan, Cornelius O.; Saccomandi, Giuseppe
2005-09-01
We consider an incompressible nonlinearly elastic material in which a matrix is reinforced by strong fibers, for example fibers of nylon or carbon aligned in one family of curves in a rubber matrix. Rather than adopting the constraint of fiber inextensibility as has been previously assumed in the literature, here we develop a theory of fiber-reinforced materials based on the less restrictive idea of limiting fiber extensibility. The motivation for such an approach is provided by recent research on limiting chain extensibility models for rubber. Thus the basic idea of the present paper is simple: we adapt the limiting chain extensibility concept to limiting fiber extensibility so that the usual inextensibility constraint traditionally used is replaced by a unilateral constraint. We use a strain-energy density composed with two terms, the first being associated with the isotropic matrix or base material and the second reflecting the transversely isotropic character of the material due to the uniaxial reinforcement introduced by the fibers. We consider a base neo-Hookean model plus a special term that takes into account the limiting extensibility in the fiber direction. Thus our model introduces an additional parameter, namely that associated with limiting extensibility in the fiber direction, over previously investigated models. The aim of this paper is to investigate the mathematical and mechanical feasibility of this new model and to examine the role played by the extensibility parameter. We examine the response of the proposed models in some basic homogeneous deformations and compare this response to those of standard models for fiber reinforced rubber materials. The role of the strain-stiffening of the fibers in the new models is examined. The enhanced stability of the new models is then illustrated by investigation of cavitation instabilities. One of the motivations for the work is to apply the model to the biomechanics of soft tissues and the potential merits
A nonlinear generalized continuum approach for electro-elasticity including scale effects
Skatulla, S.; Arockiarajan, A.; Sansour, C.
2009-01-01
Materials characterized by an electro-mechanically coupled behaviour fall into the category of so-called smart materials. In particular, electro-active polymers (EAP) recently attracted much interest, because, upon electrical loading, EAP exhibit a large amount of deformation while sustaining large forces. This property can be utilized for actuators in electro-mechanical systems, artificial muscles and so forth. When it comes to smaller structures, it is a well-known fact that the mechanical response deviates from the prediction of classical mechanics theory. These scale effects are due to the fact that the size of the microscopic material constituents of such structures cannot be considered to be negligible small anymore compared to the structure's overall dimensions. In this context so-called generalized continuum formulations have been proven to account for the micro-structural influence to the macroscopic material response. Here, we want to adopt a strain gradient approach based on a generalized continuum framework [Sansour, C., 1998. A unified concept of elastic-viscoplastic Cosserat and micromorphic continua. J. Phys. IV Proc. 8, 341-348; Sansour, C., Skatulla, S., 2007. A higher gradient formulation and meshfree-based computation for elastic rock. Geomech. Geoeng. 2, 3-15] and extend it to also encompass the electro-mechanically coupled behaviour of EAP. The approach introduces new strain and stress measures which lead to the formulation of a corresponding generalized variational principle. The theory is completed by Dirichlet boundary conditions for the displacement field and its derivatives normal to the boundary as well as the electric potential. The basic idea behind this generalized continuum theory is the consideration of a micro- and a macro-space which together span the generalized space. As all quantities are defined in this generalized space, also the constitutive law, which is in this work conventional electro-mechanically coupled nonlinear
Energy Technology Data Exchange (ETDEWEB)
Byers, Loren W. [Los Alamos National Laboratory; Ten Cate, James A. [Los Alamos National Laboratory; Johnson, Paul A. [Los Alamos National Laboratory
2012-06-28
Nonlinear resonance ultrasound spectroscopy experiments conducted on concrete cores, one chemically and mechanically damaged by alkali-silica reactivity, and one undamaged, show that this material displays highly nonlinear wave behavior, similar to many other damaged materials. They find that the damaged sample responds more nonlinearly, manifested by a larger resonant peak and modulus shift as a function of strain amplitude. The nonlinear response indicates that there is a hysteretic influence in the stress-strain equation of state. Further, as in some other materials, slow dynamics are present. The nonlinear response they observe in concrete is an extremely sensitive indicator of damage. Ultimately, nonlinear wave methods applied to concrete may be used to guide mixing, curing, or other production techniques, in order to develop materials with particular desired qualities such as enhanced strength or chemical resistance, and to be used for damage inspection.
Nitzan, Sarah H; Zega, Valentina; Li, Mo; Ahn, Chae H; Corigliano, Alberto; Kenny, Thomas W; Horsley, David A
2015-01-01
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.
Energy Technology Data Exchange (ETDEWEB)
Bemer, E.; Bouteca, M.; Vincke, O. [Institut Francais du Petrole (IFP), 92 - Rueil-Malmaison (France); Hoteit, N.; Ozanam, O. [Agence Nationale pour la Gestion des Dechets Radioactifs ANDRA, 92 - Chatenay Malabry (France)
2001-07-01
Due to the impact on productivity and oil an place estimates, reliable modeling of rock behavior is essential in reservoir engineering. This paper examines several aspects of rock poro-elastic behavior within the framework of Biot's mechanics of fluid saturated porous solids. Constitutive laws of linear and nonlinear poro-elasticity are first determined from a fundamental stress decomposition, which allows to clearly connect linear and nonlinear models. Concept of effective stress and rock compressibility are considered. Linear incremental stress-strain relations are derived from the proposed nonlinear constitutive law by defining tangent elastic properties. These characteristics are naturally functions of strains and pore pressure, but explicit expressions as functions of stresses and pore pressure are established herein. Experiments performed on a reservoir sandstone illustrate these points. A constitutive law of poro-visco-elasticity is finally presented and applied to experimental data obtained on clay. (authors)
Strain-enhanced stress relaxation impacts nonlinear elasticity in collagen gels.
Nam, Sungmin; Hu, Kenneth H; Butte, Manish J; Chaudhuri, Ovijit
2016-05-17
The extracellular matrix (ECM) is a complex assembly of structural proteins that provides physical support and biochemical signaling to cells in tissues. The mechanical properties of the ECM have been found to play a key role in regulating cell behaviors such as differentiation and malignancy. Gels formed from ECM protein biopolymers such as collagen or fibrin are commonly used for 3D cell culture models of tissue. One of the most striking features of these gels is that they exhibit nonlinear elasticity, undergoing strain stiffening. However, these gels are also viscoelastic and exhibit stress relaxation, with the resistance of the gel to a deformation relaxing over time. Recent studies have suggested that cells sense and respond to both nonlinear elasticity and viscoelasticity of ECM, yet little is known about the connection between nonlinear elasticity and viscoelasticity. Here, we report that, as strain is increased, not only do biopolymer gels stiffen but they also exhibit faster stress relaxation, reducing the timescale over which elastic energy is dissipated. This effect is not universal to all biological gels and is mediated through weak cross-links. Mechanistically, computational modeling and atomic force microscopy (AFM) indicate that strain-enhanced stress relaxation of collagen gels arises from force-dependent unbinding of weak bonds between collagen fibers. The broader effect of strain-enhanced stress relaxation is to rapidly diminish strain stiffening over time. These results reveal the interplay between nonlinear elasticity and viscoelasticity in collagen gels, and highlight the complexity of the ECM mechanics that are likely sensed through cellular mechanotransduction.
Nonlinear Electromagnetic Interactions in Energetic Materials
Wood, M A; Moore, D S
2016-01-01
We study the scattering of electromagnetic waves in anisotropic energetic materials. Nonlinear light-matter interactions in molecular crystals result in frequency-conversion and polarization changes. Applied electromagnetic fields of moderate intensity can induce these nonlinear effects without triggering chemical decomposition, offering a mechanism for non-ionizing identification of explosives. We use molecular dynamics simulations to compute such two-dimensional Raman spectra in the terahertz range for planar slabs made of PETN and ammonium nitrate. We discuss third-harmonic generation and polarization-conversion processes in such materials. These observed far-field spectral features of the reflected or transmitted light may serve as an alternative tool for stand-off explosive detection.
Ansari, R.; Faraji Oskouie, M.; Gholami, R.
2016-01-01
In recent decades, mathematical modeling and engineering applications of fractional-order calculus have been extensively utilized to provide efficient simulation tools in the field of solid mechanics. In this paper, a nonlinear fractional nonlocal Euler-Bernoulli beam model is established using the concept of fractional derivative and nonlocal elasticity theory to investigate the size-dependent geometrically nonlinear free vibration of fractional viscoelastic nanobeams. The non-classical fractional integro-differential Euler-Bernoulli beam model contains the nonlocal parameter, viscoelasticity coefficient and order of the fractional derivative to interpret the size effect, viscoelastic material and fractional behavior in the nanoscale fractional viscoelastic structures, respectively. In the solution procedure, the Galerkin method is employed to reduce the fractional integro-partial differential governing equation to a fractional ordinary differential equation in the time domain. Afterwards, the predictor-corrector method is used to solve the nonlinear fractional time-dependent equation. Finally, the influences of nonlocal parameter, order of fractional derivative and viscoelasticity coefficient on the nonlinear time response of fractional viscoelastic nanobeams are discussed in detail. Moreover, comparisons are made between the time responses of linear and nonlinear models.
Nonlinear mechanics of soft fibrous materials
Ogden, Raymond
2015-01-01
The book presents a state-of-the-art overview of the fundamental theories, established models and ongoing research related to the modeling of these materials. Two approaches are conventionally used to develop constitutive relations for highly deformable fibrous materials. According to the phenomenological approach, a strain energy density function can be defined in terms of strain invariants. The other approach is based on kinetic theories, which treats a fibrous material as a randomly oriented inter-tangled network of long molecular chains bridged by permanent and temporary junctions. At the micro-level, these are associated with chemical crosslinks and active entanglements, respectively. The papers include carefully crafted overviews of the fundamental formulation of the three-dimensional theory from several points of view, and address their equivalences and differences. Also included are solutions to boundary-value problems which are amenable to experimental verification. A further aspect is the elasticity...
Adhikari, S. K.
2016-09-01
We consider the statics and dynamics of a stable, mobile three-dimensional (3D) spatiotemporal light bullet in a cubic-quintic nonlinear medium with a focusing cubic nonlinearity above a critical value and any defocusing quintic nonlinearity. The 3D light bullet can propagate with a constant velocity in any direction. Stability of the light bullet under a small perturbation is established numerically. We consider frontal collision between two light bullets with different relative velocities. At large velocities the collision is elastic with the bullets emerge after collision with practically no distortion. At small velocities two bullets coalesce to form a bullet molecule. At a small range of intermediate velocities the localized bullets could form a single entity which expands indefinitely, leading to a destruction of the bullets after collision. The present study is based on an analytic Lagrange variational approximation and a full numerical solution of the 3D nonlinear Schrödinger equation.
Electrets in soft materials: nonlinearity, size effects, and giant electromechanical coupling.
Deng, Qian; Liu, Liping; Sharma, Pradeep
2014-07-01
Development of soft electromechanical materials is critical for several tantalizing applications such as soft robots and stretchable electronics, among others. Soft nonpiezoelectric materials can be coaxed to behave like piezoelectrics by merely embedding charges and dipoles in their interior and assuring some elastic heterogeneity. Such so-called electret materials have been experimentally shown to exhibit very large electromechanical coupling. In this work, we derive rigorous nonlinear expressions that relate effective electromechanical coupling to the creation of electret materials. In contrast to the existing models, we are able to both qualitatively and quantitatively capture the known experimental results on the nonlinear response of electret materials. Furthermore, we show that the presence of another form of electromechanical coupling, flexoelectricity, leads to size effects that dramatically alter the electromechanical response at submicron feature sizes. One of our key conclusions is that nonlinear deformation (prevalent in soft materials) significantly enhances the flexoelectric response and hence the aforementioned size effects.
Three kinds of nonlinear dispersive waves in elastic rods with finite deformation
Institute of Scientific and Technical Information of China (English)
ZHANG Shan-yuan; LIU Zhi-fang
2008-01-01
On the basis of classical linear theory on longitudinal, torsional and flexural waves in thin elastic rods, and taking finite deformation and dispersive effects into consideration, three kinds of nonlinear evolution equations are derived. Qualitative analysis of three kinds of nonlinear equations are presented. It is shown that these equations have homoclinic or heteroclinic orbits on the phase plane, corresponding to solitary wave or shock wave solutions, respectively. Based on the principle of homogeneous balance, these equations are solved with the Jacobi elliptic function expansion method. Results show that existence of solitary wave solution and shock wave solution is possible under certain conditions. These conclusions are consistent with qualitative analysis.
Highly Nonlinear Wave Propagation in Elastic Woodpile Periodic Structures
2016-08-03
enabled a wide range of proposals for applications. Among others, we note shock and energy absorbing lay- ers [5–7], acoustic lenses [8], acoustic diodes...found in the Supplemental Material [41]. We record the transmit- ted stress waves using a piezoelectric force sensor (PCB C02) placed at the bottom of...the contacts in the presence of internal vibration modes that can store energy in their own right. The effective parameters m1,M and k1 of this DEM
A Reformulation of Nonlinear Anisotropic Elasticity for Impact Physics
2014-02-01
Polycrystals. International Journal of Plasticity 2003, 19, 1401–1444. 26. Clayton, J. D.; McDowell, D. L. Homogenized Finite Elastoplasticity and Damage ...Materials and Technology 2002, 124, 302– 313. 25. Clayton, J. D.; McDowell, D. L. A Multiscale Multiplicative Decomposition for Elastoplasticity of...29. Clayton, J. D. Continuum Multiscale Modeling of Finite Deformation Plasticity and Anisotropic Damage in Polycrystals. Theoretical and Applied
Finsler Geometry of Nonlinear Elastic Solids with Internal Structure
2017-01-01
generality has resulted in its use in field-theoretical descriptions of nearly all branches of physics : general relativity [1], gravitation [2], quantum ...John D Clayton A reprint from the Journal of Geometry and Physics . 2017;112:118–146. Approved for public release...Materials Research Directorate, ARL A reprint from the Journal of Geometry and Physics . 2017;112:118–146. Approved for
Control of an extending nonlinear elastic cable with an active vibration control strategy
Dai, L.; Sun, L.; Chen, C.
2014-10-01
An active control strategy based on the fuzzy sliding mode control (FSMC) is developed in this research for controlling the large-amplitude vibrations of an extending nonlinear elastic cable. The geometric nonlinearity of the cable and the fixed-fixed boundary of the cable are considered. For effectively and accurately control the motion of the cable with the active control strategy developed, the governing equation of the elastic cable is established and transformed into a multi-dimensional dynamic system with the 3rd order Galerkin method. The active control strategy is developed on the basis of the dynamic system, and the control strategy is applicable to multi-dimensional dynamic systems. In the numerical simulation, large-amplitude vibrations of the cable are effectively controlled with the control strategy. The results of the research demonstrate significances for controlling the cable vibrations of an elevator in practice.
Mathematical model predicts the elastic behavior of composite materials
Directory of Open Access Journals (Sweden)
Zoroastro de Miranda Boari
2005-03-01
Full Text Available Several studies have found that the non-uniform distribution of reinforcing elements in a composite material can markedly influence its characteristics of elastic and plastic deformation and that a composite's overall response is influenced by the physical and geometrical properties of its reinforcing phases. The finite element method, Eshelby's method and dislocation mechanisms are usually employed in formulating a composite's constitutive response. This paper discusses a composite material containing SiC particles in an aluminum matrix. The purpose of this study was to find the correlation between a composite material's particle distribution and its resistance, and to come up with a mathematical model to predict the material's elastic behavior. The proposed formulation was applied to establish the thermal stress field in the aluminum-SiC composite resulting from its fabrication process, whereby the mixture is prepared at 600 °C and the composite material is used at room temperature. The analytical results, which are presented as stress probabilities, were obtained from the mathematical model proposed herein. These results were compared with the numerical ones obtained by the FEM method. A comparison of the results of the two methods, analytical and numerical, reveals very similar average thermal stress values. It is also shown that Maxwell-Boltzmann's distribution law can be applied to identify the correlation between the material's particle distribution and its resistance, using Eshelby's thermal stresses.
Institute of Scientific and Technical Information of China (English)
Xingzhe Wang; Xiaojing Zheng
2009-01-01
Based on the generalized variational principle of magneto-thermo-elasticity of the ferromagnetic elastic medium, a nonlinear coupling theoretical modeling for a ferromagnetic thin shell is developed. All governing equations and boundary conditions for the ferromagnetic shell are obtained from the variational manipulations on the magnetic scalar potential, temperature and the elastic displacement related to the total energy functional. The multi-field couplings and geometrical nonlinearity of the ferromagnetic thin shell are taken into account in the modeling. The general modeling can be further deduced to existing models of the magneto-elasticity and the thermo-elasticity of a ferromagnetic shell and magneto-thermo-elasticity of a ferromagnetic plate, which axe coincident with the ones in literature.
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.
Water jet indentation for local elasticity measurements of soft materials.
Chevalier, N R; Dantan, Ph; Gazquez, E; Cornelissen, A J M; Fleury, V
2016-01-01
We present a novel elastography method for soft materials (100Pa-100kPa) based on indentation by a μm-sized water jet. We show that the jet creates a localized deformation ("cavity") of the material that can be easily visualized. We study experimentally how cavity width and depth depend on jet speed, height, incidence angle and sample elasticity. We describe how to calibrate the indenter using gels of known stiffness. We then demonstrate that the indenter yields quantitative elasticity values within 10% of those measured by shear rheometry. We corroborate our experimental findings with fluid-solid finite-element simulations that quantitatively predict the cavity profile and fluid flow lines. The water jet indenter permits in situ local stiffness measurements of 2D or 3D gels used for cell culture in physiological buffer, is able to assess stiffness heterogeneities with a lateral resolution in the range 50-500μm (at the tissue scale) and can be assembled at low cost with standard material from a biology laboratory. We therefore believe it will become a valuable method to measure the stiffness of a wide range of soft, synthetic or biological materials.
Poole, L. R.
1972-01-01
A computer program is presented by which the effects of nonlinear suspension-system elastic characteristics on parachute inflation loads and motions can be investigated. A mathematical elastic model of suspension-system geometry is coupled to the planar equations of motion of a general vehicle and canopy. Canopy geometry and aerodynamic drag characteristics and suspension-system elastic properties are tabular inputs. The equations of motion are numerically integrated by use of an equivalent fifth-order Runge-Kutta technique.
Nonlinear size-dependent longitudinal vibration of carbon nanotubes embedded in an elastic medium
Fernandes, R.; El-Borgi, S.; Mousavi, S. M.; Reddy, J. N.; Mechmoum, A.
2017-04-01
In this paper, we study the longitudinal linear and nonlinear free vibration response of a single walled carbon nanotube (CNT) embedded in an elastic medium subjected to different boundary conditions. This formulation is based on a large deformation analysis in which the linear and nonlinear von Kármán strains and their gradient are included in the expression of the strain energy and the velocity and its gradient are taken into account in the expression of the kinetic energy. Therefore, static and kinetic length scales associated with both energies are introduced to model size effects. The governing motion equation along with the boundary conditions are derived using Hamilton's principle. Closed-form solutions for the linear free vibration problem of the embedded CNT rod are first obtained. Then, the nonlinear free vibration response is investigated for various values of length scales using the method of multiple scales.
Acoustic scattering reduction using layers of elastic materials
Dutrion, Cécile; Simon, Frank
2017-02-01
Making an object invisible to acoustic waves could prove useful for military applications or measurements in confined space. Different passive methods have been proposed in recent years to avoid acoustic scattering from rigid obstacles. These techniques are exclusively based on acoustic phenomena, and use for instance multiple resonators or scatterers. This paper examines the possibility of designing an acoustic cloak using a bi-layer elastic cylindrical shell to eliminate the acoustic field scattered from a rigid cylinder hit by plane waves. This field depends on the dimensional and mechanical characteristics of the elastic layers. It is computed by a semi-analytical code modelling the vibrations of the coating under plane wave excitation. Optimization by genetic algorithm is performed to determine the characteristics of a bi-layer material minimizing the scattering. Considering an external fluid consisting of air, realistic configurations of elastic coatings emerge, composed of a thick internal orthotopic layer and a thin external isotropic layer. These coatings are shown to enable scattering reduction at a precise frequency or over a larger frequency band.
Stojanović, Vladimir; Petković, Marko D.
2016-12-01
Geometrically nonlinear free and forced vibrations of damaged high order shear deformable beams resting on a nonlinear Pasternak foundation are investigated in this paper. Equations of motion are derived for the beam which is under subjected combined action of arbitrarily distributed or concentrated transverse loading as well as axial loading. To account for shear deformations, the concept of high order shear deformation is used in comparison with the concept of first order shear deformation theory. Analyses are performed to investigate the effects of the specific stiffness of the foundation on the damaged beam frequencies and displacements with the aim of equalising the response of a damaged and an intact beam. According to that, functions of the foundation stiffness are determined depending on the location and size of the damage as a result of the possibility for the damaged beam to behave like one that is intact. An advanced p-version of the finite element method is developed for geometrically nonlinear vibrations of damaged Reddy-Bickford beams. The present study gives a clear view of the nonlinear dynamical behaviour of four types of beams according to high order shear deformation theory - an intact beam, a damaged beam, a damaged beam on an elastic foundation and intact beam on elastic foundation. The paper also presents the derivation of a new set of two nonlinear partial differential equations where only the transverse and axial displacements figure. The forced nonlinear vibrations problem is solved in the time domain using the Newmark integration method. Free vibration analysis carried out by harmonic balance and the use of continuation methods and backbone curves are constructed.
Non-linear elasticity of core/shell spun PGS/PLLA fibres and their effect on cell proliferation.
Xu, Bing; Rollo, Ben; Stamp, Lincon A; Zhang, Dongcheng; Fang, Xiya; Newgreen, Donald F; Chen, Qizhi
2013-09-01
An efficient delivery system is critical for the success of cell therapy. To deliver cells to a dynamic organ, the biomaterial vehicle should mechanically match with the non-linearly elastic host tissue. In this study, non-linearly elastic biomaterials have been fabricated from a chemically crosslinked elastomeric poly(glycerol sebacate) (PGS) and thermoplastic poly(l-lactic acid) (PLLA) using the core/shell electrospinning technique. The spun fibrous materials containing a PGS core and PLLA shell demonstrate J-shaped stress-strain curves, having ultimate tensile strength (UTS), rupture elongation and stiffness constants of 1 ± 0.2 MPa, 25 ± 3% and 12 ± 2, respectively, which are comparable to skin tissue properties reported previously. Our ex vivo and in vivo trials have shown that the elastomeric mesh supports and fosters the growth of enteric neural crest (ENC) progenitor cells, and that the cell-seeded elastomeric fibrous sheet physically remains in intimate contact with guts after grafting, providing the effective delivery of the progenitor cells to an embryonic and post-natal gut environment.
Measuring the elastic strain of individual grains in polycrystalline materials
DEFF Research Database (Denmark)
on some of the important aspects you have to take into account in order to determine the strain tensors of the individual grains to the desired accuracy of 10-4. The first thing is how to handle the peak overlaps that will inevitably occur, especially for textured and/or deformed materials. Secondly...... within FitAllB. In addition to the centre-of-mass grain positions, orientations and strain tensors, FitAllB also calculates the relative volumes of the grains based on the peak intensities, so using a tessellation routine a crude 3D map of the elastic strain in the polycrystal can be obtained....
Soutas-Little, Robert William
2010-01-01
According to the author, elasticity may be viewed in many ways. For some, it is a dusty, classical subject . . . to others it is the paradise of mathematics."" But, he concludes, the subject of elasticity is really ""an entity itself,"" a unified subject deserving comprehensive treatment. He gives elasticity that full treatment in this valuable and instructive text. In his preface, Soutas-Little offers a brief survey of the development of the theory of elasticity, the major mathematical formulation of which was developed in the 19th century after the first concept was proposed by Robert Hooke
Directory of Open Access Journals (Sweden)
Jessamine P Winer
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.
Energy Technology Data Exchange (ETDEWEB)
Vladas Tvaskis; John Arrington; Michael Christy; Rolf Ent; Cynthia Keppel; Yongguang Liang; Grahame Vittorini
2006-01-26
The effects of two-photon exchange corrections, suggested to explain the difference between measurements of the proton elastic electromagnetic form factors using the polarization transfer and Rosenbluth techniques, have been studied in elastic and inelastic scattering data. Such corrections could introduce epsilon-dependent non-linearities in inelastic Rosenbluth separations, where epsilon is the virtual photon polarization parameter. It is concluded that such non-linear effects are consistent with zero for elastic, resonance, and deep-inelastic scattering for all Q{sup 2} and W{sup 2} values measured.
Eliminating material constraints for nonlinearity with plasmonic metamaterials
Neira, Andres D.; Olivier, Nicolas; Nasir, Mazhar E.; Dickson, Wayne; Wurtz, Gregory A.; Zayats, Anatoly V.
2015-01-01
Nonlinear optical materials comprise the foundation of modern photonics, offering functionalities ranging from ultrafast lasers to optical switching, harmonic and soliton generation. Optical nonlinearities are typically strong near the electronic resonances of a material and thus provide limited tuneability for practical use. Here we show that in plasmonic nanorod metamaterials, the Kerr-type nonlinearity is not limited by the nonlinear properties of the constituents. Compared with gold's nonlinearity, the measured nonlinear absorption and refraction demonstrate more than two orders of magnitude enhancement over a broad spectral range that can be engineered via geometrical parameters. Depending on the metamaterial's effective plasma frequency, either a focusing or defocusing nonlinearity is observed. The ability to obtain strong and fast optical nonlinearities in a given spectral range makes these metamaterials a flexible platform for the development of low-intensity nonlinear applications. PMID:26195182
Loyer, A.; Sinou, J.-J.; Chiello, O.; Lorang, X.
2012-02-01
As noise reduction tends to be part of environmental directives, predicting squeal noise generated by disc brakes is an important industrial issue. It involves both the transient and stationary nonlinear dynamics of self-excited systems with frictional contact. Time simulation of the phenomenon is an attractive option for reducing experiment costs. However, since such computations using full finite element models of industrial disc brake systems is time-consuming, model reduction has to be performed. In this paper, both the transient and stationary nonlinear behaviors of the friction destabilized system and the effect of dynamical reduction on the nonlinear response of a simple friction destabilized system are carried out. The first part provides a description of the general modeling retained for friction destabilized systems. Then, discretization and solving processes for the stability analysis and the temporal evolution are presented. The third part presents an analysis of a sliding elastic layer for different operating conditions, in order to better understand the nonlinear behavior of such systems. Finally, spatial model reduction is performed with different kinds of reduction bases in order to analyze the different effects of modal reductions. This clearly shows the necessity of including static modes in the reduction basis and that nonlinear interactions between unstable modes are very difficult to represent with reduced bases. Finally, the proposed model and the associated studies are intended to be the benchmark cases for future comparison.
Institute of Scientific and Technical Information of China (English)
Miha Brojan; Matjaz Cebron; Franc Kosel
2012-01-01
This work studies large deflections of slender,non-prismatic cantilever beams subjected to a combined loading which consists of a non-uniformly distributed continuous load and a concentrated load at the free end of the beam.The material of the cantilever is assumed to be nonlinearly elastic.Different nonlinear relations between stress and strain in tensile and compressive domain are considered.The accuracy of numerical solutions is evaluated by comparing them with results from previous studies and with a laboratory experiment.
Scaling functional patterns of skeletal and cardiac muscles: New non-linear elasticity approach
Kokshenev, Valery B
2009-01-01
Responding mechanically to environmental requests, muscles show a surprisingly large variety of functions. The studies of in vivo cycling muscles qualified skeletal muscles into four principal locomotor patterns: motor, brake, strut, and spring. While much effort of has been done in searching for muscle design patterns, no fundamental concepts underlying empirically established patterns were revealed. In this interdisciplinary study, continuum mechanics is applied to the problem of muscle structure in relation to function. The ability of a powering muscle, treated as a homogenous solid organ, tuned to efficient locomotion via the natural frequency is illuminated through the non-linear elastic muscle moduli controlled by contraction velocity. The exploration of the elastic force patterns known in solid state physics incorporated in activated skeletal and cardiac muscles via the mechanical similarity principle yields analytical rationalization for locomotor muscle patterns. Besides the explanation of the origin...
Propagation of ultrasonic Love waves in nonhomogeneous elastic functionally graded materials.
Kiełczyński, P; Szalewski, M; Balcerzak, A; Wieja, K
2016-02-01
This paper presents a theoretical study of the propagation behavior of ultrasonic Love waves in nonhomogeneous functionally graded elastic materials, which is a vital problem in the mechanics of solids. The elastic properties (shear modulus) of a semi-infinite elastic half-space vary monotonically with the depth (distance from the surface of the material). The Direct Sturm-Liouville Problem that describes the propagation of Love waves in nonhomogeneous elastic functionally graded materials is formulated and solved by using two methods: i.e., (1) Finite Difference Method, and (2) Haskell-Thompson Transfer Matrix Method. The dispersion curves of phase and group velocity of surface Love waves in inhomogeneous elastic graded materials are evaluated. The integral formula for the group velocity of Love waves in nonhomogeneous elastic graded materials has been established. The effect of elastic non-homogeneities on the dispersion curves of Love waves is discussed. Two Love wave waveguide structures are analyzed: (1) a nonhomogeneous elastic surface layer deposited on a homogeneous elastic substrate, and (2) a semi-infinite nonhomogeneous elastic half-space. Obtained in this work, the phase and group velocity dispersion curves of Love waves propagating in the considered nonhomogeneous elastic waveguides have not previously been reported in the scientific literature. The results of this paper may give a deeper insight into the nature of Love waves propagation in elastic nonhomogeneous functionally graded materials, and can provide theoretical guidance for the design and optimization of Love wave based devices.
Global well-posedness for nonlinear nonlocal Cauchy problems arising in elasticity
Directory of Open Access Journals (Sweden)
Hantaek Bae
2017-02-01
Full Text Available In this article, we prove global well-posedness for a family of one dimensional nonlinear nonlocal Cauchy problems arising in elasticity. We consider the equation $$ u_{tt}-\\delta Lu_{xx}=\\big(\\beta \\ast [(1-\\deltau+u^{2n+1}]\\big_{xx}\\,, $$ where $L$ is a differential operator, $\\beta$ is an integral operator, and $\\delta =0$ or 1. (Here, the case $\\delta=1$ represents the additional doubly dispersive effect. We prove the global well-posedness of the equation in energy spaces.
Nonlinear Elastic Deformation of Thin Composite Shells of Discretely Variable Thickness
Lutskaya, I. V.; Maksimyuk, V. A.; Storozhuk, E. A.; Chernyshenko, I. S.
2016-11-01
A method for analyzing the stress-strain state of nonlinear elastic orthotropic thin shells with reinforced holes and shells of discretely variable thickness is developed. The reference surface is not necessarily the midsurface. The constitutive equations are derived using Lomakin's theory of anisotropic plasticity. The methods of successive approximations and variational differences are used. The Kirchhoff-Love hypotheses are implemented using Lagrange multipliers. The method allows analyzing the stress-strain state of shells with arbitrarily varying thickness and ribbed shells. The numerical results are presented in the form of tables and analyzed
Laser And Nonlinear Optical Materials For Laser Remote Sensing
Barnes, Norman P.
2005-01-01
NASA remote sensing missions involving laser systems and their economic impact are outlined. Potential remote sensing missions include: green house gasses, tropospheric winds, ozone, water vapor, and ice cap thickness. Systems to perform these measurements use lanthanide series lasers and nonlinear devices including second harmonic generators and parametric oscillators. Demands these missions place on the laser and nonlinear optical materials are discussed from a materials point of view. Methods of designing new laser and nonlinear optical materials to meet these demands are presented.
Organosilicon Polymeric Nonlinear Optical Materials for Optical Switching and Modulation
1994-02-28
Organosilicon Polymeric Nonlinear Optical Materials for Optical C: F49620-93-C-0039 Switching and Modulation 6. AUTHOR(S) Mr. Sandip K. Sengupta, Dr...D FINAL REPORT for Organosilicon Polymeric Nonlinear Optical Materials for Optical Switching and Modulation Prepared for: USAF, AFMC (AFOSR) Air Force...34Organosilicon Polymeric Nonlinear Optical Materials for Optical Switching and Modulation," contract number F49620-93-C-0039. The work has been performed by Dr
Characterizaticr of Solid State Laser and Nonlinear Optical Materials.
1995-02-02
materials useful in the different methods for obtaining frequency agility: narrow line emitters with multiple lasing channels and nonlinear optical materials . In...codoped with two or more rare earth ions were studied and computers models developed to explain their spectral dynamics. The nonlinear optical materials investigated
Novel Super-Elastic Materials for Advanced Bearing Applications
Dellacorte, Christopher
2014-01-01
Tribological surfaces of mechanical components encounter harsh conditions in terrestrial, marine and aerospace environments. Brinell denting, abrasive wear and fatigue often lead to life-limiting bearing and gear failures. Novel superelastic materials based upon Ni-Ti alloys are an emerging solution. Ni-Ti alloys are intermetallic materials that possess characteristics of both metals and ceramics. Ni-Ti alloys have intrinsically good aqueous corrosion resistance (they cannot rust), high hardness, relatively low elastic modulus, are chemically inert and readily lubricated. Ni-Ti alloys also belong to the family of superelastics and, despite high hardness, are able to withstand large strains without suffering permanent plastic deformation. In this paper, the use of hard, resilient Ni-Ti alloys for corrosion-proof, shockproof bearing and gear applications are presented. Through a series of bearing and gear development projects, it is demonstrated that Ni-Tis unique blend of materials properties lead to significantly improved load capacity, reduced weight and intrinsic corrosion resistance not found in any other bearing materials. Ni-Ti thus represents a new materials solution to demanding tribological applications.
Hieber, Simone E.; Koumoutsakos, Petros
2008-11-01
We present a novel Lagrangian particle method for the simulation of linear and nonlinear elastic models of soft tissue. Linear solids are represented by the Lagrangian formulation of the stress-strain relationship that is extended to nonlinear solids by using the Lagrangian evolution of the deformation gradient described in a moving framework. The present method introduces a level set description, along with the particles, to capture the body deformations and to enforce the boundary conditions. Furthermore, the accuracy of the method in cases of large deformations is ensured by implementing a particle remeshing procedure. The method is validated in several benchmark problems, in two and three dimensions and the results compare well with the results of respective finite elements simulations. In simulations of large solid deformation under plane strain compression, the finite element solver exhibits spurious structures that are not present in the Lagrangian particle simulations. The particle simulations are compared with experimental results in an aspiration test of liver tissue.
Study on Attenuation, Modulus of Elasticity and Nonlinearity in Thermowood Using Ultrasound
Hæggström, E.; Wallin, A.; Hoffren, H.; Hassinen, T.; Viitaniemi, P.
2005-04-01
We determined ultrasonically the attenuation, modulus of elasticity (MOE), and nonlinearity parameter (B/A) of dry defect-free thermally modified wood samples ("thick" 10 × 50 × 100 mm3 and "thin" 2 × 40 × 150 mm3) of Finnish pine, Pinus Sylvestris, as a function of treatment temperature (60-240 °C, three hours in protective water steam). The samples were cut as radial-tangential (RT) planes, and as longitudinal-radial (LR) planes. Two distinct regions of change in mechanical parameters were seen: one around 140 C where both the linear and nonlinear parameters increased and one around 230 C where the mechanical parameters decreased. These treatment temperatures thus serves as candidates for quality class delimiters for these soft wood samples.
Possible second-order nonlinear interactions of plane waves in an elastic solid.
Korneev, V A; Demčenko, A
2014-02-01
There exist ten possible nonlinear elastic wave interactions for an isotropic solid described by three constants of the third order. All other possible interactions out of 54 combinations (triplets) of interacting and resulting waves are prohibited, because of restrictions of various kinds. The considered waves include longitudinal and two shear waves polarized in the interacting plane and orthogonal to it. The amplitudes of scattered waves have simple analytical forms, which can be used for experimental setup and design. The analytic results are verified by comparison with numerical solutions of initial equations. Amplitude coefficients for all ten interactions are computed as functions of frequency for polyvinyl chloride, together with interaction and scattering angles. The nonlinear equation of motion is put into a general vector form and can be used for any coordinate system.
Unsymmetrical squaraines for nonlinear optical materials
Marder, Seth R. (Inventor); Chen, Chin-Ti (Inventor); Cheng, Lap-Tak (Inventor)
1996-01-01
Compositions for use in non-linear optical devices. The compositions have first molecular electronic hyperpolarizability (.beta.) either positive or negative in sign and therefore display second order non-linear optical properties when incorporated into non-linear optical devices.
Non-linear Constitutive Model for the Oligocarbonate Polyurethane Material
Institute of Scientific and Technical Information of China (English)
Marek Pawlikowski
2014-01-01
The polyurethane,which was the subject of the constitutive research presented in the paper,was based on oligocarbonate diols Desmophen C2100 produced by Bayer@.The constitutive modelling was performed with a view to applying the material as the inlay of intervertebral disc prostheses.The polyurethane was assumed to be non-linearly viscohyperelastic,isotropic and incompressible.The constitutive equation was derived from the postulated strain energy function.The elastic and rheological constants were identified on the basis of experimental tests,i.e.relaxation tests and monotonic uniaxial tests at two different strain rates,i.e.λ =0.1 min-1 and λ =1.0 min-1.The stiffness tensor was derived and introduced to Abaqus@finite element (FE) software in order to numerically validate the constitutive model.The results of the constants identification and numerical implementation show that the derived constitutive equation is fully adequate to model stress-strain behavior of the polyurethane material.
Wang, Chenju; Gu, Jianbing; Kuang, Xiaoyu; Xiang, Shikai
2015-06-01
Nonlinear elastic properties of diamond-cubic silicon and germanium have not been investigated sufficiently to date. Knowledge of these properties not only can help us to understand nonlinear mechanical effects but also can assist us to have an insight into the related anharmonic properties, so we investigate the nonlinear elastic behaviour of single silicon and germanium by calculating their second- and third-order elastic constants. All the results of the elastic constants show good agreement with the available experimental data and other theoretical calculations. Such a phenomenon indicates that the present values of the elastic constants are accurate and can be used to further study the related anharmonic properties. Subsequently, the anharmonic properties such as the pressure derivatives of the second-order elastic constants, Grüneisen constants of long-wavelength acoustic modes, and ultrasonic nonlinear parameters are explored. All the anharmonic properties of silicon calculated in the present work also show good agreement with the existing experimental results; this consistency not only reveals that the calculation method of the anharmonic properties is feasible but also illuminates that the anharmonic properties obtained in the present work are reliable. For the anharmonic properties of germanium, since there are no experimental result and other theoretical data till now, we hope that the anharmonic properties of germanium first offered in this work would serve as a reference for future studies.
Energy Technology Data Exchange (ETDEWEB)
Wang, Chenju [Sichuan Univ., Chengdu (China). Inst. of Atomic and Molecular Physics; Institute of Fluid Physics, Sichuan (China). National Key Laboratory of Shock Wave and Detonation Physics; Gu, Jianbing [Institute of Fluid Physics, Sichuan (China). National Key Laboratory of Shock Wave and Detonation Physics; Sichuan Univ., Chengdu (China). College of Physical Science and Technology; Kuang, Xiaoyu [Sichuan Univ., Chengdu (China). Inst. of Atomic and Molecular Physics; Xiang, Shikai [Institute of Fluid Physics, Sichuan (China). National Key Laboratory of Shock Wave and Detonation Physics
2015-10-01
Nonlinear elastic properties of diamond-cubic silicon and germanium have not been investigated sufficiently to date. Knowledge of these properties not only can help us to understand nonlinear mechanical effects but also can assist us to have an insight into the related anharmonic properties, so we investigate the nonlinear elastic behaviour of single silicon and germanium by calculating their second- and third-order elastic constants. All the results of the elastic constants show good agreement with the available experimental data and other theoretical calculations. Such a phenomenon indicates that the present values of the elastic constants are accurate and can be used to further study the related anharmonic properties. Subsequently, the anharmonic properties such as the pressure derivatives of the second-order elastic constants, Grueneisen constants of long-wavelength acoustic modes, and ultrasonic nonlinear parameters are explored. All the anharmonic properties of silicon calculated in the present work also show good agreement with the existing experimental results; this consistency not only reveals that the calculation method of the anharmonic properties is feasible but also illuminates that the anharmonic properties obtained in the present work are reliable. For the anharmonic properties of germanium, since there are no experimental result and other theoretical data till now, we hope that the anharmonic properties of germanium first offered in this work would serve as a reference for future studies.
Elastic, plastic, and fracture mechanisms in graphene materials.
Daniels, Colin; Horning, Andrew; Phillips, Anthony; Massote, Daniel V P; Liang, Liangbo; Bullard, Zachary; Sumpter, Bobby G; Meunier, Vincent
2015-09-23
In both research and industry, materials will be exposed to stresses, be it during fabrication, normal use, or mechanical failure. The response to external stress will have an important impact on properties, especially when atomic details govern the functionalities of the materials. This review aims at summarizing current research involving the responses of graphene and graphene materials to applied stress at the nanoscale, and to categorize them by stress-strain behavior. In particular, we consider the reversible functionalization of graphene and graphene materials by way of elastic deformation and strain engineering, the plastic deformation of graphene oxide and the emergence of such in normally brittle graphene, the formation of defects as a response to stress under high temperature annealing or irradiation conditions, and the properties that affect how, and mechanisms by which, pristine, defective, and polycrystalline graphene fail catastrophically during fracture. Overall we find that there is significant potential for the use of existing knowledge, especially that of strain engineering, as well as potential for additional research into the fracture mechanics of polycrystalline graphene and device functionalization by way of controllable plastic deformation of graphene.
Interfacial elastic fingering in Hele-Shaw cells: A weakly nonlinear study
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.
Evaluation of elastic constants of materials using the frequency spectrum
Energy Technology Data Exchange (ETDEWEB)
Silva Neto, Ramiro J. da; Baroni, Douglas B.; Bittencourt, Marcelo de S.Q., E-mail: ramirobd@gmail.com [Instituto de Engenharia Nuclear (IEN/CNEN-RJ), Rio de Janeiro, RJ (Brazil). Departamento de Materiais Nucleares. Laboratorio de Ultrassom
2015-07-01
The characterization of materials made with the support of non-destructive techniques has great importance in industrial applications. The ultrasonic techniques are distinguished by good resolution to measure small variations of wave velocities as a result of changes in the character suffered by a particular material. In general these ultrasonic techniques are studied in the time domain, which represents an experimental difficulties when thin materials are analyzed, as well as to attenuate the ultrasonic signal drastically. An ultrasonic technique that uses the frequency domain is used in this study aiming to provide good time measurements to calculate the elastic constants of the first order in an aluminum alloy 6351. With the aid of a statistical approach was possible to have good results of tests performed when compared by a time domain technique already well explored in Ultrasound works produced in the Nuclear Engineering Institute Laboratory (LABUS / IEN) and also presented in most of the package, in good agreement with the theoretical model established in literature and used to validate the experiment, which was found in the results with good approximation. The relevance of this work in the nuclear area is associated with the interest to know the mechanical properties of structural components of the nuclear industry, which is currently studied as a rule, resorting to the computer simulations or previously during the operation of the system. (author)
Institute of Scientific and Technical Information of China (English)
Xingzhe Wang; Xiaojing Zheng
2009-01-01
Based on the generalized variational principle of magneto-thermo-elasticity of a ferromagnetic thin shell established (see, Analyses on nonlinear coupling of magneto-thermo-elasticity of ferromagnetic thin shell-Ⅰ), the present paper developed a finite element modeling for the mechanical-magneto-thermal multi-field coupling of a ferromagnetic thin shell. The numerical modeling composes of finite element equations for three sub-systems of magnetic, thermal and deformation fields, as well as iterative methods for nonlinearities of the geometrical large-deflection and the multi-field coupling of the ferromagnetic shell. As examples, the numerical simulations on magneto-elastic behaviors of a ferromagnetic cylindrical shell in an applied magnetic field, and magneto-thermo-elastic behaviors of the shell in applied magnetic and thermal fields are carried out. The results are in good agreement with the experimental ones.
Laser and nonlinear optical materials: SPIE volume 681
Energy Technology Data Exchange (ETDEWEB)
De Shazer, L.G.
1987-01-01
This book contains papers arranged under the following session headings: Nonlinear optical crystals; Laser host crystals; Electro-optic and magneto-optic materials; and Characterization of optical materials.
Non-linear Elasticity and Monitoring of Stress in the Focus of an Earthquake
Bakulin, V.; Bakulin, A.
2001-05-01
Non-linear elasticity proved to give comprehensive framework for relating seismic velocities in rocks to stress. This powerful theory allows attacking the problem of estimating stress state at the focus of earthquakes. Such idea has been proposed long time ago [Kostrov and Nikitin, 1968] however its implementation requires a-priori knowledge of non-linear rock properties. Three non-linear constants needed to describe variation of any velocity with stress are typically estimated from core measurements [Bakulin et al., 2000]. More reliable estimates can be obtained from multi-mode inversions of borehole acoustic data [Sinha, 1996]. Nevertheless database of non-linear formation constants is still very limited. More measurements are required to estimate non-linear rock properties on larger scale and with independent stress constraints. Such measurements can be done in mines [Bakulin and Bakulin, 1999] or in hydrocarbon reservoirs where time-dependent pressure measurements are available. Without knowledge of non-linear rock properties seismic waves can still bring information about directions of tectonic stresses. In particular, shear wave polarizations can deliver directions of principal stresses in the focus of an earthquake, provided the overburden effects were removed. If rock non-linear properties are independently derived then estimation of stress magnitudes becomes feasible. Such techniques were applied in mining environment [Bakulin and Bakulin, 1999]. They may become routine for monitoring stress state in the focus of earthquakes and therefore can be used for forecasting the seismic activity. Bakulin, A. V., Troyan, V. N., and Bakulin, V. N., 2000, Acoustoelasticity of rocks, St. Petersburg (in Russian). Bakulin, V. and Bakulin, A., 1999, Acoustopolarizational method of measuring stress in rock mass and determination of Murnaghan constants: 69th Annual Internat. Mtg., Soc. Expl. Geophys., 1971-1974. Kostrov, B.V., and Nikitin, L.V., 1968, Influence of initial
Vassiliev, Dmitri
2017-04-01
We consider an infinite three-dimensional elastic continuum whose material points experience no displacements, only rotations. This framework is a special case of the Cosserat theory of elasticity. Rotations of material points are described mathematically by attaching to each geometric point an orthonormal basis that gives a field of orthonormal bases called the coframe. As the dynamical variables (unknowns) of our theory, we choose the coframe and a density. We write down the general dynamic variational functional for our rotational theory of elasticity, assuming our material to be physically linear but the kinematic model geometrically nonlinear. Allowing geometric nonlinearity is natural when dealing with rotations because rotations in dimension three are inherently nonlinear (rotations about different axes do not commute) and because there is no reason to exclude from our study large rotations such as full turns. The main result of the talk is an explicit construction of a class of time-dependent solutions that we call plane wave solutions; these are travelling waves of rotations. The existence of such explicit closed-form solutions is a non-trivial fact given that our system of Euler-Lagrange equations is highly nonlinear. We also consider a special case of our rotational theory of elasticity which in the stationary setting (harmonic time dependence and arbitrary dependence on spatial coordinates) turns out to be equivalent to a pair of massless Dirac equations. The talk is based on the paper [1]. [1] C.G.Boehmer, R.J.Downes and D.Vassiliev, Rotational elasticity, Quarterly Journal of Mechanics and Applied Mathematics, 2011, vol. 64, p. 415-439. The paper is a heavily revised version of preprint https://arxiv.org/abs/1008.3833
Investigating nonlinear distortion in the photopolymer materials
Malallah, Ra'ed; Cassidy, Derek; Muniraj, Inbarasan; Zhao, Liang; Ryle, James P.; Sheridan, John T.
2017-05-01
Propagation and diffraction of a light beam through nonlinear materials are effectively compensated by the effect of selftrapping. The laser beam propagating through photo-sensitive polymer PVA/AA can generate a waveguide of higher refractive index in direction of the light propagation. In order to investigate this phenomenon occurring in light-sensitive photopolymer media, the behaviour of a single light beam focused on the front surface of photopolymer bulk is investigated. As part of this work the self-bending of parallel beams separated in spaces during self-writing waveguides are studied. It is shown that there is strong correlation between the intensity of the input beams and their separation distance and the resulting deformation of waveguide trajectory during channels formation. This self-channeling can be modelled numerically using a three-dimension model to describe what takes place inside the volume of a photopolymer media. Corresponding numerical simulations show good agreement with experimental observations, which confirm the validity of the numerical model that was used to simulate these experiments.
Konovalenko, Igor S.; Shilko, Evgeny V.; Konovalenko, Ivan S.; Vodopjyanov, Egor M.
2016-11-01
A two-scale mechanical model of brittle porous material partially filled with plastic filler (inclusions) was developed within the framework of the formalism of movable cellular automaton method. The model was applied to study the mechanical properties of mesoscopic samples with a linear distribution of the local porosity in the depth of the material. Calculation results showed essentially nonlinear dependence of their elastic and strength properties on the degree of pore space filling. It is found that depending on the sign of the gradient of porosity the value of shear strength of partially filled samples can significantly increase or remain constant with increase in the value of the degree of filling.
Probing material nonlinearity at various depths by time reversal mirrors
Payan, C.; Ulrich, T. J.; Le Bas, P. Y.; Griffa, M.; Schuetz, P.; Remillieux, M. C.; Saleh, T. A.
2014-04-01
In this Letter, the time reversal mirror is used to focus elastic energy at a prescribed location and to analyze the amplitude dependence of the focus signal, thus providing the nonlinearity of the medium. By varying the frequency content of the focused waveforms, the technique can be used to probe the surface, by penetrating to a depth defined by the wavelength of the focused waves. The validity of this concept is shown in the presence of gradual and distributed damage in concrete by comparing actual results with a reference nonlinear measurement and X ray tomography images.
Probing material nonlinearity at various depths by time reversal mirrors
Energy Technology Data Exchange (ETDEWEB)
Payan, C. [LMA UPR CNRS 7051, Aix Marseille Université, 31 Chemin Joseph Aiguier, 13402 Marseille (France); Ulrich, T. J.; Le Bas, P. Y.; Remillieux, M. C. [Los Alamos National Laboratory, EES-17, Los Alamos, New Mexico 87545 (United States); Griffa, M.; Schuetz, P. [Swiss Federal Laboratories for Materials Science and Technology (EMPA), Überlandstrasse 129, 8600 Dübendorf (Switzerland); Saleh, T. A. [Los Alamos National Laboratory, MST-16, Los Alamos, New Mexico 87545 (United States)
2014-04-07
In this Letter, the time reversal mirror is used to focus elastic energy at a prescribed location and to analyze the amplitude dependence of the focus signal, thus providing the nonlinearity of the medium. By varying the frequency content of the focused waveforms, the technique can be used to probe the surface, by penetrating to a depth defined by the wavelength of the focused waves. The validity of this concept is shown in the presence of gradual and distributed damage in concrete by comparing actual results with a reference nonlinear measurement and X ray tomography images.
All-optical signal processing in quadratic nonlinear materials
DEFF Research Database (Denmark)
Johansen, Steffen Kjær
2002-01-01
of materials with a second order nonlinearity, the so-called X(2) materials, is faster and stronger than that of more conventional materials with a cubic nonlinearity. The X(2) materials support spatial solitons consisting of two coupled components, the fundamental wave (FW) and its second harmonic (SH......). During this project the interaction between such spatial solitons has been investigated theoretically through perturbation theory and experimentally via numerical simulations. The outcome of this research isnew theoretical tools for quantitatively predicting the escape angle, i.e. the angle of incidence...... and exploitation of these cubic nonlinearities in two-period QPM wave-guides has been another area of investigation. Introducing the second period might make practical engineering of the nonlinearities possible. A major result is the discovery that cubic nonlinearities leads to an enhancement of the bandwidth...
Nonlinear constitutive behavior of ferroelectric materials
Institute of Scientific and Technical Information of China (English)
2008-01-01
The ferroelectric specimen is considered as an aggregation of many randomly oriented domains. According to this mechanism,a multi-domain mechanical model is developed in this paper. Each domain is represented by one element. The applied stress and electric field are taken to be the stress and electric field in the formula of the driving force of domain switching for each element in the specimen. It means that the macroscopic switching criterion is used for calculating the volume fraction of domain switching for each element. By using the hardening relation between the driving force of domain switching and the volume fraction of domain switching calibrated,the volume fraction of domain switching for each element is calculated. Substituting the stress and electric field and the volume fraction of domain switching into the constitutive equation of ferroelectric material,one can easily get the strain and electric displacement for each element. The macroscopic behavior of the ferroelectric specimen is then directly calculated by volume averaging. Mean-while,the nonlinear finite element analysis for the ferroelectric specimen is carried out. In the finite element simulation,the volume fraction of domain switching for each element is calculated by using the same method mentioned above. The in-teraction between different elements is taken into account in the finite element simulation and the local stress and electric field for each element is obtained. The macroscopic behavior of the specimen is then calculated by volume averaging. The computation results involve the electric butterfly shaped curves of axial strain versus the axial electric field and the hysteresis loops of electric displacement versus the electric field for ferroelectric specimens under the uniaxial coupled stress and electric field loading. The present theoretical prediction agrees reasonably with the experimental results.
Lohar, Hareram; Mitra, Anirban; Sahoo, Sarmila
2016-09-01
In the present study non-linear free vibration analysis is performed on a tapered Axially Functionally Graded (AFG) beam resting on an elastic foundation with different boundary conditions. Firstly the static problem is carried out through an iterative scheme using a relaxation parameter and later on the subsequent dynamic problem is solved as a standard eigen value problem. Minimum potential energy principle is used for the formulation of the static problem whereas for the dynamic problem Hamilton's principle is utilized. The free vibrational frequencies are tabulated for different taper profile, taper parameter and foundation stiffness. The dynamic behaviour of the system is presented in the form of backbone curves in dimensionless frequency-amplitude plane.
On Exact Controllability of Networks of Nonlinear Elastic Strings in 3-Dimensional Space
Institute of Scientific and Technical Information of China (English)
Günter R. LEUGERING; E. J. P. Georg SCHMIDT
2012-01-01
This paper concerns a system of nonlinear wave equations describing the vibrations of a 3-dimensional network of elastic strings.The authors derive the equations and appropriate nodal conditions,determine equilibrium solutions,and,by using the methods of quasilinear hyperbolic systems,prove that for tree networks the natural initial,bound-ary value problem has classical solutions existing in neighborhoods of the "stretched" equilibrium solutions.Then the local controllability of such networks near such equilibrium configurations in a certain specified time interval is proved.Finally,it is proved that,given two different equilibrium states satisfying certain conditions,it is possible to control the network from states in a small enough neighborhood of one equilibrium to any state in a suitable neighborhood of the second equilibrium over a sufficiently large time interval.
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.
Geometric method for stability of non-linear elastic thin shells
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...
A sandwich bar element for geometric nonlinear thermo-elastic analysis
Directory of Open Access Journals (Sweden)
Murín J.
2008-11-01
Full Text Available This contribution deals with a two-node straight sandwich composite bar element with constant double symmetric rectangular cross-sectional area. This new bar element (based on the non-linear second-order theory is intended to perform the non-incremental full geometric non-linear analysis. Stiffness matrix of this composite bar contains transfer constants, which accurately describe polynomial uniaxial variation of the material thermo-physical properties.In the numerical experiments the weak coupled thermo-structural geometric non-linear problem was solved. Obtained results were compared with several analyses made by ANSYS programme. Findings show good accuracy of this new finite element. The results obtained with this element do not depend on the element mesh density.
THE STUDY OF HYPER ELASTIC MATERIAL CHARACTERISTICS IN CASE OF THIN ROD STRUCTURE CALCULATION
Directory of Open Access Journals (Sweden)
Mr. Mikhail R. Petrov
2016-12-01
Full Text Available The article investigates the deformation hyper elastic material characteristics, i.e. rubber, and determines a mathematical model to calculate the characteristics of test material structure.
1992-02-13
niobate and absolute measurements of nonlinear optical coefficients of six different commonly used nonlinear optical materials. The refractometry data for...applied radiation and is now an established technology for Nd:YAG lasers. Optical parametric oscillation and amplification provide a method of generating...continuously tunable output -3- The relative advantages of nonlinear optical frequency conversion compared to other methods for the generation of near
Tetherless mobile micrograsping using a magnetic elastic composite material
Zhang, Jiachen; Diller, Eric
2016-11-01
In this letter, we propose and characterize a new type of tetherless mobile microgripper for micrograsping that is made of a magnetic elastic composite material. Its magnetically-programmable material and structures make it the first three-dimensional (3D) mobile microgripper that is directly actuated and controlled by magnetic forces and torques. With a symmetric four-limb structure, the microgripper is 3.5 mm long from tip to tip when it is open and 30 μm thick. It forms an approximate 700 μm cube when it is closed. The orientation and 3D shape of the microgripper are determined by the direction and strength of the applied magnetic field, respectively. As a mobile device, the microgripper can be moved through aqueous environments for precise grasping and transportation of micro-objects, pulled by magnetic gradients directly or rolled in rotating magnetic fields. The deformation of the microgripper under magnetic actuation is characterized by modeling and confirmed experimentally. Being directly controlled by magnetic forces and torques, the microgripper is easier and more intuitive to control than other magnetic microgrippers that require other inputs such as thermal and chemical responses. In addition, the microgripper is capable of performing fast repeatable grasping motions, requiring no more than 25 ms to change from fully open to fully closed in water at room temperature. As a result of its large-amplitude 3D deformation, the microgripper can accommodate cargoes with a wide range of geometries and dimensions. A pick-and-place experiment demonstrates the efficacy of the microgripper and its potentials in biomedical, microfluidic, and microrobotic applications.
The Structural Design for Hyper-Elastic Materials Using Cfd Analysis
Park, Young-Chul; Jung, Dae-Seok; Kim, Ji-Young
The usage of hyper-elastic material has been increasing gradually and its application has extended over a wide range of various industries. Implementing experimental and numerical methods, performance of hyper-elastic material can be predicted. Proposed in this study is the process by which the material coefficient can be obtained and applied to seat-ring of butterfly valve. Considering the mechanical properties and material conditions, optimum model was constructed and applied to obtain the coefficient by using CFD analysis.
Directory of Open Access Journals (Sweden)
Kim Gaik Tay
2010-04-01
Full Text Available In the present work, by considering the artery as a prestressed thin-walled elastic tube with a symmetrical stenosis and the blood as an incompressible viscous fluid, we have studied the amplitude modulation of nonlinear waves in such a composite medium through the use of the reductive perturbation method [23]. The governing evolutions can be reduced to the dissipative non-linear Schrodinger (NLS equation with variable coefficient. The progressive wave solution to the above non-linear evolution equation is then sought.
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.
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.
柴田, 信一; 曹, 勇; 福本, 功; Shibata, Shin-ichi; Cao, Yong; Fukumoto, Isao
2005-01-01
Bending modulus of elasticity of the composite material from bagasse fiber (remains after sugar cane squeezed) and biodegradable resin was investigated in view of the content of bagasse fiber and the fiber length. The result was validated by short fiber strengthen theory. The result is as followings. Bending modulus of elasticity increased with increasing the content of bagasse fiber. The increase of Bending modulus of elasticity is predicted by short fiber strengthen theory incorporated with...
Molecular and crystal design of nonlinear optical organic materials
Energy Technology Data Exchange (ETDEWEB)
Suponitsky, Kirill Yu; Antipin, Mikhail Yu [A.N. Nesmeyanov Institute of Organoelement Compounds, Russian Academy of Sciences, Moscow (Russian Federation); Timofeeva, Tatiana V [Department of Chemistry, New Mexico Highlands University (United States)
2006-06-30
The results of theoretical and experimental studies on the second-order molecular and crystal nonlinear optical susceptibilities of organic and several classes of organoelement compounds are summarised. Modern methods used in these studies are briefly characterised, their advantages and drawbacks are outlined as regards their application to the systematic search for efficient nonlinear optical materials. Recent achievements and the main challenges in the field are thoroughly discussed and an optimum algorithm of the design of such materials is proposed.
Organic/Organometallic Hybrids as Broadband Nonlinear Transmission Materials
2010-06-01
property correlation in organometallic complexes in order to develop broadband nonlinear transmission materials . To realize this goal, we have...platinum complexes and 10 zinc phthalocyanine derivatives provided by collaborators in China. From these studies, we have discovered that in order to...in the near-IR region still limited their application as broadband nonlinear absorbing materials . To solve this problem, two approaches were
Jiang, Yi; Li, Guo-Yang; Qian, Lin-Xue; Hu, Xiang-Dong; Liu, Dong; Liang, Si; Cao, Yanping
2015-02-01
Dynamic elastography has become a new clinical tool in recent years to characterize the elastic properties of soft tissues in vivo, which are important for the disease diagnosis, e.g., the detection of breast and thyroid cancer and liver fibrosis. This paper investigates the supersonic shear imaging (SSI) method commercialized in recent years with the purpose to determine the nonlinear elastic properties based on this promising technique. Particularly, we explore the propagation of the shear wave induced by the acoustic radiation force in a stressed hyperelastic soft tissue described via the Demiray-Fung model. Based on the elastodynamics theory, an analytical solution correlating the wave speed with the hyperelastic parameters of soft tissues is first derived. Then an inverse approach is established to determine the hyperelastic parameters of biological soft tissues based on the measured wave speeds at different stretch ratios. The property of the inverse method, e.g., the existence, uniqueness and stability of the solution, has been investigated. Numerical experiments based on finite element simulations and the experiments conducted on the phantom and pig livers have been employed to validate the new method. Experiments performed on the human breast tissue and human heel fat pads have demonstrated the capability of the proposed method for measuring the in vivo nonlinear elastic properties of soft tissues. Generalization of the inverse analysis to other material models and the implication of the results reported here for clinical diagnosis have been discussed. Copyright © 2014 Elsevier B.V. All rights reserved.
Nagode, Marko; Šeruga, Domen
An approach is presented that enables the calculation of elastic strain energy in linear and nonlinear elastic solids during arbitrary thermomechanical load cycles. The approach uses the simple fact that the variation of both strain and complementary energies always forms a rectangular shape in stress-strain space, hence integration is no longer required to calculate the energy. Furthermore, the approach considers the mean stress effect so that predictions of fatigue damage are more realistically representative of real-life experimental observations. By doing so, a parameter has been proposed to adjust the mean stress effect. This parameter α is based on the well-known Smith-Watson-Topper energy criterion, but allows consideration of other arbitrary mean stress effects, e.g. the Bergmann type criterion. The approach has then been incorporated into a numerical method which can be applied to uniaxial and multiaxial, proportional and non-proportional loadings to predict fatigue damage. The end result of the method is the cyclic evolution of accumulated damage. Numerical examples show how the method presented in this paper could be applied to a nonlinear elastic material.
A Large Deformation Model for the Elastic Moduli of Two-dimensional Cellular Materials
Institute of Scientific and Technical Information of China (English)
HU Guoming; WAN Hui; ZHANG Youlin; BAO Wujun
2006-01-01
We developed a large deformation model for predicting the elastic moduli of two-dimensional cellular materials. This large deformation model was based on the large deflection of the inclined members of the cells of cellular materials. The deflection of the inclined member, the strain of the representative structure and the elastic moduli of two-dimensional cellular materials were expressed using incomplete elliptic integrals. The experimental results show that these elastic moduli are no longer constant at large deformation, but vary significantly with the strain. A comparison was made between this large deformation model and the small deformation model proposed by Gibson and Ashby.
Energy Technology Data Exchange (ETDEWEB)
Cho, Seung Hyun; Park, Choon Su; Seo, Dae Cheol [Korea Research Institute of Standards and Science, Daejeon (Korea, Republic of); Cho, Seung Wan [Dept. of Mechanical Engineering, Sunngkyunkwan University, Suwon (Korea, Republic of); Jhang, Kyung Young [Dept. of Mechanical Engineering, Hanyang University, Seoul (Korea, Republic of)
2014-08-15
Recently, much attention has been paid to nonlinear ultrasonic technology as a potential tool to assess hidden damages that cannot be detected by conventional ultrasonic testing. One nonlinear ultrasonic technique is measurement of the resonance frequency shift, which is based on the hysteresis of the material elasticity. Sophisticated measurement of resonance frequency is required, because the change in resonance frequency is usually quite small. In this investigation, the nonlinear electromagnetic acoustic resonance (NEMAR) method was employed. The NEMAR method uses noncontact electromagnetic acoustic transducers (EMATs) in order to minimize the effect of the transducer on the frequency response of the object. Aluminum plate specimens that underwent three point bending fatigue were tested witha shear wave EMAT. The hysteretic nonlinear parameter α, a key indicator of damage, was calculated from the resonance frequency shift at several levels of input voltage. The hysteretic nonlinear parameter of a damaged sample was compared to that of an intact one, showing a difference in the values.
Directory of Open Access Journals (Sweden)
Şeref Doğuşcan Akbaş
2013-01-01
Full Text Available Geometrically nonlinear static analysis of edge cracked cantilever Timoshenko beams composed of functionally graded material (FGM subjected to a nonfollower transversal point load at the free end of the beam is studied with large displacements and large rotations. Material properties of the beam change in the height direction according to exponential distributions. The cracked beam is modeled as an assembly of two subbeams connected through a massless elastic rotational spring. In the study, the finite element of the beam is constructed by using the total Lagrangian Timoshenko beam element approximation. The nonlinear problem is solved by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. The convergence study is performed for various numbers of finite elements. In the study, the effects of the location of crack, the depth of the crack, and various material distributions on the nonlinear static response of the FGM beam are investigated in detail. Also, the difference between the geometrically linear and nonlinear analysis of edge cracked FGM beam is investigated in detail.
Polydimethylsiloxane as an elastic material applied in a capacitive accelerometer
Lötters, Joost Conrad; Lotters, Joost Conrad; Olthuis, Wouter; Veltink, Petrus H.; Bergveld, Piet
1996-01-01
Polydimethylsiloxane is a silicone rubber. It has a unique flexibility, resulting in one of the lowest glass-transition temperatures of any polymer. Furthermore, it shows a low elasticity change versus temperature, a high thermal stability, chemical inertness, dielectric stability, shear stability
Polydimethylsiloxane as an elastic material applied in a capacitive accelerometer
Lotters, Joost C.; Olthuis, Wouter; Veltink, Peter H.; Bergveld, Piet
1996-01-01
Polydimethylsiloxane is a silicone rubber. It has a unique flexibility, resulting in one of the lowest glass-transition temperatures of any polymer. Furthermore, it shows a low elasticity change versus temperature, a high thermal stability, chemical inertness, dielectric stability, shear stability a
A Strategy for the Development of Macromolecular Nonlinear Optical Materials
1990-01-01
obsolete. SECURITY CLASSIFICATION OF THIS PAGE STRATEGY FOR THE DEVELOPMENT OF MACROMOLECULAR NONLINEAR OPTICAL MATERIALS Braja K. Mandala , Jan-Chan...materials is significantly different from the conventional inorganic NLO materials. The extent of second order (quadratic) NLO effect such as second...is a criterion of paramount importance for a large second order electro-optic effect in organic materials 8 ,9 . The most common approach to obtain
Pouya, Ahmad
2010-01-01
Several families of elastic anisotropies were introduced by Saint Venant (1863) for which the polar diagram of elastic parameters in different directions of the material (indicator surface) are ellipsoidal. These families recover a large variety of models introduced in recent years for damaged materials or as effective modulus of heterogeneous materials. On the other hand, ellipsoidal anisotropy has been used as a guideline in phenomenological modeling of materials. A question that then naturally arises is to know in which conditions the assumption that some indicator surfaces are ellipsoidal allows one to entirely determine the elastic constants. This question has not been rigorously studied in the literature. In this paper, first several basic classes of ellipsoidal anisotropy are presented. Then the problem of determination of the elastic parameters from indicator surfaces is discussed in several basic cases that can occur in phenomenological modelling. Finally the compatibility between the assumption of e...
Design of advanced materials for linear and nonlinear dynamics
DEFF Research Database (Denmark)
Frandsen, Niels Morten Marslev
The primary catalyst of this PhD project has been an ambition to design advanced materials and structural systems including, and possibly even exploiting, nonlinear phenomena such as nonlinear modal interaction leading to energy conversion between modes. An important prerequisite for efficient...... design is accurate and somewhat simple analysis tools, as well as a fundamental understanding of the physical phenomena responsible for the relevant effects. The emphasis of this work lies primarily in the investigation of various advanced material models, developing the necessary analytical tools...... to reveal the fundamental dynamic characteristics and thus the relevant design parameters.The thesis is built around the characterization of two one-dimensional, periodic material systems. The first is a nonlinear mass-spring chain with periodically varying material properties, representing a simple...
Nonlinear normal modes of a two degree of freedom oscillator with a bilateral elastic stop
Moussi, El Hadi; Cochelin, Bruno; Nistor, I
2013-01-01
A study of the non linear modes of a two degree of freedom mechanical system with bilateral elastic stop is considered. The issue related to the non-smoothness of the impact force is handled through a regularization technique. In order to obtain the Nonlinear Normal Mode (NNM), the harmonic balance method with a large number of harmonics, combined with the asymptotic numerical method, is used to solve the regularized problem. These methods are present in the software "package" MANLAB. The results are validated from periodic orbits obtained analytically in the time domain by direct integration of the non regular problem. The two NNMs starting respectively from the two linear normal modes of the associated underlying linear system are discussed. The energy-frequency plot is used to present a global vision of the behavior of the modes. The dynamics of the modes are also analyzed comparing each periodic orbits and modal lines. The first NNM shows an elaborate dynamics with the occurrence of multiple impacts per p...
Will Nonlinear Backcalculation Help?
DEFF Research Database (Denmark)
Ullidtz, Per
2000-01-01
demonstrates, that treating the subgrade as a nonlinear elastic material, can result in more realistic moduli and a much better agreement between measured and calculated stresses and strains.The response of nonlinear elastic materials can be calculated using the Finite Element Method (FEM). A much simpler...... approach is to use the Method of Equivalent Thicknesses (MET), modified for a nonlinear subgrade. The paper includes an example where moduli backcalculated using FEM, linear elastic theory and MET are compared. Stresses and strains predicted by the three methods are also compared to measured values...
Application of Novel Nonlinear Optical Materials to Optical Processing
Banerjee, Partha P.
1999-01-01
We describe wave mixing and interactions in nonlinear photorefractive polymers and disodium flourescein. Higher diffracted orders yielding forward phase conjugation can be generated in a two-wave mixing geometry in photorefractive polymers, and this higher order can be used for image edge enhancement and correlation. Four-wave mixing and phase conjugation is studied using nonlinear disodium floureschein, and the nature and properties of gratings written in this material are investigated.
Directory of Open Access Journals (Sweden)
P. A. Johnson
1996-01-01
Full Text Available Nonlinear elastic response in rock is established as a robust and representative characteristic rock rather than a curiosity. We show measurements of this behaviour from a variety of experiments on rock taken over many orders of magnitude in strain and frequency. The evidence leads to a pattern of unifying behaviour in rock: (1 Nonlinear response in rock is ubiquitous. (2 The response takes place over a large frequency interval (dc to 105 kHz at least. (3 The response not only occurs, as is commonly appreciated, large strains but also at small strains where this behaviour and the manifestations of this behaviour are commonly disregarded.
Polydimethylsiloxane as an elastic material applied in a capacitive accelerometer
Lötters, Joost Conrad; Lotters, Joost Conrad; Olthuis, Wouter; Veltink, Petrus H.; Bergveld, Piet
1996-01-01
Polydimethylsiloxane is a silicone rubber. It has a unique flexibility, resulting in one of the lowest glass-transition temperatures of any polymer. Furthermore, it shows a low elasticity change versus temperature, a high thermal stability, chemical inertness, dielectric stability, shear stability and high compressibility. Because of its high flexibility and the very low drift of its properties with time and temperature, polydimethylsiloxane could be well suited for mechanical sensors, such a...
Penta, Raimondo; Gerisch, Alf
2017-01-01
The classical asymptotic homogenization approach for linear elastic composites with discontinuous material properties is considered as a starting point. The sharp length scale separation between the fine periodic structure and the whole material formally leads to anisotropic elastic-type balance equations on the coarse scale, where the arising fourth rank operator is to be computed solving single periodic cell problems on the fine scale. After revisiting the derivation of the problem, which here explicitly points out how the discontinuity in the individual constituents' elastic coefficients translates into stress jump interface conditions for the cell problems, we prove that the gradient of the cell problem solution is minor symmetric and that its cell average is zero. This property holds for perfect interfaces only (i.e., when the elastic displacement is continuous across the composite's interface) and can be used to assess the accuracy of the computed numerical solutions. These facts are further exploited, together with the individual constituents' elastic coefficients and the specific form of the cell problems, to prove a theorem that characterizes the fourth rank operator appearing in the coarse-scale elastic-type balance equations as a composite material effective elasticity tensor. We both recover known facts, such as minor and major symmetries and positive definiteness, and establish new facts concerning the Voigt and Reuss bounds. The latter are shown for the first time without assuming any equivalence between coarse and fine-scale energies ( Hill's condition), which, in contrast to the case of representative volume elements, does not identically hold in the context of asymptotic homogenization. We conclude with instructive three-dimensional numerical simulations of a soft elastic matrix with an embedded cubic stiffer inclusion to show the profile of the physically relevant elastic moduli (Young's and shear moduli) and Poisson's ratio at increasing (up to
Penta, Raimondo; Gerisch, Alf
2016-08-01
The classical asymptotic homogenization approach for linear elastic composites with discontinuous material properties is considered as a starting point. The sharp length scale separation between the fine periodic structure and the whole material formally leads to anisotropic elastic-type balance equations on the coarse scale, where the arising fourth rank operator is to be computed solving single periodic cell problems on the fine scale. After revisiting the derivation of the problem, which here explicitly points out how the discontinuity in the individual constituents' elastic coefficients translates into stress jump interface conditions for the cell problems, we prove that the gradient of the cell problem solution is minor symmetric and that its cell average is zero. This property holds for perfect interfaces only (i.e., when the elastic displacement is continuous across the composite's interface) and can be used to assess the accuracy of the computed numerical solutions. These facts are further exploited, together with the individual constituents' elastic coefficients and the specific form of the cell problems, to prove a theorem that characterizes the fourth rank operator appearing in the coarse-scale elastic-type balance equations as a composite material effective elasticity tensor. We both recover known facts, such as minor and major symmetries and positive definiteness, and establish new facts concerning the Voigt and Reuss bounds. The latter are shown for the first time without assuming any equivalence between coarse and fine-scale energies (Hill's condition), which, in contrast to the case of representative volume elements, does not identically hold in the context of asymptotic homogenization. We conclude with instructive three-dimensional numerical simulations of a soft elastic matrix with an embedded cubic stiffer inclusion to show the profile of the physically relevant elastic moduli (Young's and shear moduli) and Poisson's ratio at increasing (up to
2014-04-01
irreversible deformation, the three-term model allows for residual elastic strains— including dilatation observed in experiments and atomic simulations...residual elastic strains—including dilatation observed in experiments and atomic simulations—not addressed by conventional two-term crystal plasticity...gradient for an element of crystalline material. For simplicity, thermal effects are omitted, gliding dislocations are the only kind of defect considered
Measurement of third-order elastic constants and applications to loaded structural materials.
Takahashi, Sennosuke; Motegi, Ryohei
2015-01-01
The objective of this study is to obtain the propagation velocity of an elastic wave in a loaded isotropic solid and to show the usefulness of the third-order elastic constant in determining properties of practical materials. As is well known, the infinitesimal elastic theory is unable to express the influence of stress on elastic wave propagating in loaded materials. To solve this problem, the authors derive an equation of motion for elastic wave in a finitely deformed state and use the Lagrangian description where the state before deformation is used as a reference, and Murnaghans finite deformation theory for the unidirectional deformed isotropic solid. Ordinary derivatives were used for the mathematical treatment and although the formulas are long the content is simple. The theory is applied to the measurement of the third-order elastic constants of common steels containing carbon of 0.22 and 0.32 wt%. Care is taken in preparing specimens to precise dimensions, in properly adhering of transducer to the surface of the specimen, and in having good temperature control during the measurements to obtain precise data. As a result, the stress at various sites in the structural materials could be estimated by measuring the elastic wave propagation times. The results obtained are graphed for illustration.
Organic materials with nonlinear optical properties
Stupp, Samuel I.; Son, Sehwan; Lin, Hong-Cheu
1995-01-01
The present invention is directed to organic materials that have the ability to double or triple the frequency of light that is directed through the materials. Particularly, the present invention is directed to the compound 4-[4-(2R)-2-cyano-7-(4'-pentyloxy-4-biphenylcarbonyloxy)phenylheptylidene) phenylcarbonyloxy]benzaldehyde, which can double the frequency of light that is directed through the compound. The invention is also directed to the compound (12-hydroxy-5,7-dodecadiynyl) 4'-[(4'-pentyloxy-4-biphenyl)carbonyloxy]-4-biphenylcarboxylate, and its polymeric form. The polymeric form can triple the frequency of light directed through it.
Polydimethylsiloxane as an elastic material applied in a capacitive accelerometer
Lötters, Joost C.; Olthuis, Wouter; Veltink, Peter H.; Bergveld, Piet
1996-03-01
Polydimethylsiloxane is a silicone rubber. It has a unique flexibility, resulting in one of the lowest glass-transition temperatures of any polymer. Furthermore, it shows a low elasticity change versus temperature, a high thermal stability, chemical inertness, dielectric stability, shear stability and high compressibility. Because of its high flexibility and the very low drift of its properties with time and temperature, polydimethylsiloxane could be well suited for mechanical sensors, such as accelerometers. A novel capacitive accelerometer with polydimethylsiloxane layers as springs has been realized. The obtained measurement results are promising and show a good correspondence with the theoretical values.
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
Materials for Nonlinear Optics Chemical Perspectives
1991-01-01
introduced into LB muldilayers built from 1/1 mixtures with an amphiphilic cyclodextrin . The polyenic chains are again perpendicular to the substrate...molecules in inorganic matrices. The encapsulated molecules can be used to induce new optical properties in the material or to probe the changes at the...glass are discussed here. First, laser dyes including rhodamines and coumarins are encapsulated . The resulting doped gel-glasses exhibit optical gain
非线弹性索对系泊系统性能的影响%The impact of nonlinear elastic cable on the performance of mooring system
Institute of Scientific and Technical Information of China (English)
张欣欣; 郭小天; 张亮
2014-01-01
随着船舶的大型化、海洋平台的多样化以及其工作水深的不断加深，锚泊设计过程中锚泊线的成分也由设计初期的单一化向多成分化发展。材料的多样化更是为锚泊设计提供了丰富的选择空间，将对加入非线弹性拉伸材料的系泊线进行数值模拟分析，采用分段外推-校正的方法，计算分析了相同水深下非线弹性拉伸材料对系泊系统变形、张力以及刚度的影响，并且进一步研究了不同水深的情况。结果表明，加入非线弹性拉伸的材料能够有效地降低系泊线张力及自身刚度，加入此种材料的组合系泊系统更适用于浅水。%With the enlarging of ship scale, diversification of offshore platform and increasing of water depth, the composition of mooring line is developing toward diversification from single component at the early stage of the design, and at the same time, diversified types of mooring line material provide more choices for the mooring design. In this paper numerical simulation analysis is conducted on the mooring line added into non-linear elastic stretch material, using the piecewise extrapolating-correction method. The influence of non-linear elastic stretch materials on the mooring system performance such as deformation, tension and rigidity is analyzed under the same water depth. And the application in the situation of different water depths is further studied. The results show that, non-linear elastic stretching of the material can effectively reduce the tension of mooring line and its stiffness, in addition, the research indicated that this kind of material combined with mooring system is more suitable for shallow water.
Effects of nonlinear muscle elasticity on pelvic floor mechanics during vaginal childbirth.
Li, Xinshan; Kruger, Jennifer A; Nash, Martyn P; Nielsen, Poul M F
2010-11-01
The role of the pelvic floor soft tissues during the second stage of labor, particularly the levator ani muscle, has attracted much interest recently. It has been postulated that the passage of the fetal head through the pelvis may cause excessive stretching of the levator ani muscle, which may lead to pelvic floor dysfunction and pelvic organ prolapse later in life. In order to study the complex biomechanical interactions between the levator ani muscle and the fetal head during the second stage of labor, finite element models have been developed for quantitative analysis of this process. In this study we have simulated vaginal delivery using individual-specific anatomical computer models of the pelvic floor interacting with a fetal head model with minimal restrictions placed upon its motion. Two constitutive relations were considered for the levator ani muscle (of exponential and neo-Hookean forms). For comparison purposes, the exponential relation was chosen to exhibit much greater stiffening at higher strains beyond the range of the experimental data. We demonstrated that increased nonlinearity in the elastic response of the tissues leads to considerably higher (56%) estimated force required for delivery, accompanied by a more homogeneous spatial distribution of maximum principal stretch ratio across the muscle. These results indicate that the form of constitutive relation beyond the presently available experimental data markedly affects the estimated function of the levator ani muscle during vaginal delivery, due to the large strains that occur. Further experimental data at higher strains are necessary in order to more reliably characterize the constitutive behavior required for modeling vaginal childbirth.
Stress effects on the elastic properties of amorphous polymeric materials
Energy Technology Data Exchange (ETDEWEB)
Caponi, S., E-mail: silvia.caponi@cnr.it, E-mail: silvia.corezzi@unipg.it [Istituto Officina dei Materiali del CNR (CNR-IOM) - Unità di Perugia, c/o Dipartimento di Fisica e Geologia, Perugia I-06100 (Italy); Corezzi, S., E-mail: silvia.caponi@cnr.it, E-mail: silvia.corezzi@unipg.it [Dipartimento di Fisica e Geologia, Università di Perugia, Via A. Pascoli, I-06100 Perugia (Italy); CNR-ISC (Istituto dei Sistemi Complessi), c/o Università di Roma “LaSapienza,” Piazzale A. Moro 2, I-00185 Roma (Italy); Mattarelli, M. [NiPS Laboratory, Dipartimento di Fisica e Geologia, Università di Perugia, Via A. Pascoli, I-06100 Perugia (Italy); Fioretto, D. [Dipartimento di Fisica e Geologia, Università di Perugia, Via A. Pascoli, I-06100 Perugia (Italy)
2014-12-07
Brillouin light scattering measurements have been used to study the stress induced modification in the elastic properties of two glass forming polymers: polybutadiene and epoxy-amine resin, prototypes of linear and network polymers, respectively. Following the usual thermodynamic path to the glass transition, polybutadiene has been studied as a function of temperature from the liquid well into the glassy phase. In the epoxy resin, the experiments took advantage of the system ability to reach the glass both via the chemical vitrification route, i.e., by increasing the number of covalent bonds among the constituent molecules, as well as via the physical thermal route, i.e., by decreasing the temperature. Independently from the particular way chosen to reach the glassy phase, the measurements reveal the signature of long range tensile stresses development in the glass. The stress presence modifies both the value of the sound velocities and their mutual relationship, so as to break the generalized Cauchy-like relation. In particular, when long range stresses, by improvise sample cracking, are released, the frequency of longitudinal acoustic modes increases more than 10% in polybutadiene and ∼4% in the epoxy resin. The data analysis suggests the presence of at least two different mechanisms acting on different length scales which strongly affect the overall elastic behaviour of the systems: (i) the development of tensile stress acting as a negative pressure and (ii) the development of anisotropy which increases its importance deeper and deeper in the glassy state.
Dai, H H
2009-01-01
Buckling and barrelling instabilities in the uniaxial compressions of an elastic rectangle have been studied by many authors under lubricated end conditions. However, in practice it is very difficult to realize such conditions due to friction. Here, we study the compressions of a two-dimensional nonlinearly elastic rectangle under clamped end conditions.
The Overall Response of Composite Materials Undergoing Large Elastic Deformations
1990-06-13
by Willis (1990), and the new results are found to be superior . In particular, the physically unrealistic discontinuous behavior of Willis’ model...6, 1990. Instituto de Investigaciones en Matematicas Applicadas y en Systemas, Universidad Nacional Autonoma de Mexico, Mexico City, July 1990...energy. O. the other hand, the nonlinear bounds corresponding to the Hashin- Shtrikman bounds for the linear isotropic composite turn out to be superior
Lee, Hyung Jin; Lee, Heung Son; Ma, Pyung Sik; Kim, Yoon Young
2016-09-01
In this paper, the scattering (S-) parameter retrieval method is presented specifically for anisotropic elastic metamaterials; so far, no retrieval has been accomplished when elastic metamaterials exhibit fully anisotropic behavior. Complex constitutive property and intrinsic scattering behavior of elastic metamaterials make their characterization far more complicated than that for acoustic and electromagnetic metamaterials. In particular, elastic metamaterials generally exhibit anisotropic scattering behavior due to higher scattering modes associated with shear deformation. They also exhibit nonlocal responses to some degrees, which originate from strong multiple scattering interactions even in the long wavelength limit. Accordingly, the conventional S-parameter retrieval methods cannot be directly used for elastic metamaterials, because they determine only the diagonal components in effective tensor property. Also, the conventional methods simply use the analytic inversion formulae for the material characterization so that inherent nonlocality cannot be taken into account. To establish a retrieval method applicable to anisotropic elastic metamaterials, we propose an alternative S-parameter method to deal with full anisotropy of elastic metamaterials. To retrieve the whole effective anisotropic parameter, we utilize not only normal but also oblique wave incidences. For the retrieval, we first retrieve the ratio of the effective stiffness tensor to effective density and then determine the effective density. The proposed retrieval method is validated by characterizing the effective material parameters of various types of non-resonant anisotropic metamaterials. It is found that the whole effective parameters are retrieved consistently regardless of used retrieval conditions in spite of inherent nonlocality.
CSIR Research Space (South Africa)
De Beer, Morris
2008-07-01
Full Text Available during tensile (or compressive) tests conducted on a sample of the material. Young’s Modulus is named after Thomas Young, the 18th Century British scientist. The SI unit of modulus of elasticity, E is the pascal. Given the large values typical of many... stream_source_info De Beer1_2008.pdf.txt stream_content_type text/plain stream_size 31159 Content-Encoding UTF-8 stream_name De Beer1_2008.pdf.txt Content-Type text/plain; charset=UTF-8 1 Some fundamental definitions...
A Unified Guide to Two Opposite Size Effects in Nano Elastic Materials
Institute of Scientific and Technical Information of China (English)
TANG Yi-Zhe; ZHENG Zhi-Jun; XIA Meng-Fen; BAI Yi-Long
2009-01-01
The microstructural variation near surface of nano elastic materials is analyzed based on different potentials.The atomic/molecular mechanism underlying the variation and its effect on elastic modulus are such that the nature of long-range interactions(attractive or repulsive)in the atomic/molecular potentials essentially governs the variation near surface(looser or tighter)and results in two opposite size effects(decreasing or increasing modulus)with decreasing size.
Detection of electromagnetic radiation using nonlinear materials
Energy Technology Data Exchange (ETDEWEB)
Hwang, Harold Y.; Liu, Mengkun; Averitt, Richard D.; Nelson, Keith A.; Sternbach, Aaron; Fan, Kebin
2016-06-14
An apparatus for detecting electromagnetic radiation within a target frequency range is provided. The apparatus includes a substrate and one or more resonator structures disposed on the substrate. The substrate can be a dielectric or semiconductor material. Each of the one or more resonator structures has at least one dimension that is less than the wavelength of target electromagnetic radiation within the target frequency range, and each of the resonator structures includes at least two conductive structures separated by a spacing. Charge carriers are induced in the substrate near the spacing when the resonator structures are exposed to the target electromagnetic radiation. A measure of the change in conductivity of the substrate due to the induced charge carriers provides an indication of the presence of the target electromagnetic radiation.
Surface Wave Speed of Functionally Graded Magneto-Electro-Elastic Materials with Initial Stresses
Directory of Open Access Journals (Sweden)
Li Li
2014-09-01
Full Text Available The shear surface wave at the free traction surface of half- infinite functionally graded magneto-electro-elastic material with initial stress is investigated. The material parameters are assumed to vary ex- ponentially along the thickness direction, only. The velocity equations of shear surface wave are derived on the electrically or magnetically open circuit and short circuit boundary conditions, based on the equations of motion of the graded magneto-electro-elastic material with the initial stresses and the free traction boundary conditions. The dispersive curves are obtained numerically and the influences of the initial stresses and the material gradient index on the dispersive curves are discussed. The investigation provides a basis for the development of new functionally graded magneto-electro-elastic surface wave devices.
Belli, Renan; Wendler, Michael; de Ligny, Dominique; Cicconi, Maria Rita; Petschelt, Anselm; Peterlik, Herwig; Lohbauer, Ulrich
2017-01-01
A deeper understanding of the mechanical behavior of dental restorative materials requires an insight into the materials elastic constants and microstructure. Here we aim to use complementary methodologies to thoroughly characterize chairside CAD/CAM materials and discuss the benefits and limitations of different analytical strategies. Eight commercial CAM/CAM materials, ranging from polycrystalline zirconia (e.max ZirCAD, Ivoclar-Vivadent), reinforced glasses (Vitablocs Mark II, VITA; Empress CAD, Ivoclar-Vivadent) and glass-ceramics (e.max CAD, Ivoclar-Vivadent; Suprinity, VITA; Celtra Duo, Dentsply) to hybrid materials (Enamic, VITA; Lava Ultimate, 3M ESPE) have been selected. Elastic constants were evaluated using three methods: Resonant Ultrasound Spectroscopy (RUS), Resonant Beam Technique (RBT) and Ultrasonic Pulse-Echo (PE). The microstructures were characterized using Scanning Electron Microscopy (SEM), Energy Dispersive X-ray Spectroscopy (EDX), Raman Spectroscopy and X-ray Diffraction (XRD). Young's modulus (E), Shear modulus (G), Bulk modulus (B) and Poisson's ratio (ν) were obtained for each material. E and ν reached values ranging from 10.9 (Lava Ultimate) to 201.4 (e.max ZirCAD) and 0.173 (Empress CAD) to 0.47 (Lava Ultimate), respectively. RUS showed to be the most complex and reliable method, while the PE method the easiest to perform but most unreliable. All dynamic methods have shown limitations in measuring the elastic constants of materials showing high damping behavior (hybrid materials). SEM images, Raman spectra and XRD patterns were made available for each material, showing to be complementary tools in the characterization of their crystal phases. Here different methodologies are compared for the measurement of elastic constants and microstructural characterization of CAD/CAM restorative materials. The elastic properties and crystal phases of eight materials are herein fully characterized. Copyright © 2016 The Academy of Dental Materials
A stabilized complementarity formulation for nonlinear analysis of 3D bimodular materials
Zhang, L.; Zhang, H. W.; Wu, J.; Yan, B.
2016-06-01
Bi-modulus materials with different mechanical responses in tension and compression are often found in civil, composite, and biological engineering. Numerical analysis of bimodular materials is strongly nonlinear and convergence is usually a problem for traditional iterative schemes. This paper aims to develop a stabilized computational method for nonlinear analysis of 3D bimodular materials. Based on the parametric variational principle, a unified constitutive equation of 3D bimodular materials is proposed, which allows the eight principal stress states to be indicated by three parametric variables introduced in the principal stress directions. The original problem is transformed into a standard linear complementarity problem (LCP) by the parametric virtual work principle and a quadratic programming algorithm is developed by solving the LCP with the classic Lemke's algorithm. Update of elasticity and stiffness matrices is avoided and, thus, the proposed algorithm shows an excellent convergence behavior compared with traditional iterative schemes. Numerical examples show that the proposed method is valid and can accurately analyze mechanical responses of 3D bimodular materials. Also, stability of the algorithm is greatly improved.
Modeling of Z-scan characteristics for one-dimensional nonlinear photonic bandgap materials.
Chen, Shuqi; Zang, Weiping; Schülzgen, Axel; Liu, Xin; Tian, Jianguo; Moloney, Jerome V; Peyghambarian, Nasser
2009-12-01
We propose a Z-scan theory for one-dimensional nonlinear photonic bandgap materials. The Z-scan characteristics for this material are analyzed. Results show that the Z-scan curves for photonic bandgap materials with nonlinear refraction are similar to those of uniform materials exhibiting both nonlinear refraction and nonlinear absorption simultaneously. Effects of nonlinear absorption on reflected and transmitted Z-scan results are also discussed.
Directory of Open Access Journals (Sweden)
Hwa Kian Chai
2016-04-01
Full Text Available Concrete is the most ubiquitous construction material. Apart from the fresh and early age properties of concrete material, its condition during the structure life span affects the overall structural performance. Therefore, development of techniques such as non-destructive testing which enable the investigation of the material condition, are in great demand. Tomography technique has become an increasingly popular non-destructive evaluation technique for civil engineers to assess the condition of concrete structures. In the present study, this technique is investigated by developing reconstruction procedures utilizing different parameters of elastic waves, namely the travel time, wave amplitude, wave frequency, and Q-value. In the development of algorithms, a ray tracing feature was adopted to take into account the actual non-linear propagation of elastic waves in concrete containing defects. Numerical simulation accompanied by experimental verifications of wave motion were conducted to obtain wave propagation profiles in concrete containing honeycomb as a defect and in assessing the tendon duct filling of pre-stressed concrete (PC elements. The detection of defects by the developed tomography reconstruction procedures was evaluated and discussed.
Peng, Qing; De, Suvranu
2014-10-21
Silicane is a fully hydrogenated silicene-a counterpart of graphene-having promising applications in hydrogen storage with capacities larger than 6 wt%. Knowledge of its elastic limit is critical in its applications as well as tailoring its electronic properties by strain. Here we investigate the mechanical response of silicane to various strains using first-principles calculations based on density functional theory. We illustrate that non-linear elastic behavior is prominent in two-dimensional nanomaterials as opposed to bulk materials. The elastic limits defined by ultimate tensile strains are 0.22, 0.28, and 0.25 along armchair, zigzag, and biaxial directions, respectively, an increase of 29%, 33%, and 24% respectively in reference to silicene. The in-plane stiffness and Poisson ratio are reduced by a factor of 16% and 26%, respectively. However, hydrogenation/dehydrogenation has little effect on its ultimate tensile strengths. We obtained high order elastic constants for a rigorous continuum description of the nonlinear elastic response. The limitation of second, third, fourth, and fifth order elastic constants are in the strain range of 0.02, 0.08, and 0.13, and 0.21, respectively. The pressure effect on the second order elastic constants and Poisson's ratio were predicted from the third order elastic constants. Our results could provide a safe guide for promising applications and strain-engineering the functions and properties of silicane monolayers.
Evaluation of the Elastic Properties of Thirteen Silicone Interocclusal Recording Materials
Mieszko Wieckiewicz; Natalia Grychowska; Marek Zietek; Wlodzimierz Wieckiewicz
2016-01-01
Background. Addition silicones are popular as dental impression materials and are used in bite registration procedures. Objective. This study aimed to compare the postsetting elasticities and other mechanical properties of thirteen addition silicone interocclusal recording materials. Materials and Methods. The following materials were investigated: Colorbite D, Futar D, Genie Bite, Jet Blue Bite fast, Memoreg 2, O-Bite, Occlufast Rock, Omni-Bite Plus, Regidur i, Registrado X-tra, Regofix tran...
Angela Mihai, L.
2013-03-01
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 manifested by specific models. As the finite element method computes uniform deformations exactly, for simple shear deformation and pure shear stress, the Poynting effect is represented exactly, while for the generalised shear and simple torsion, where the deformation is non-uniform, the solution is approximated efficiently and guaranteed computational bounds on the magnitude of the Poynting effect are obtained. The numerical results further indicate that, for a given elastic material, the same sign effect occurs under different shearing mechanisms, showing the genericity of the Poynting effect under a variety of shearing loads. In order to derive numerical models that exhibit either the positive or the negative Poynting effect, the so-called generalised empirical inequalities, which are less restrictive than the usual empirical inequalities involving material parameters, are assumed. © 2012 Elsevier Ltd.
Dingreville, Remi
the effects of surface free energy on the effective modulus of nano-particles, nano-wires and nano-films as well as nanostructured crystalline materials and propose a general framework valid for any shape of nanostructural elements/nano-inclusions (integral forms) that characterizes the size-dependency of the elastic properties. This approach bridges the gap between discrete systems (atomic level interactions) and continuum mechanics. Finally this continuum outline is used to understand the effects of surfaces on the overall behavior of nano-size structural elements (particles, films, fibers, etc.) and nanostructured materials. More specifically we will discuss the impact of surface relaxation, surface elasticity and non-linearity of the underlying bulk on the properties nanostructured materials. In terms of engineering applications, this approach proves to be a useful tool for multi-scale modeling of heterogeneous materials with nanometer scale microstructures and provides insights on surface properties for several material systems; these will be very useful in many fields including surface science, tribology, fracture mechanics, adhesion science and engineering, and more. It will accelerate the insertion of nano-size structural elements, nano-composite and nanocrystalline materials into engineering applications.
Paul, Shirshendu; Katiyar, Amit; Sarkar, Kausik; Chatterjee, Dhiman; Shi, William T; Forsberg, Flemming
2010-06-01
Two nonlinear interfacial elasticity models--interfacial elasticity decreasing linearly and exponentially with area fraction--are developed for the encapsulation of contrast microbubbles. The strain softening (decreasing elasticity) results from the decreasing association between the constitutive molecules of the encapsulation. The models are used to find the characteristic properties (surface tension, interfacial elasticity, interfacial viscosity and nonlinear elasticity parameters) for a commercial contrast agent. Properties are found using the ultrasound attenuation measured through a suspension of contrast agent. Dynamics of the resulting models are simulated, compared with other existing models and discussed. Imposing non-negativity on the effective surface tension (the encapsulation experiences no net compressive stress) shows "compression-only" behavior. The exponential and the quadratic (linearly varying elasticity) models result in similar behaviors. The validity of the models is investigated by comparing their predictions of the scattered nonlinear response for the contrast agent at higher excitations against experimental measurement. All models predict well the scattered fundamental response. The nonlinear strain softening included in the proposed elastic models of the encapsulation improves their ability to predict subharmonic response. They predict the threshold excitation for the initiation of subharmonic response and its subsequent saturation.
Elastic constants at low temperatures - Recent measurements on technological materials at NBS
Ledbetter, H. M.
1978-01-01
Solid-state low-temperature elastic properties have been experimentally studied at the NBS Cryogenic Division for four years. Most studies were between room temperature and liquid-helium temperature; some were only to liquid-nitrogen temperature. Two dynamic (high-frequency) experimental methods were used, pulse-echo and resonance, resulting in adiabatic elastic constants. The present paper reviews these studies for 47 technological materials - metals, alloys, and composites. The elastic constants primarily discussed are Young's modulus, the shear modulus, the bulk modulus (reciprocal compressibility), and Poisson's ratio. A summary table is presented to show which base metals tend to exhibit regular, irregular, or anomalous behavior in their elastic constant/temperature curves.
Enhanced nonlinear refractive index in epsilon-near-zero materials
Caspani, L; Clerici, M; Ferrera, M; Roger, T; Di Falco, A; Kim, J; Kinsey, N; Shalaev, V M; Boltasseva, A; Faccio, D
2016-01-01
New propagation regimes for light arise from the ability to tune the dielectric permittivity to extremely low values. Here we demonstrate a universal approach based on the low linear permittivity values attained in the epsilon-near-zero (ENZ) regime for enhancing the nonlinear refractive index, which enables remarkable light-induced changes of the material properties. Experiments performed on Al-doped ZnO (AZO) thin films show a six-fold increase of the Kerr nonlinear refractive index ($n_2$) at the ENZ wavelength, located in the 1300 nm region. This in turn leads to light-induced refractive index changes of the order of unity, thus representing a new paradigm for nonlinear optics.
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.
Energy Technology Data Exchange (ETDEWEB)
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.
Optimal Three-Material Wheel Assemblage of Conducting and Elastic Composites
Cherkaev, Andrej
2011-01-01
We describe a new type of three material microstructures which we call wheel assemblages, that correspond to extremal conductivity and extremal bulk modulus for a composite made of two materials and an ideal material. The exact lower bounds for effective conductivity and matching laminates was found in (Cherkaev, 2009) and for anisotropic composites, in (Cherkaev, Zhang, 2011). Here, we show different optimal structures that generalize the classical Hashin-Shtrikman coated spheres (circles). They consist of circular inclusions which contain a solid central circle (hub) and radial spikes in a surrounding annulus, and (for larger volume fractions of the best material) an annulus filled with it. The same wheel assemblages are optimal for the pair of dual problems of minimal conductivity (resistivity) of a composite made from two materials and an ideal conductor (insulator), in the problem of maximal effective bulk modulus of elastic composites made from two linear elastic material and void, and the dual minimum ...
Nonlinearity-induced PT-symmetry without material gain
Miri, Mohammad-Ali; Alù, Andrea
2016-06-01
Parity-time symmetry has raised a great deal of attention in optics in recent years, yet its application has been so far hindered by the stringent requirements on coherent gain balanced with loss. In this paper, we show that the conditions to enable parity and time symmetry can be simultaneously satisfied for a pair of modes with mixed frequencies interacting in a nonlinear medium, without requiring the presence of material gain. First, we consider a guided wave structure with second order nonlinearity and we derive the PT-symmetric Hamiltonian that governs the interaction of two waves of mixed frequencies when accompanied by a high intensity pump beam at the sum frequency. We also extend the results to an array of coupled nonlinear waveguide channels. It is shown that the evolution dynamics of the low-frequency waves is associated with a periodic PT-symmetric lattice while the phase of the pump beams can be utilized as a control parameter to modify the gain and loss distribution, thus realizing different PT lattices by design. Our results suggest that nonlinear wave mixing processes can form a rich platform to realize PT-symmetric Hamiltonians of arbitrary dimensions in optical systems, without requiring material gain.
2009-09-01
reference state. After efining average strain energies on a per-reference-volume basis s ournal of Engineering Materials and Technology aded 27 Aug 2009...with the absolute density f dislocations. Dislocation line densities in the preceding developments are efined per unit reference volume equivalent in
Dimitrova, Zlatinka I
2015-01-01
We investigate flow of incompressible fluid in a cylindrical tube with elastic walls. The radius of the tube may change along its length. The discussed problem is connected to the blood flow in large human arteries and especially to nonlinear wave propagation due to the pulsations of the heart. The long-wave approximation for modeling of waves in blood is applied. The obtained model Korteweg-deVries equation possessing a variable coefficient is reduced to a nonlinear dynamical system of 3 first order differential equations. The low probability of arising of a solitary wave is shown. Periodic wave solutions of the model system of equations are studied and it is shown that the waves that are consequence of the irregular heart pulsations may be modeled by a sequence of parts of such periodic wave solutions.
Super-elastic and fatigue resistant carbon material with lamellar multi-arch microstructure
Gao, Huai-Ling; Zhu, Yin-Bo; Mao, Li-Bo; Wang, Feng-Chao; Luo, Xi-Sheng; Liu, Yang-Yi; Lu, Yang; Pan, Zhao; Ge, Jin; Shen, Wei; Zheng, Ya-Rong; Xu, Liang; Wang, Lin-Jun; Xu, Wei-Hong; Wu, Heng-An; Yu, Shu-Hong
2016-09-01
Low-density compressible materials enable various applications but are often hindered by structure-derived fatigue failure, weak elasticity with slow recovery speed and large energy dissipation. Here we demonstrate a carbon material with microstructure-derived super-elasticity and high fatigue resistance achieved by designing a hierarchical lamellar architecture composed of thousands of microscale arches that serve as elastic units. The obtained monolithic carbon material can rebound a steel ball in spring-like fashion with fast recovery speed (~580 mm s-1), and demonstrates complete recovery and small energy dissipation (~0.2) in each compress-release cycle, even under 90% strain. Particularly, the material can maintain structural integrity after more than 106 cycles at 20% strain and 2.5 × 105 cycles at 50% strain. This structural material, although constructed using an intrinsically brittle carbon constituent, is simultaneously super-elastic, highly compressible and fatigue resistant to a degree even greater than that of previously reported compressible foams mainly made from more robust constituents.
Role of Elastic Compatibility and Disorder in Texture Evolution in Martensitic Materials.
Kerr, W. C.; Shenoy, S. R.; Saxena, A.; Swart, P. J.; Bishop, A. R.; Killough, M. G.
1997-03-01
Based on a k-space analysis of the 2D elastic compatibility condition, we derive an anisotropic long-range elastic interaction that is responsible for twinning in martensitic materials. This 2D condition is operational only for textures that have nonzero "elastic quadrupole" moment such as twins impinging on a martensite-austenite interface or tweed intersections. The long-range interaction, previously obtained (G.R. Barsch, B. Horovitz, and J.A. Krumhansl, PRL 59, 1251 (1987); PR B 43, 1021 (1991).) by integrating out the elastic fringing field energy contribution in the austenite, is thus shown as a direct consequence of elastic compatibility. Using both annealed and quenched averaging over compositional disorder, we derive an effective cross-gradient elastic energy contribution that is fourth-order in gradient and second-order in strain. The coefficient of this term is negative in a limited temperature range, indicating the presence of tweed texture and its coarsening with cooling. These results are borne out by integration of the equations of motion for rectangular and shear strains, obtained from the Ginzburg-Landau functional with the compatibility condition.
NONLINEAR BUCKLING CHARACTERISTIC OF GRADED MULTIWEB STRUCTURE OF HETEROGENEOUS MATERIALS
Institute of Scientific and Technical Information of China (English)
LI Yong; ZHANG Zhi-min
2005-01-01
The graded multiweb structure of heterogeneous anisotropic materials, which makes full use of the continuous, gradual and changing physical mechanical performance of material properties, has a widespread application in aeroplane aerofoil structure and automobile lightweight structure. On the basis of laminate buckling theory,the equivalent rigidity method is adopted to establish the corresponding constitutive relation and the non-linear buckling governing equation for the graded multiweb structure. In finding the solution, the critical load of buckling under different complicated boundary conditions together with combined loads were obtained and testification of the experimental analysis shows that the calculation results can satisfy the requirements of engineering design in a satisfactory way. Results obtained from the research say that: graded materials can reduce the concentrated stress on the interface in an effective way and weaken the effect of initial defect in materials and thereby improve the strength and toughness of materials.
Korman, Murray S.; Sabatier, James M.
2006-05-01
The vibration interaction between the top-plate of a buried VS 2.2 plastic, anti-tank landmine and the soil above it appears to exhibit similar characteristics to the nonlinear mesoscopic/nanoscale effects that are observed in geomaterials like rocks or granular materials. [J. Acoust. Soc. Am. 116, 3354-3369 (2004)]. When airborne sound at two primary frequencies f1 and f2 (closely spaced near resonance) undergo acoustic-to-seismic coupling, (A/S), interactions with the mine and soil generate combination frequencies | n f1 ± m f2 | which affect the surface vibration velocity. Profiles at f1, f2, f1 -(f2 - f1) and f2 +(f2 - f1) exhibit single peaks whereas other combination frequencies may involve higher order modes. A family of increasing amplitude tuning curves, involving the surface vibration over the landmine, exhibits a linear relationship between the peak particle velocity and corresponding resonant frequency. Subsequent decreasing amplitude tuning curves exhibit hysteresis effects. New experiments for a buried VS 1.6 anti-tank landmine and a "plastic drum head" mine simulant behave similarly. Slow dynamics explains the amplitude difference in tuning curves for first sweeping upward and then downward through resonance, provided the soil modulus drops after periods of high strain. [Support by U.S. Army RDECOM CERDEC, NVESD, Fort Belvoir, VA.
Rezaee, Mousa; Jahangiri, Reza
2015-05-01
In this study, in the presence of supersonic aerodynamic loading, the nonlinear and chaotic vibrations and stability of a simply supported Functionally Graded Piezoelectric (FGP) rectangular plate with bonded piezoelectric layer have been investigated. It is assumed that the plate is simultaneously exposed to the effects of harmonic uniaxial in-plane force and transverse piezoelectric excitations and aerodynamic loading. It is considered that the potential distribution varies linearly through the piezoelectric layer thickness, and the aerodynamic load is modeled by the first order piston theory. The von-Karman nonlinear strain-displacement relations are used to consider the geometrical nonlinearity. Based on the Classical Plate Theory (CPT) and applying the Hamilton's principle, the nonlinear coupled partial differential equations of motion are derived. The Galerkin's procedure is used to reduce the equations of motion to nonlinear ordinary differential Mathieu equations. The validity of the formulation for analyzing the Limit Cycle Oscillation (LCO), aero-elastic stability boundaries is accomplished by comparing the results with those of the literature, and the convergence study of the FGP plate is performed. By applying the Multiple Scales Method, the case of 1:2 internal resonance and primary parametric resonance are taken into account and the corresponding averaged equations are derived and analyzed numerically. The results are provided to investigate the effects of the forcing/piezoelectric detuning parameter, amplitude of forcing/piezoelectric excitation and dynamic pressure, on the nonlinear dynamics and chaotic behavior of the FGP plate. It is revealed that under the certain conditions, due to the existence of bi-stable region of non-trivial solutions, system shows the hysteretic behavior. Moreover, in absence of airflow, it is observed that variation of control parameters leads to the multi periodic and chaotic motions.
Strength of anisotropy in a granular material: Linear versus nonlinear contact model.
La Ragione, Luigi; Gammariello, Marica; Recchia, Giuseppina
2016-12-01
In this paper, we deal with anisotropy in an idealized granular material made of a collection of frictional, elastic, contacting particles. We present a theoretical analysis for an aggregate of particles isotropically compressed and then sheared, in which two possible contacts laws between particles are considered: a linear contact law, where the contact stiffness is constant; and a nonlinear contact law, where the contact stiffness depends on the overlapping between particles. In the former case the anisotropy observed in the aggregate is associated with particle arrangement. In fact, although the aggregate is initially characterized by an isotropic network of contacts, during the loading, an anisotropic texture develops, which is measured by a fabric tensor. With a nonlinear contact law it is possible to develop anisotropy because contacting stiffnesses are different, depending on the orientation of the contact vectors with respect to the axis of the applied deformation. We find that before the peak load is reached, an aggregate made of particles with a linear contact law develops a much smaller anisotropy compared with that of an aggregate with a nonlinear law.
Strength of anisotropy in a granular material: Linear versus nonlinear contact model
La Ragione, Luigi; Gammariello, Marica; Recchia, Giuseppina
2016-12-01
In this paper, we deal with anisotropy in an idealized granular material made of a collection of frictional, elastic, contacting particles. We present a theoretical analysis for an aggregate of particles isotropically compressed and then sheared, in which two possible contacts laws between particles are considered: a linear contact law, where the contact stiffness is constant; and a nonlinear contact law, where the contact stiffness depends on the overlapping between particles. In the former case the anisotropy observed in the aggregate is associated with particle arrangement. In fact, although the aggregate is initially characterized by an isotropic network of contacts, during the loading, an anisotropic texture develops, which is measured by a fabric tensor. With a nonlinear contact law it is possible to develop anisotropy because contacting stiffnesses are different, depending on the orientation of the contact vectors with respect to the axis of the applied deformation. We find that before the peak load is reached, an aggregate made of particles with a linear contact law develops a much smaller anisotropy compared with that of an aggregate with a nonlinear law.
Ganesh, R.; Gonella, S.
2017-02-01
The motive of this work is to understand the complex spatial characteristics of finite-amplitude elastic wave propagation in periodic structures and leverage the unique opportunities offered by nonlinearity to activate complementary functionalities and design adaptive spatial wave manipulators. The underlying assumption is that the magnitude of wave propagation is small with respect to the length scale of the structure under consideration, albeit large enough to elicit the effects of finite deformation. We demonstrate that the interplay of dispersion, nonlinearity and modal complexity involved in the generation and propagation of higher harmonics gives rise to secondary wave packets that feature multiple characteristics, one of which conforms to the dispersion relation of the corresponding linear structure. This provides an opportunity to engineer desired wave characteristics through a geometric and topological design of the unit cell, and results in the ability to activate complementary functionalities, typical of high frequency regimes, while operating at low frequencies of excitation - an effect seldom observed in linear periodic structures. The ability to design adaptive switches is demonstrated here using lattice configurations whose response is characterized by geometric and/or material nonlinearities.
DEFF Research Database (Denmark)
Palleti, Hara Naga Krishna Teja; Thomsen, Ole Thybo; Taher, Siavash Talebi;
In this paper, polymer foam cored sandwich structures with fibre reinforced composite face sheets subjected to combined mechanical and thermal loads will be analysed using the commercial FE code ABAQUS® incorporating both material and geometrical nonlinearity. Large displacements and rotations ar...... are included in the analysis. The full nonlinear stress-strain curves up to failure will be considered for the polymer foams at different temperatures to study the effect of material nonlinearity in detail....
The role of elasticity in the wetting and adhesion of soft materials
Webber, Rebecca Elisabeth
In this work, the effect of elasticity on the adhesive behavior of soft materials is investigated by studying three model systems: an elastic gel, a viscoelastic hydrogel, and nonelastic liquid interfaces. These systems span the elastic spectrum and represent a wide range of matter in the increasingly important category of soft materials. The first system is a thermally reversible gel made from a triblock copolymer, wherein physical gelation occurs upon dissolution in a selective solvent for the midblock. The triblock copolymer gel is perfectly elastic at room temperature, with debonding behavior affected by the degree of geometric confinement. The effect of confinement on the mechanical and adhesive response of the triblock gels is investigated and quantified using an axisymmetric probe tack test and a compliance-based analysis method. It is found that as confinement increases, the debonding morphology of elastic gels changes, with finger-like interfacial instabilities appearing at very high confinement. Additionally, four dimensionless ratios that predict the tensile detachment behavior of soft materials have been defined as a result of this work. The viscoelastic material is an ionically-crosslinked alginate hydrogel with a strain-dependent mechanical response. These soft hydrogels exhibit elastic behavior at small strains, but possess dissipative ability that allows toughness at higher strains. The stress relaxation and strain hardening behavior of alginate hydrogels has been investigated and quantified using an axisymmetric probe tack apparatus. It was found that stress relaxation serves to regain an elastic response in the hydrogels at strains as high as 4.4 and that permanent deformation is induced above strains of 0.23. A study of the strain-dependent rheological response revealed time-dependent adhesion in these materials. To complete the elastic spectrum, the adhesive interactions created by wetting a polymer surface with various liquids were explored. A
MULTISCALE FINITE ELEMENT METHOD FOR SUBDIVIDED PERIODIC ELASTIC STRUCTURES OF COMPOSITE MATERIALS
Institute of Scientific and Technical Information of China (English)
Li-qun Cao; Jun-zhi Cui; De-chao Zhu; Jian-lan Luo
2001-01-01
In this paper, from the view of point of macro- and meso- scalecoupling, we discuss the mechanical behaviour for subdivided periodic elastic structures of composite materials. A multiscale numerical method and its error estimate are reported. Finally, numerical experiments results supports strongly the theoretical ones presented in the paper.
Directory of Open Access Journals (Sweden)
Mihai-Victor PRICOP
2010-09-01
Full Text Available The present paper introduces a numerical approach of static linear elasticity equations for anisotropic materials. The domain and boundary conditions are simple, to enhance an easy implementation of the finite difference scheme. SOR and gradient are used to solve the resulting linear system. The simplicity of the geometry is also useful for MPI parallelization of the code.
Measurement of nonlinear elastic response in rock by the resonant bar method
Energy Technology Data Exchange (ETDEWEB)
Johnson, P.A. [Los Alamos National Lab., NM (United States); Rasolofosaon, P.; Zinszner, B. [Institut Francais du Petrole (IFP), 92 - Rueil-Malmaison (France)
1993-04-01
In this work we are studying the behavior of the fundamental (Young`s) mode resonant peak as a function of drive amplitude in rock samples. Our goal from these studies is to obtain nonlinear moduli for many rock types, and to study the nonlinear moduli as a function of water saturation and other changes in physical properties. Measurements were made on seven different room dry rock samples. For one sample measurements were taken at 16 saturation levels between 1 and 98%. All samples display a ``softening`` nonlinearity, that is, the resonant frequency shifts downward with increasing drive amplitude. In extreme cases, the resonant frequency changes by as much as 25% over a strain interval of 10{sup {minus}7} to {approximately}4 {times} 10{sup {minus}5}. Measurements indicate that the nonlinear response is extremely sensitive to saturation. Estimates of a combined cubic and quartic nonlinear parameter {Gamma} range from approximately {minus}300 to {minus}10{sup 9} for the rock samples.
Zhang, Haifeng; Kosinski, John A; Zuo, Lei
2016-09-01
In this paper, we examine the significance of the various higher-order effects regarding calculating temperature behavior from a set of material constants and their temperature coefficients. Temperature-induced velocity shifts have been calculated for quartz surface acoustic wave (SAW) resonators and the contributions of different groups of nonlinear material constants (third-order elastic constants (TOE), third-order piezoelectric constants (TOP), third-order dielectric constants (TOD) and electrostrictive constants (EL)) to the temperature-induced velocity shifts have been analyzed. The analytical methodology has been verified through the comparison of experimental and analytical results for quartz resonators. In general, the third-order elastic constants were found to contribute most significantly to the temperature-induced shifts in the SAW velocity. The contributions from the third-order dielectric constants and electrostrictive constants were found to be negligible. For some specific cases, the third-order piezoelectric constants were found to make a significant contribution to the temperature-induced shifts. The significance of each third-order elastic constant as a contributor to the temperature-velocity effect was analyzed by applying a 10% variation to each of the third-order elastic constants separately. Additionally, we have considered the issues arising from the commonly used thermoelastic expansions that provide a good but not exact description of the temperature effects on frequency in piezoelectric resonators as these commonly used expansions do not include the effects of higher-order material constants.
Intrinsic optical bistability between left-handed material and nonlinear optical materials
Institute of Scientific and Technical Information of China (English)
Shi Hong-Yan; Jiang Yong-Yuan; Sun Xiu-Dong; Guo Ru-Hai; Zhao Yi-Ping
2005-01-01
The electromagnetic properties of the interface between a left-handed material and a conventional nonlinear material were investigated theoretically and numerically. We found a new phenomenon-optical bistability of the interface.It was shown that the incident intensity, incident angle and permeability ratio between the left-handed and the nonlinear materials could dramatically affect the optical bistable behaviour. We also compared the bistable behaviours of different electromagnetic modes. The results indicated that the TE mode was prior to the TM mode to obtain optical bistability for the same parameter.
Korjik, M. V.; Buganov, O.; Fedorov, A. A.; Emelianchik, I.; Griesmayer, E.; Mechinsky, V.; Nargelas, S.; Sidletskiy, O.; Tamulaitis, G.; Tikhomirov, S. N.; Vaitkevicius, A.
2016-01-01
The time resolution of the detectors currently in use is limited by 50-70 ps due to the spontaneous processes involved in the development of the response signal, which forms after the relaxation of carriers generated during the interaction. In this study, we investigate the feasibility of exploiting sub-picosecond phenomena occurring after the interaction of scintillator material with ionizing radiation by probing the material with ultra-short laser pulses. One of the phenomena is the elastic polarization due to the local lattice distortion caused by the displacement of electrons and holes generated by ionization. The key feature of the elastic polarization is its short response time, which makes it prospective for using as an optically detectable time mark. The nonlinear optical absorption of femtosecond light pulses of appropriate wavelength is demonstrated to be a prospective tool to form the mark. This study was aimed at searching for inorganic crystalline media combining scintillation properties and non-...
VISCO-ELASTIC PROPERTIES OF SOFT RELINING MATERIALS – REVIEW
Directory of Open Access Journals (Sweden)
Ilian Hristov
2017-05-01
Full Text Available Despite the achievements of modern dentistry in fields of implantology and CAD-CAM technologies, the challenges associated with edentulous patients, treatment are still remaining. Difficulties are getting even greater, when it is a matter of highly atrophied alveolar ridges, covered with very thin mucosa, people suffering from xerostomia, exostosis, very well developed torus palatinus or tuberae maxillae. Problems of the patients with removable dentures usually are poor adhesion and stability, pain, wounds, difficult adaptation with the new dentures, etc. At this moment there are only two possibilities to help these people. The first one is the use of implants; the second one is to use soft relining materials. There are some obstacles that reduce the use of implants in all patients, because of medical, anatomical, psychological and financial concerns. While in the second option the contraindications are quite less.
Numerical estimation of 3D mechanical forces exerted by cells on non-linear materials.
Palacio, J; Jorge-Peñas, A; Muñoz-Barrutia, A; Ortiz-de-Solorzano, C; de Juan-Pardo, E; García-Aznar, J M
2013-01-04
The exchange of physical forces in both cell-cell and cell-matrix interactions play a significant role in a variety of physiological and pathological processes, such as cell migration, cancer metastasis, inflammation and wound healing. Therefore, great interest exists in accurately quantifying the forces that cells exert on their substrate during migration. Traction Force Microscopy (TFM) is the most widely used method for measuring cell traction forces. Several mathematical techniques have been developed to estimate forces from TFM experiments. However, certain simplifications are commonly assumed, such as linear elasticity of the materials and/or free geometries, which in some cases may lead to inaccurate results. Here, cellular forces are numerically estimated by solving a minimization problem that combines multiple non-linear FEM solutions. Our simulations, free from constraints on the geometrical and the mechanical conditions, show that forces are predicted with higher accuracy than when using the standard approaches.
Frequency Response of Synthetic Vocal Fold Models with Linear and Nonlinear Material Properties
Shaw, Stephanie M.; Thomson, Scott L.; Dromey, Christopher; Smith, Simeon
2012-01-01
Purpose: The purpose of this study was to create synthetic vocal fold models with nonlinear stress-strain properties and to investigate the effect of linear versus nonlinear material properties on fundamental frequency (F[subscript 0]) during anterior-posterior stretching. Method: Three materially linear and 3 materially nonlinear models were…
Institute of Scientific and Technical Information of China (English)
ZHANG Hong-wu; WANG Hui
2006-01-01
The Voronoi cell finite element method (VCFEM) is adopted to overcome the limitations of the classic displacement based finite element method in the numerical simulation of heterogeneous materials. The parametric variational principle and quadratic programming method are developed for elastic-plastic Voronoi finite element analysis of two-dimensional problems. Finite element formulations are derived and a standard quadratic programming model is deduced from the elastic-plastic equations. Influence of microscopic heterogeneities on the overall mechanical response of heterogeneous materials is studied in detail. The overall properties of heterogeneous materials depend mostly on the size, shape and distribution of the material phases of the microstructure. Numerical examples are presented to demonstrate the validity and effectiveness of the method developed.
Menzel, Andreas M
2016-01-01
One possibility to adjust material properties to a specific need is to embed units of one substance into a matrix of another substance. Even materials that are readily tunable during operation can be generated in this way. In (visco)elastic substances, both the matrix material as well as the inclusions and/or their immediate environment can be dynamically deformed. If the typical dynamic response time of the inclusions and their surroundings approach the macroscopic response time, their deformation processes need to be included into a dynamic macroscopic characterization. Along these lines, we present a hydrodynamic description of (visco)elastic composite materials. For this purpose, additional strain variables reflect the state of the inclusions and their immediate environment. These additional strain variables in general are not set by a coarse-grained macroscopic displacement field. Apart from that, during our derivation, we also include the macroscopic variables of relative translations and relative rotat...
DEFF Research Database (Denmark)
Barari, Amin; Ganjavi, B.; Jeloudar, M. Ghanbari
2010-01-01
Purpose – In the last two decades with the rapid development of nonlinear science, there has appeared ever-increasing interest of scientists and engineers in the analytical techniques for nonlinear problems. This paper considers linear and nonlinear systems that are not only regarded as general...... and fluid mechanics. Design/methodology/approach – Two new but powerful analytical methods, namely, He's VIM and HPM, are introduced to solve some boundary value problems in structural engineering and fluid mechanics. Findings – Analytical solutions often fit under classical perturbation methods. However...
ASYMPTOTIC ELASTIC STRESS FIELD NEAR A BLUNT CRACK TIP IN AN ANISOTROPIC MATERIAL
Institute of Scientific and Technical Information of China (English)
HUANG; Zhen-yu(
2001-01-01
［1］Williams M L.Oh the stress distribution at the base of a stationary crack[J].ASME J App Mech,1957,24:109～114.［2］Creager M,Paris P C,Elastic field equations for blunt cracks with reference to stress corrosion crack-ing[J].Int J Fracture,1967,3:247～251［3］Kuang Z B.The stress field near the blunt crack tip and the fracture criterion[J].Engng Fracture Mech,1982,16:19～33.［4］Ting T C T.Anisotropic Elasticity and its applica-tion[M].London:Oxford University Press,1996.［5］Ting T C T ,Hwu C.Sextic formalism in anisotropic elasticity for almost non-semisimple matrix N[J].Int J S olids Structures,1988,24:65～76.［6］Yang X X,Shen S,Kuang Z B.The degenerate so-lution for piezothermoelastic materials[J].Eur J Mech A/Solid,1997,16:779～793［7］Hwu C,Yen W J.On the anisotropic elastic inclu-sions in plane elastostatics[J].ASME J A pp Mech,1993,60:626～632.［8］Lekhnitskii S G.Theory of elasticity of an anisotrop-ic elastic body[M].Moscow:Mir Publishers,1981.［9］Hoenig A.Near-tip behavior of a crack in a plane anisotropic elastic body[J].Engng Fracture Mech,1982,16:393～403.［10］匡震邦，马法尚。裂纹端部场[M].西安：西安交通大学出版社，2001
Institute of Scientific and Technical Information of China (English)
XIAO Yong-gang; FU Yi-ming; ZHA Xu-dong
2005-01-01
Based on Reissner plate theory and Hamilton variational principle, the nonlinear equations of motion were derived for the moderate thickness rectangular plates with transverse surface penetrating crack on the two-parameter foundation. Under the condition of free boundary, a set of trial functions satisfying all boundary conditions and crack's continuous conditions were proposed. By employing the Galerkin method and the harmonic balance method, the nonlinear vibration equations were solved and the nonlinear vibration behaviors of the plate were analyzed. In numerical computation, the effects of the different location and depth of crack, the different structural parameters of plates and the different physical parameters of foundation on the nonlinear amplitude frequency response curves of the plate were discussed.
Computation of displacements for nonlinear elastic beam models using monotone iterations
Directory of Open Access Journals (Sweden)
Philip Korman
1988-01-01
Full Text Available We study displacement of a uniform elastic beam subject to various physically important boundary conditions. Using monotone methods, we discuss stability and instability of solutions. We present computations, which suggest efficiency of monotone methods for fourth order boundary value problems.
Nonlinear phononics and structural control of strongly correlated materials
Energy Technology Data Exchange (ETDEWEB)
Mankowsky, Roman
2016-01-20
Mid-infrared light pulses can be used to resonantly excite infrared-active vibrational modes for the phase control of strongly correlated materials on subpicosecond timescales. As the energy is transferred directly into atomic motions, dissipation into the electronic system is reduced, allowing for the emergence of unusual low energy collective properties. Light-induced superconductivity, insulator-metal transitions and melting of magnetic order demonstrate the potential of this method. An understanding of the mechanism, by which these transitions are driven, is however missing. The aim of this work is to uncover this process by investigating the nonlinear lattice dynamics induced by the excitation and to elucidate their contribution to the modulation of collective properties of strongly correlated materials. The first signature of nonlinear lattice dynamics was reported in the observation of coherent phonon oscillations, resonant with the excitation of an infrared-active phonon mode in a manganite. This nonlinear phononic coupling can be described within a model, which predicts not only oscillatory coherent phonons dynamics but also directional atomic displacements along the coupled modes on average, which could cause the previously observed transitions. We verified this directional response and quantified the anharmonic coupling constant by tracing the atomic motions in a time-resolved hard X-ray diffraction experiment with sub-picometer spatial and femtosecond temporal resolution. In a subsequent study, we investigated the role of nonlinear lattice dynamics in the emergence of superconductivity far above the equilibrium transition temperature, an intriguing effect found to follow lattice excitation of YBa{sub 2}Cu{sub 3}O{sub 6+x}. By combining density functional theory (DFT) calculations of the anharmonic coupling constants with time-resolved X-ray diffraction experiments, we identified a structural rearrangement, which appears and decays with the same temporal
Reliability-based design optimization of a nonlinear elastic plastic thin-walled T-section beam
Ba-Abbad, Mazen A.
A two part study is performed to investigate the application of reliability-based design optimization (RBDO) approach to design elastic-plastic stiffener beams with T-section. The objectives of this study are to evaluate the benefits of reliability-based optimization over deterministic optimization, and to illustrate through a practical design example some of the difficulties that a design engineer may encounter while performing reliability-based optimization. Other objectives are to search for a computationally economic RBDO method and to utilize that method to perform RBDO to design an elastic-plastic T-stiffener under combined loads and with flexural-torsional buckling and local buckling failure modes. First, a nonlinear elastic-plastic T-beam was modeled using a simple 6 degree-of-freedom non-linear beam element. To address the problems of RBDO, such as the high non-linearity and derivative discontinuity of the reliability function, and to illustrate a situation where RBDO fails to produce a significant improvement over the deterministic optimization, a graphical method was developed. The method started by obtaining a deterministic optimum design that has the lowest possible weight for a prescribed safety factor (SF), and based on that design, the method obtains an improved optimum design that has either a higher reliability or a lower weight or cost for the same level of reliability as the deterministic design. Three failure modes were considered for an elastic-plastic beam of T cross-section under combined axial and bending loads. The failure modes are based on the total plastic failure in a beam section, buckling, and maximum allowable deflection. The results of the first part show that it is possible to get improved optimum designs (more reliable or lighter weight) using reliability-based optimization as compared to the design given by deterministic optimization. Also, the results show that the reliability function can be highly non-linear with respect to
Schindler, Stefan; Mergheim, Julia; Zimmermann, Marco; Aurich, Jan C.; Steinmann, Paul
2017-01-01
A two-scale material modeling approach is adopted in order to determine macroscopic thermal and elastic constitutive laws and the respective parameters for metal matrix composite (MMC). Since the common homogenization framework violates the thermodynamical consistency for non-constant temperature fields, i.e., the dissipation is not conserved through the scale transition, the respective error is calculated numerically in order to prove the applicability of the homogenization method. The thermomechanical homogenization is applied to compute the macroscopic mass density, thermal expansion, elasticity, heat capacity and thermal conductivity for two specific MMCs, i.e., aluminum alloy Al2024 reinforced with 17 or 30 % silicon carbide particles. The temperature dependency of the material properties has been considered in the range from 0 to 500°C, the melting temperature of the alloy. The numerically determined material properties are validated with experimental data from the literature as far as possible.
2D crack problems in functionally graded magnet-electro-elastic materials
Stoynov, Yonko
2016-12-01
Magneto-electro-elastic composite materials have extensive application in modern smart structures, because they possess good coupling between mechanical, electrical and magnetic fields. This new effect was reported for the first time by Van Suchtelen [1] in 1972. Due to their ceramic structure cracks inevitably exists in these materials. In this study we consider functionally graded magneto-electro-elastic materials subjected to anti-plane time harmonic load. We use Boundary integral equation method (BIEM) to evaluate the dependence of stress concentration near the crack tip on the frequency of the applied external load. For complex crack configurations numerical calculations are tedious and need too much time. Here we present a new analytical approach that will significantly improve the numerical procedure for calculation of stress intensity factors (SIF).
Vaidyanathan, Tritala K; Vaidyanathan, Jayalakshmi; Arghavani, David
2016-12-01
Purpose: The goal of this investigation was to characterize the compliance properties in selected polymers used for temporary (provisional crown and bridge) applications. Method: Polymethyl methacrylate (PMMA)- and polyethyl methacrylate (PEMA)-based JET and TRIM II were investigated along with two bisacryl composite resins (LUXATEMP and PROTEMP 3 GARANT). Rectangular samples of the resins were subjected to creep-recovery tests in a dynamic mechanical analyzer at and near the oral temperature (27 °C, 37 °C and 47 °C). The instantaneous (elastic), and time-dependent viscoelastic, and viscoplastic compliance profiles of the materials were determined and analyzed as a function of materials and temperature. Results: Highly significant (p = 0.0001) differences among means of elastic, viscoelastic and viscoplastic compliance values were found as a function of materials. TRIM II showed an order of magnitude higher viscoplastic deformation than the other three materials (LUXATEMP, PROTEMP 3 GARANT and JET). Conclusions: The results indicate that PEMA is susceptible to significantly greater elastic, viscoelastic, and more importantly to viscoplastic compliant behavior compared with bisacryl composite and PMMA provisional crown and bridge materials. This indicates high-dimensional instability and poor stiffness and resiliency in PEMA appliances vis-à-vis those of PMMA and bisacryl composites.
Nonlinear Optical Materials for the Smart Filtering of Optical Radiation.
Dini, Danilo; Calvete, Mário J F; Hanack, Michael
2016-11-23
The control of luminous radiation has extremely important implications for modern and future technologies as well as in medicine. In this Review, we detail chemical structures and their relevant photophysical features for various groups of materials, including organic dyes such as metalloporphyrins and metallophthalocyanines (and derivatives), other common organic materials, mixed metal complexes and clusters, fullerenes, dendrimeric nanocomposites, polymeric materials (organic and/or inorganic), inorganic semiconductors, and other nanoscopic materials, utilized or potentially useful for the realization of devices able to filter in a smart way an external radiation. The concept of smart is referred to the characteristic of those materials that are capable to filter the radiation in a dynamic way without the need of an ancillary system for the activation of the required transmission change. In particular, this Review gives emphasis to the nonlinear optical properties of photoactive materials for the function of optical power limiting. All known mechanisms of optical limiting have been analyzed and discussed for the different types of materials.
Directory of Open Access Journals (Sweden)
Woo-Young Jung
2013-01-01
Full Text Available Based on a nonlocal elasticity theory, a model for sigmoid functionally graded material (S-FGM nanoscale plate with first-order shear deformation is studied. The material properties of S-FGM nanoscale plate are assumed to vary according to sigmoid function (two power law distribution of the volume fraction of the constituents. Elastic theory of the sigmoid FGM (S-FGM nanoscale plate is reformulated using the nonlocal differential constitutive relations of Eringen and first-order shear deformation theory. The equations of motion of the nonlocal theories are derived using Hamilton’s principle. The nonlocal elasticity of Eringen has the ability to capture the small scale effect. The solutions of S-FGM nanoscale plate are presented to illustrate the effect of nonlocal theory on bending and vibration response of the S-FGM nanoscale plates. The effects of nonlocal parameters, power law index, aspect ratio, elastic modulus ratio, side-to-thickness ratio, and loading type on bending and vibration response are investigated. Results of the present theory show a good agreement with the reference solutions. These results can be used for evaluating the reliability of size-dependent S-FGM nanoscale plate models developed in the future.
Structure/property relationships in non-linear optical materials
Energy Technology Data Exchange (ETDEWEB)
Cole, J.M. [Institut Max von Laue - Paul Langevin (ILL), 38 - Grenoble (France)]|[Durham Univ. (United Kingdom); Howard, J.A.K. [Durham Univ. (United Kingdom); McIntyre, G.J. [Institut Max von Laue - Paul Langevin (ILL), 38 - Grenoble (France)
1997-04-01
The application of neutrons to the study of structure/property relationships in organic non-linear optical materials (NLOs) is described. In particular, charge-transfer effects and intermolecular interactions are investigated. Charge-transfer effects are studied by charge-density analysis and an example of one such investigation is given. The study of intermolecular interactions concentrates on the effects of hydrogen-bonding and an example is given of two structurally similar molecules with very disparate NLO properties, as a result of different types of hydrogen-bonding. (author). 3 refs.
Measurement of nonlinear elastic response in rock by the resonant bar method
Energy Technology Data Exchange (ETDEWEB)
Johnson, P.A. (Los Alamos National Lab., NM (United States)); Rasolofosaon, P.; Zinszner, B. (Institut Francais du Petrole (IFP), 92 - Rueil-Malmaison (France))
1993-01-01
In this work we are studying the behavior of the fundamental (Young's) mode resonant peak as a function of drive amplitude in rock samples. Our goal from these studies is to obtain nonlinear moduli for many rock types, and to study the nonlinear moduli as a function of water saturation and other changes in physical properties. Measurements were made on seven different room dry rock samples. For one sample measurements were taken at 16 saturation levels between 1 and 98%. All samples display a softening'' nonlinearity, that is, the resonant frequency shifts downward with increasing drive amplitude. In extreme cases, the resonant frequency changes by as much as 25% over a strain interval of 10[sup [minus]7] to [approximately]4 [times] 10[sup [minus]5]. Measurements indicate that the nonlinear response is extremely sensitive to saturation. Estimates of a combined cubic and quartic nonlinear parameter [Gamma] range from approximately [minus]300 to [minus]10[sup 9] for the rock samples.
Dynamics behaviour of an elastic non-ideal (NIS) portal frame, including fractional nonlinearities
Balthazar, J. M.; Brasil, R. M. L. F.; Felix, J. L. P.; Tusset, A. M.; Picirillo, V.; Iluik, I.; Rocha, R. T.; Nabarrete, A.; Oliveira, C.
2016-05-01
This paper overviews recent developments on some problems related to elastic structures, such as portal frames, taking into account the full interactions of the vibrating systems, with an energy source of limited power supply (small motors, electro-mechanical shakers). We include a discussion on fractional (rational) damping and stiffness effects on the adopted modelling. This was a plenary lecture, delivered in the event titled: Mechanics of Slender Structures, organized in Northampton, England from 21-22, September 2015.
Periyannan, Suresh; Balasubramaniam, Krishnan
2015-11-01
A novel technique for simultaneously measuring the moduli of elastic isotropic material, as a function of temperature, using two ultrasonic guided wave modes that are co-generated using a single probe is presented here. This technique can be used for simultaneously measuring Young's modulus (E) and shear modulus (G) of different materials over a wide range of temperatures (35 °C-1200 °C). The specimens used in the experiments have special embodiments (for instance, a bend) at one end of the waveguide and an ultrasonic guided wave generator/detector (transducer) at the other end for obtaining reflected signals in a pulse-echo mode. The orientation of the transducer can be used for simultaneously generating/receiving the L(0,1) and/or T(0,1) using a single transducer in a waveguide on one end. The far end of the waveguides with the embodiment is kept inside a heating device such as a temperature-controlled furnace. The time of flight difference, as a function of uniform temperature distribution region (horizontal portion) of bend waveguides was measured and used to determine the material properties. Several materials were tested and the comparison between values reported in the literature and measured values were found to be in agreement, for both elastic moduli (E and G) measurements, as a function of temperature. This technique provides significant reduction in time and effort over conventional means of measurement of temperature dependence of elastic moduli.
Nonlinear shear wave in a non Newtonian visco-elastic medium
Energy Technology Data Exchange (ETDEWEB)
Banerjee, D.; Janaki, M. S.; Chakrabarti, N. [Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Calcutta 700 064 (India); Chaudhuri, M. [Max-Planck-Institut fuer extraterrestrische Physik, 85741 Garching (Germany)
2012-06-15
An analysis of nonlinear transverse shear wave has been carried out on non-Newtonian viscoelastic liquid using generalized hydrodynamic model. The nonlinear viscoelastic behavior is introduced through velocity shear dependence of viscosity coefficient by well known Carreau-Bird model. The dynamical feature of this shear wave leads to the celebrated Fermi-Pasta-Ulam problem. Numerical solution has been obtained which shows that initial periodic solutions reoccur after passing through several patterns of periodic waves. A possible explanation for this periodic solution is given by constructing modified Korteweg de Vries equation. This model has application from laboratory to astrophysical plasmas as well as in biological systems.
Nonlinear response of plain concrete shear walls with elastic-damaging behavior
Energy Technology Data Exchange (ETDEWEB)
Yazdani, S.; Schreyer, H.L.
1997-02-01
This report summarizes the theoretical and computational efforts on the modeling of small scale shear walls. Small scale shear walls are used extensively in the study of shear wall behavior because the construction and testing of full size walls are rather expensive. A finite element code is developed which incorporates nonlinear constitutive relations of damage mechanics. The program is used to obtain nonlinear load-deformation curves and to address the initial loss of stiffness due to shrinkage cracking. The program can also be used to monitor the continuous degradation of the fundamental frequency due to progressive damage.
Effect of transverse shears on complex nonlinear vibrations of elastic beams
Krysko, V. A.; Zhigalov, M. V.; Saltykova, O. A.; Krysko, A. V.
2011-09-01
Models of geometrically nonlinear Euler-Bernoulli, Timoshenko, and Sheremet'ev-Pelekh beams under alternating transverse loading were constructed using the variational principle and the hypothesis method. The obtained differential equation systems were analyzed based on nonlinear dynamics and the qualitative theory of differential equations with using the finite difference method with the approximation O(h2) and the Bubnov-Galerkin finite element method. It is shown that for a relative thickness λ ⩽ 50, accounting for the rotation and bending of the beam normal leads to a significant change in the beam vibration modes.
Nonlinear Shear Wave in a Non Newtonian Visco-elastic Medium
Janaki, D Banerjee M S; Chaudhuri, M
2013-01-01
An analysis of nonlinear transverse shear wave has been carried out on non-Newtonian viscoelastic liquid using generalized hydrodynamic(GH) model. The nonlinear viscoelastic behavior is introduced through velocity shear dependence of viscosity coefficient by well known Carreau -Bird model. The dynamical feature of this shear wave leads to the celebrated Fermi-Pasta-Ulam (FPU) problem. Numerical solution has been obtained which shows that initial periodic solutions reoccur after passing through several patterns of periodic waves. A possible explanation for this periodic solution is given by constructing modified Korteweg de Vries (mKdV) equation. This model has application from laboratory to astrophysical plasmas as well as biological systems.
Non-linear modeling of active biohybrid materials
Paetsch, C.
2013-11-01
Recent advances in engineered muscle tissue attached to a synthetic substrate motivate the development of appropriate constitutive and numerical models. Applications of active materials can be expanded by using robust, non-mammalian muscle cells, such as those of Manduca sexta. In this study, we propose a model to assist in the analysis of biohybrid constructs by generalizing a recently proposed constitutive law for Manduca muscle tissue. The continuum model accounts (i) for the stimulation of muscle fibers by introducing multiple stress-free reference configurations for the active and passive states and (ii) for the hysteretic response by specifying a pseudo-elastic energy function. A simple example representing uniaxial loading-unloading is used to validate and verify the characteristics of the model. Then, based on experimental data of muscular thin films, a more complex case shows the qualitative potential of Manduca muscle tissue in active biohybrid constructs. © 2013 Elsevier Ltd. All rights reserved.
Rofooei, Fayaz R.; Enshaeian, Alireza; Nikkhoo, Ali
2017-04-01
Dynamic deformations of beams and plates under moving objects have extensively been studied in the past. In this work, the dynamic response of geometrically nonlinear rectangular elastic plates subjected to moving mass loading is numerically investigated. A rectangular von Karman plate with various boundary conditions is modeled using specifically developed geometrically nonlinear plate elements. In the available finite element (FE) codes the only way to distinguish between moving masses from moving loads is to model the moving mass as a separate entity. However, these procedures still do not guarantee the inclusion of all inertial effects associated with the moving mass. In a prepared finite element code, the plate elements are developed using the conventional nonlinear methods, i.e., Total Lagrangian technique, but all inertial components associated with the travelling mass are taken into account. Since inertial components affect the mass, damping, and stiffness matrices of the system as the moving mass traverses the plate, appropriate time increments shall be selected to avoid numerical instability. The dynamic response of the plate induced by the moving mass is evaluated and compared to previous studies. Also, unlike the existing FE programs, the different inertial components of the normal contact force between the moving mass and the plate are computed separately to substantiate the no-separation assumption made for the moving mass. Also, it is observed that for large moving mass velocities, the peak plate deformation occurs somewhere away from the plate center point. Under the two extreme in-plane boundary conditions considered in this study, it is shown that if the geometrical nonlinearity of plate is accounted for, the deformations obtained would be less than the case with classical linear plate theory.
Knight, Norman F., Jr.; Song, Kyongchan; Elliott, Kenny B.; Raju, Ivatury S.; Warren, Jerry E.
2012-01-01
Elastic-plastic, large-deflection nonlinear stress analyses are performed for the external hat-shaped stringers (or stiffeners) on the intertank portion of the Space Shuttle s external tank. These stringers are subjected to assembly strains when the stringers are initially installed on an intertank panel. Four different stringer-feet configurations including the baseline flat-feet, the heels-up, the diving-board, and the toes-up configurations are considered. The assembly procedure is analytically simulated for each of these stringer configurations. The location, size, and amplitude of the strain field associated with the stringer assembly are sensitive to the assumed geometry and assembly procedure. The von Mises stress distributions from these simulations indicate that localized plasticity will develop around the first eight fasteners for each stringer-feet configuration examined. However, only the toes-up configuration resulted in high assembly hoop strains.
Wang, Ji; Yang, Jiashi; Li, Jiangyu
2007-03-01
Energy trapping has important applications in the design of thickness-shear resonators. Considerable efforts have been made for the effective utilization and improvement of energy trapping with variations of plate configurations, such as adding electrodes and contouring. As a new approach in seeking improved energy trapping feature, we analyze thickness-shear vibrations in an elastic plate with functionally graded material (FGM) of in-plane variation of mechanical properties, such as elastic constants and density. A simple and general equation governing the thickness-shear modes is derived from a variational analysis. A plate with piecewise constant material properties is analyzed as an example. It is shown that such a plate can support thickness-shear vibration modes with obvious energy trapping. Bechmann's number for the existence of only one trapped mode also can be determined accordingly.
Generalised Thermo-Elasticity When the Material Coupling Parameter Equals Unity
Directory of Open Access Journals (Sweden)
D. Rama Murthy
1979-04-01
Full Text Available Analytical solutions of three problems using the theory of generalised thermo-elasticity are presented for the case when the material coupling parameter equals unity (lambda =1. The problems considered are (1 Constant velocity impact, (2 Daniloviskaya's problem, and (3 Step in strain. Solutions are presented for the case of thin bars (one dimensional stress and are obtained using Laplace transform. There is a great simplification in the equations of generalised thermo-elasticity when the material coupling parameter equals unity, which permits the straight forward inversion of the transformed solutions. The solutions obtained are more general which includes the effect of relaxation time also. The important feature of this paper is that the solutions of coupled theory can be readily obtained simply by putting the relaxation constant equals to zero (Beta=0.
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.
Thermal conductivities of some novel nonlinear optical materials.
Beasley, J D
1994-02-20
Results of thermal conductivity measurements are reported for several of the more recently developed nonlinear optical crystals. New or substantially revised values of thermal conductivity were obtained in six materials. Notable thermal conductivities measured were those for AgGaS(2) [0.014 W/(cm K) and 0.015 W/(cm K)], AgGaSe(2) [0.010 W/(cm K) and 0.011 W/(cm K)], beta barium borate [0.016 W/(cm K) and 0.012 W/(cm K)], and ZnGeP(2) [0.36 W/(cm K) and 0.35 W/(cm K)], with values quoted for directions respectively parallel and perpendicular to the optic axis for each material. These new data provide necessary input for the design of high-power optical frequency converters.
Thioborates: potential nonlinear optical materials with rich structural chemistry.
Lian, Yu-Kun; Wu, Li-Ming; Chen, Ling
2017-03-27
Nonlinear optical (NLO) crystal materials with good performance are urgently needed. Various compounds have been explored to date. Metal chalcogenides and borates are common sources of potential NLO materials with desirable properties, particularly in the IR and UV regions, respectively. However, these two types of crystals have their specific drawbacks. Thioborates, as an emerging system, have unique advantages by combining the merits of borates and sulfides, i.e., the high laser damage thresholds and rich structural diversity of borates with large optical nonlinearity and the favorable transparency range of sulfides. However, only a limited number of thioborates are known. This paper summarizes the known thioborates according to structural motifs that range from zero-dimension to three-dimension, most of which are formed by sharing corners of the basic building units (BS3)(3-) and (BS4)(5-). Although nearly one-third of the known thioborates are noncentrosymmetric, most of their properties, especially their NLO behaviors, are unexplored. Further attempts and additional investigations are required with respect to design syntheses, property improvements and micro-mechanism studies.
CAVITY FORMATION AT THE CENTER OF A SPHERE COMPOSED OF TWO COMPRESSIBLE HYPER-ELASTIC MATERIALS
Institute of Scientific and Technical Information of China (English)
任九生; 程昌钧; 朱正佑
2003-01-01
The cavitated bifurcation problem in a solid sphere composed of two compressible hyper-elastic materials under a uniform boundary radial stretch was examined.The solutions, including the trivial solution and the cavitated solutions, were obtained.The bifurcation curves and the stress contributions subsequent to cavitation were discussed.The phenomena of the right and the left bifurcations as well as the catastrophe and concentration of stresses are observed. The stability of solutions is discussed through the energy comparison.
Ultrasonic measurement of the moduli of elasticity of refractory materials at high temperatures
Fargeot, D.; Gault, C.; Platon, F.
1980-02-01
A method of ultrasonic measurement of moduli of elasticity of refractory materials up to temperatures of the order of 2000 K is described. The use of magnetostrictive transducers allows operation in the 150-350 kHz frequency range of filamentary test samples with a diameter of about 2 mm and a length of 40-50 mm. Two practical examples are considered, for alpha alumina and for gamma alumina obtained by plasma torch projection.
A 3D Orthotropic Strain-Rate Dependent Elastic Damage Material Model.
Energy Technology Data Exchange (ETDEWEB)
English, Shawn Allen
2014-09-01
A three dimensional orthotropic elastic constitutive model with continuum damage and cohesive based fracture is implemented for a general polymer matrix composite lamina. The formulation assumes the possibility of distributed (continuum) damage followed b y localized damage. The current damage activation functions are simply partially interactive quadratic strain criteria . However, the code structure allows for changes in the functions without extraordinary effort. The material model formulation, implementation, characterization and use cases are presented.
Kobayashi, Hirohito; Vanderby, Ray
2007-02-01
Many materials (e.g., rubber or biologic tissues) are "nearly" incompressible and often assumed to be incompressible in their constitutive equations. This assumption hinders realistic analyses of wave motion including acoustoelasticity. In this study, this constraint is relaxed and the reflected waves from nearly incompressible, hyper-elastic materials are examined. Specifically, reflection coefficients are considered from the interface of water and uni-axially prestretched rubber. Both forward and inverse problems are experimentally and analytically studied with the incident wave perpendicular to the interface. In the forward problem, the wave reflection coefficient at the interface is evaluated with strain energy functions for nearly incompressible materials in order to compute applied strain. For the general inverse problem, mathematical relations are derived that identify both uni-axial strains and normalized material constants from reflected wave data. The validity of this method of analysis is demonstrated via an experiment with stretched rubber. Results demonstrate that applied strains and normalized material coefficients can be simultaneously determined from the reflected wave data alone if they are collected at several different (but unknown) levels of strain. This study therefore indicates that acoustoelasticity, with an appropriate constitutive formulation, can determine strain and material properties in hyper-elastic, nearly incompressible materials.
Relationships between elastic anisotropy and thermal expansion in A2Mo3O12 materials.
Romao, Carl P; Donegan, S P; Zwanziger, J W; White, Mary Anne
2016-11-09
We report calculated elastic tensors, axial Grüneisen parameters, and thermal stress distributions in Al2Mo3O12, ZrMgMo3O12, Sc2Mo3O12, and Y2Mo3O12, a series of isomorphic materials for which the coefficients of thermal expansion range from low-positive to negative. Thermal stress in polycrystalline materials arises from interactions between thermal expansion and mechanical properties, and both can be highly anisotropic. Thermal expansion anisotropy was found to be correlated with elastic anisotropy: axes with negative thermal expansion were less compliant. Calculations of axial Grüneisen parameters revealed that the thermal expansion anisotropy in these materials is in part due to the Poisson effect. Models of thermal stress due to thermal expansion anisotropy in polycrystals following cooling showed thermal stresses of sufficient magnitude to cause microcracking in all cases. The thermal expansion anisotropy was found to couple to elastic anisotropy, decreasing the bulk coefficient of thermal expansion and leading to lognormal extremes of the thermal stress distributions.
Modeling and analysis of nonlinear mechanics of a super-thin elastic rod%超细长弹杆非线形力学的建模与分析
Institute of Scientific and Technical Information of China (English)
薛纭
2006-01-01
@@ Nonlinear mechanics for a super-thin elastic rod with the biological background of DNA super-coiling macromolecules is an interdisciplinary research area of classical mechanics and molecular biology. It is also a subject of dynamics and elasticity because elastic bodies are analyzed via the theory of dynamics. It is in frontiers of general mechanics (dynamics and control).
2007-05-04
amplitude of oscillation, 01 0, kF ox <<−=− and A kF ox <<−=+ 02 , , where 12 kk < . If 02 =k , the elastoplastic case of Iwan’s model for...curve identifies the system as potentially mesoscopic elastic. The elasto-slip model of elastoplastic hysteresis presented by Iwan exhibits linear...in damaged concrete: Quantitative analysis of slow and fast dynamics,” Phys. Rev. B, 73, 014116 (2006). Bolton, M.D., and Wilson, J.M.R, “An
Zhou, Hao-Miao; Li, Meng-Han; Li, Xiao-Hong; Zhang, Da-Guang
2016-08-01
For a giant magnetostrictive rod under the action of multiple physical loads, such as an external magnetic field, temperature and axial pre-stress, this paper proposes a general one-dimensional nonlinear magneto-thermo-mechanical coupled constitutive model. This model is based on the Taylor expansion of the elastic Gibbs free energy of giant magnetostrictive material and thermodynamic relations from the perspective of macro continuum mechanics. Predictions made using this model are in good agreement with experimental data for magnetization and the magnetostrictive strain curve under the collective effect of pre-stress and temperature. Additionally, the model overcomes the drawback of the existing magneto-thermo-mechanical constitutive model that cannot accurately predict the magnetization and magnetostrictive strain curve for different temperatures and pre-stresses. Furthermore, the constitutive model does not contain an implicit function and is compact, and can thus be applied in both situations of tensile and compressive stress and to both positive and negative magnetostrictive materials, and it is thus appropriate for engineering applications. Comprehensive analysis shows that the model fully describes the nonlinear coupling properties of a magnetic field, magnetostrictive strain and elasticity of a magnetostrictive material subjected to stress, a magnetic field and heat.
Chevalier, Luc; 10.1002/pen.10948
2010-01-01
We present an experimental approach to discriminate hyper-elastic models describing the mechanical behavior of rubber-like materials. An evaluation of the displacement field obtained by digital image correlation allows us to evaluate the heterogeneous strain field observed during these tests. We focus on the particular case of hyper-elastic models to simulate the behavior of some rubber-like materials. Assuming incompressibility of the material, the hyper-elastic potential is determined from tension and compression tests. A biaxial loading condition is obtained in a multiaxial testing machine and model predictions are compared with experimental results.
Institute of Scientific and Technical Information of China (English)
2008-01-01
The elastic-plastic indentation properties of materials with varying ratio of hardness to Young's modulus (H/E) were analyzed with the finite element method. And the indentation stress fields of materials with varying ratio H/E on the surface were studied by the experiment. The results show that the penetration depth, contact radius, plastic pileup and the degree of elastic recovery depend strongly on the ratio H/E. Moreover, graphs were established to describe the relationship between the elastic-plastic indentation parameters and H/E. The established graphs can be used to predict the H/E of materials when compared with experimental data.
Elastic-plastic characterization of a cast stainless steep pipe elbow material
Energy Technology Data Exchange (ETDEWEB)
Joyce, J.A. [Naval Academy, Annapolis, MD (United States); Hackett, E.M.; Roe, C. [David W. Taylor Naval Ship Research and Development Center, Annapolis, MD (United States)
1992-01-01
Tests conducted in Japan as part of the High Level Vibration Test (HLVT) program for reactor piping systems revealed fatigue crack growth in a cast stainless steel pipe elbow. The material tested was equivalent to ASME SA-351CF8M. The David Taylor Research Center (DTRC) was tasked to developed the appropriate material property data to characterize cyclic deformation, cyclic elastic-plastic crack growth and ductile tearing resistance in the pipe elbow material. It was found that the cast stainless steel was very resistant to ductile crack extension. J-R curves essentially followed a blunting behavior to very high J levels. Low cycle fatigue crack growth rate data obtained on this material using a cyclic J integral approach was consistent with the high cycle fatigue crack growth rate and with a standard textbook correlation equation typical for this type of material. Evaluation of crack closure effects was essential to accurately determine the crack driving force for cyclic elastic- plastic crack growth in this material. SEM examination of several of the cyclic J test fracture surfaces indicated that fatigue was the primary mode of fracture with ductile crack extension intervening only during the last few cycles of loading.
Belli, Renan; Petschelt, Anselm; Lohbauer, Ulrich
2014-04-01
The aim of this study was to measure the linear elastic material properties of direct dental resin composites and correlate them with their fatigue strength under cyclic loading. Bar specimens of twelve resin composites were produced according to ISO 4049 and tested for elastic modulus (Emod) in 3-point bending (n=10), flexural strength (FS) (n=15) and single-edge-notch-beam fracture toughness (FT) (n=15), both in 4-point bending. Using the same specimen geometry, the flexural fatigue strength (FFS) was determined using the staircase approach after 10(4) cycles at 0.5 Hz in 4-point bending (n=25). The observation of the fracture surface and fracture profiles was conducted using a scanning electron microscope in order to evaluate the respective fracture mechanisms according to the two different loading conditions. Materials were ranked differently according to the tested parameters. Only weak correlations were found between any of the initial properties and FFS or strength loss. The best correlation to FFS was found to be the Emod (r(2)=0.679), although only slightly. Crack path in both loading conditions was mainly interparticle, with the crack propagating mainly within the matrix phase for fatigued specimens and eventually through the filler/matrix interface for statically loaded specimens. Fracture of large particles or prepolymerized fillers was only observed in specimens of FS and FT. Initial properties were better associated with microstructural features, whereas the fatigue resistance showed to be more dependent on aspects relating to the matrix phase. Our results show that linear elastic properties such as elastic modulus, flexural strength and fracture toughness are not good descriptors of the fatigue resistance of dental resin composite under cyclic bending, and may therefore have limited clinical relevance. Copyright © 2014 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.
Directory of Open Access Journals (Sweden)
R. P. Pogrebnyak
2017-08-01
Full Text Available Purpose. The article is aimed to determine the conditions of a dynamic error formation of contour machine cutting of surface of the real railway wheel flange by the cup-tip tool and propose the ways of reducing the errors. Methodology. The problem was solved by the creation of dynamic nonlinear and elastic calculation model with further modeling of its loading by the external force factors. The values of forces were obtained by analytical and experimental methods. The calculation scheme of the equilibrium support is a nonlinear two-mass system, a dynamic model of slide - single-mass with one degree of freedom. The basis of the mathematical description of technological loads is the results of factory experiments, as well as analytical generalizations obtained as a result of the comparison of several schemes of the formation of the wheel flange. Analytical determination of the components of the cutting force takes into account the changes in the kinematic parameters of the cutting mode when the profiling is done using a shaped tool. Findings. During processing of the wheel flange the radial and axial components of the cutting forces that load slide and slide-block of machine are alternating. There are conditions in drive of slide and slide-block when the gaps appear, and it is possible at any profile geometry of the wheel. The peculiarities of loading of the slide and slide-block forming a flange (with biharmonic allowance cause the occurrence of the processing areas where the gaps increase many times in drives of mechanical transmissions and error of forms increases. The dynamic system of the drive is quite tough and high-frequency and it is sensitive to the presence of gaps. Originality. The author created elastic nonlinear dynamic models of support and slide. In accordance with the model it is written and solved equations of motion of the masses and loading of the connections. The conditions of the stable motion were found. Practical value. It
Dynamics of pre-strained bi-material elastic systems linearized three-dimensional approach
Akbarov, Surkay D
2015-01-01
This book deals with dynamics of pre-stressed or pre-strained bi-material elastic systems consisting of stack of pre-stressed layers, stack of pre-stressed layers and pre-stressed half space (or half plane), stack of pre-stressed layers as well as absolute rigid foundation, pre-stressed compound solid and hollow cylinders and pre-stressed sandwich hollow cylinders. The problems considered in the book relate to the dynamics of a moving and oscillating moving load, forced vibration caused by linearly located or point located time-harmonic forces acting to the foregoing systems. Moreover, a considerable part of the book relate to the problems regarding the near surface, torsional and axisymmetric longitudinal waves propagation and dispersion in the noted above bi-material elastic systems. The book carries out the investigations within the framework of the piecewise homogeneous body model with the use of the Three-Dimensional Linearized Theory of Elastic Waves in Initially Stressed Bodies.
Moiseenko, D. D.; Panin, S. V.; Maksimov, P. V.; Panin, V. E.; Babich, D. S.; Berto, F.
2016-11-01
The paper is devoted to detailed investigation of rotational deformation modes at the notch tip during shock loading. Using hybrid discrete-continuum approach of Excitable Cellular Automata the series of numerical experiments were conducted to simulate deformation behavior of ductile steel in the vicinities of U-, I- and V-notches. The detailed analysis of the force moment distribution at the notch tip allowed revealing the relationship between the rotational deformation modes at different scales. It was found that the elastic energy release is realized by means of the modulation of the magnitude and the sign of the force moment. The obtained results makes possible to optimize crystal structure for improvement of mechanical properties of the material in the way of elastic energy release by reversible microrotations.
Elastic-plastic deformation of sandwich rod on elastic basis
Institute of Scientific and Technical Information of China (English)
GU Yu
2008-01-01
Sandwich composite material possesses advantages of both light weight and high strength.Although the mechanical behaviors of sandwich composite material with the influence of single external environment have been intensively studied,little work has been done in the study of mechanical property,in view of the nonlinear behavior of sandwich composites in the complicated external environments.In this paper,the problem about the bending of the three-layer elastic-plastic rod located on the elastic base,with a compressibly physical nonlinear core,has been studied.The mechanical response of the designed three-layer elements consisting of two bearing layers and a core has been examined.The complicated problem about curving of the three-layer rod located on the elastic base has been solved.The convergence of the proposed method of elastic solutions is examined to convince that the solution is acceptable.The calculated results indicate that the plasticity and physical nonlinearity of materials have a great influence on the deformation of the sandwich rod on the elastic basis.
Evaluation of the Elastic Properties of Thirteen Silicone Interocclusal Recording Materials
Zietek, Marek
2016-01-01
Background. Addition silicones are popular as dental impression materials and are used in bite registration procedures. Objective. This study aimed to compare the postsetting elasticities and other mechanical properties of thirteen addition silicone interocclusal recording materials. Materials and Methods. The following materials were investigated: Colorbite D, Futar D, Genie Bite, Jet Blue Bite fast, Memoreg 2, O-Bite, Occlufast Rock, Omni-Bite Plus, Regidur i, Registrado X-tra, Regofix transparent, StoneBite, and Variotime Bite. Thirty specimens of each material were tested. The elasticities and strengths of the materials were measured with a universal testing machine, and computer software was used to determine the E-moduli, ultimate tensile strengths, and ultimate elongations of the specimens. Results. The results were subjected to statistical analysis using the Kruskal-Wallis test (p ≤ 0.05). The statistics revealed that the mean E-modulus values varied significantly across the materials (p = 0.000) and were highest for the StoneBite and Registrado X-tra and lowest for the Regofix transparent. The ultimate tensile strengths were highest for the Regofix transparent and Registrado X-tra (p = 0.000) and lowest for the Jet Blue Bite fast and Memoreg 2 (p = 0.000). The elongation percentages at the point of breaking varied significantly across the materials (p = 0.000); the lowest value was observed for the StoneBite, whereas the Regofix transparent nearly doubled original length. Conclusions. The authors concluded that materials with the high E-moduli and great ultimate tensile strengths may be most useful clinically. Registrado X-tra and StoneBite best met these criteria. PMID:27747239
Evaluation of the Elastic Properties of Thirteen Silicone Interocclusal Recording Materials
Directory of Open Access Journals (Sweden)
Mieszko Wieckiewicz
2016-01-01
Full Text Available Background. Addition silicones are popular as dental impression materials and are used in bite registration procedures. Objective. This study aimed to compare the postsetting elasticities and other mechanical properties of thirteen addition silicone interocclusal recording materials. Materials and Methods. The following materials were investigated: Colorbite D, Futar D, Genie Bite, Jet Blue Bite fast, Memoreg 2, O-Bite, Occlufast Rock, Omni-Bite Plus, Regidur i, Registrado X-tra, Regofix transparent, StoneBite, and Variotime Bite. Thirty specimens of each material were tested. The elasticities and strengths of the materials were measured with a universal testing machine, and computer software was used to determine the E-moduli, ultimate tensile strengths, and ultimate elongations of the specimens. Results. The results were subjected to statistical analysis using the Kruskal-Wallis test (p≤0.05. The statistics revealed that the mean E-modulus values varied significantly across the materials (p=0.000 and were highest for the StoneBite and Registrado X-tra and lowest for the Regofix transparent. The ultimate tensile strengths were highest for the Regofix transparent and Registrado X-tra (p=0.000 and lowest for the Jet Blue Bite fast and Memoreg 2 (p=0.000. The elongation percentages at the point of breaking varied significantly across the materials (p=0.000; the lowest value was observed for the StoneBite, whereas the Regofix transparent nearly doubled original length. Conclusions. The authors concluded that materials with the high E-moduli and great ultimate tensile strengths may be most useful clinically. Registrado X-tra and StoneBite best met these criteria.
Evaluation of the Elastic Properties of Thirteen Silicone Interocclusal Recording Materials.
Wieckiewicz, Mieszko; Grychowska, Natalia; Zietek, Marek; Wieckiewicz, Wlodzimierz
2016-01-01
Background. Addition silicones are popular as dental impression materials and are used in bite registration procedures. Objective. This study aimed to compare the postsetting elasticities and other mechanical properties of thirteen addition silicone interocclusal recording materials. Materials and Methods. The following materials were investigated: Colorbite D, Futar D, Genie Bite, Jet Blue Bite fast, Memoreg 2, O-Bite, Occlufast Rock, Omni-Bite Plus, Regidur i, Registrado X-tra, Regofix transparent, StoneBite, and Variotime Bite. Thirty specimens of each material were tested. The elasticities and strengths of the materials were measured with a universal testing machine, and computer software was used to determine the E-moduli, ultimate tensile strengths, and ultimate elongations of the specimens. Results. The results were subjected to statistical analysis using the Kruskal-Wallis test (p ≤ 0.05). The statistics revealed that the mean E-modulus values varied significantly across the materials (p = 0.000) and were highest for the StoneBite and Registrado X-tra and lowest for the Regofix transparent. The ultimate tensile strengths were highest for the Regofix transparent and Registrado X-tra (p = 0.000) and lowest for the Jet Blue Bite fast and Memoreg 2 (p = 0.000). The elongation percentages at the point of breaking varied significantly across the materials (p = 0.000); the lowest value was observed for the StoneBite, whereas the Regofix transparent nearly doubled original length. Conclusions. The authors concluded that materials with the high E-moduli and great ultimate tensile strengths may be most useful clinically. Registrado X-tra and StoneBite best met these criteria.
Converting strain maps into elasticity maps for materials with small contrast
Bellis, Cédric
2017-01-01
This study addresses the question of the quantitative reconstruction of heterogeneous distributions of isotropic elastic moduli from full strain field data. This parameter identification problem exposes the need for a local reconstruction procedure that is investigated here in the case of materials with small contrast. To begin with the integral formulation framework for the periodic linear elasticity problem, first- and second-order asymptotics are retained for the strain field solution and the effective elasticity tensor. Properties of the featured Green's tensor are investigated to characterize its decomposition into an isotropic term and an orthogonal part. The former is then shown to define a local contribution to the volume integral equations considered. Based on this property, then the combination of multiple strain field solutions corresponding to well-chosen applied macroscopic strains is shown to lead to a set of local and uncoupled identities relating, respectively, the bulk and shear moduli to the spherical and deviatoric components of the strain fields. Valid at the first-order in the weak contrast limit, such relations permit point-wise conversions of strain maps into elasticity maps. Furthermore, it is also shown that for macroscopically isotropic material configurations a single strain field solution is actually sufficient to reconstruct either the bulk or the shear modulus distribution. Those results are then revisited in the case of bounded media. Finally, some sets of analytical and numerical examples are provided for comparison and to illustrate the relevance of the obtained strain-modulus local equations for a parameter identification method based on full-field data.
Basic Studies of Nonlinear Optical Materials for Eye and Sensor Protection
2004-03-10
1 BASIC STUDIES OF NONLINEAR OPTICAL MATERIALS FOR EYE AND SENSOR PROTECTION I. Abstract: We have studied the spectroscopy, kinetics and...study liquid or solid materials from CW to 100x10-15 seconds. Basic Studies of Nonlinear Optical Materials for Eye and Sensor Protection
Piwowarczyk, Andree; Ottl, Peter; Büchler, Alfred; Lauer, Hans-Christoph; Hoffmann, Andrea
2002-01-01
This study evaluated the dimensional accuracy of various impression materials for monophase elastic impression making. To isolate this parameter, a direct measurement of the impressions was made without taking the model material into consideration. A total of eight materials were tested; six impression materials were addition-curing silicones, and two were polyether impression materials. All materials were processed according to the manufacturers' instructions. A specially developed precision mold made of stainless steel served as basis for measuring the elastomeric impression materials. Using a stereomicroscope at a temperature of 23.0 +/- 1.0 degrees C and with a precision linear adjustment and lathe, sights were set on the marking points of customized posts. The measurement was performed after the earliest time possible for fabricating the model according to the manufacturer (time 1) and after 90 minutes (time 2). In a one-way analysis of variance, multiple average comparisons of dimensional accuracy were made (P materials under investigation. Under the conditions of this study, the impression materials tested demonstrated a very high dimensional accuracy. The arithmetic means of the dimensional changes ranged from -11 to 19 microns for both measuring times. Since as a rule, no significant dimensional changes occurred for the different impression materials between time 1 and time 2, this time interval for fabricating a model can be recommended.
Biocompatibility and biomechanical analysis of elastic TPU threads as new suture material.
Vogels, Ruben R M; Lambertz, Andreas; Schuster, Philipp; Jockenhoevel, Stefan; Bouvy, Nicole D; Disselhorst-Klug, Catherine; Neumann, Ulf P; Klinge, Uwe; Klink, Christian D
2017-01-01
High suture tension is one of the causes for many wound-healing problems. Constriction of tissue within the suture loops of nonelastic sutures can lead to cutting of the suture through tissues and necrosis of the tissue within these loops. The use of elastic materials in new suture types could give the material the ability to adapt tension to the tissue requirements and subsequently lead to more vital tissue within its loops. We evaluated the foreign body host response, as indicator of biocompatibility, to a new thermoplastic poly(carbonate) urethane (TPU) synthetic suture material in a rat model compared with standard nonelastic polypropylene (PP) sutures. Tissue samples were collected at 7 and 21 days, and host response was evaluated. Subsequently, suture tension curves of the new elastic sutures for the first 30 min after knotting were recorded in a pig model. The new TPU sutures showed an improved foreign body response when compared with that of PP, with a reduction in the amount of macrophages surrounding the material. Tension experiments showed a superior tension curve for TPU sutures, with a major reduction in peak suture tension when compared with that of standard PP sutures, while still retaining adequate tension after 30 min. © 2015 Wiley Periodicals, Inc. J Biomed Mater Res Part B: Appl Biomater, 105B: 99-106, 2017.
On the prediction of stress relaxation from known creep of nonlinear materials
Energy Technology Data Exchange (ETDEWEB)
Touati, D.; Cederbaum, G. [Ben-Gurion Univ. of the Negev, Beer Sheva (Israel)
1997-04-01
A method to predict the nonlinear relaxation behavior from creep experiments of nonlinear viscoelastic materials is presented. It is shown that for given nonlinear creep properties, and creep compliance represented by the Prony series, the Schapery creep model can be transformed into a set of first order nonlinear equations. The solution of these equations enables the obtaining of the nonlinear stress relaxation curves. The strain-dependent constitutive equation can then be constructed for a given nonlinear viscoelastic model, as needed for engineering applications. A comparison example of the calculated stress relaxation curves, with test data for polyurethane demonstrates the very good accuracy of the proposed method.
Zarepour, Misagh; Amirhosein Hosseini, Seyed
2016-08-01
This study presents an examination of nonlinear free vibration of a nanobeam under electro-thermo-mechanical loading with elastic medium and various boundary conditions, especially the elastic boundary condition. The nanobeam is modeled as an Euler-Bernoulli beam. The von Kármán strain-displacement relationship together with Hamilton’s principle and Eringen’s theory are employed to derive equations of motion. The nonlinear free vibration frequency is obtained for simply supported (S-S) and elastic supported (E-E) boundary conditions. E-E boundary condition is a general and actual form of boundary conditions and it is chosen because of more realistic behavior. By applying the differential transform method (DTM), the nanobeam’s natural frequencies can be easily obtained for the two different boundary conditions mentioned above. Performing a precise study led to investigation of the influences of nonlocal parameter, temperature change, spring constants (either for elastic medium or boundary condition) and imposed electric potential on the nonlinear free vibration characteristics of nanobeam. The results for S-S and E-E nanobeams are compared with each other. In order to validate the results, some comparisons are presented between DTM results and open literature to show the accuracy of this new approach. It has been discovered that DTM solves the equations with minimum calculation cost.
Institute of Scientific and Technical Information of China (English)
黄冬梅; 徐伟; 谢文贤; 韩群
2015-01-01
In this paper, the principal resonance response of a stochastically driven elastic impact (EI) system with time-delayed cubic velocity feedback is investigated. Firstly, based on the method of multiple scales, the steady-state response and its dynamic stability are analyzed in deterministic and stochastic cases, respectively. It is shown that for the case of the multi-valued response with the frequency island phenomenon, only the smallest amplitude of the steady-state response is stable under a certain time delay, which is different from the case of the traditional frequency response. Then, a design criterion is proposed to suppress the jump phenomenon, which is induced by the saddle-node bifurcation. The effects of the feedback parameters on the steady-state responses, as well as the size, shape, and location of stability regions are studied. Results show that the system responses and the stability boundaries are highly dependent on these parameters. Furthermore, with the purpose of suppressing the amplitude peak and governing the resonance stability, appropriate feedback gain and time delay are derived.
Influence of spiral framework on nonlinear optical materials.
Hu, Yang-Yang; Sun, Shi-Ling; Tian, Wen-Tao; Tian, Wei Quan; Xu, Hong-Liang; Su, Zhong-Min
2014-04-04
A series of spiral donor-π-acceptor frameworks (i.e. 2-2, 3-3, 4-4, and 5-5) based on 4-nitrophenyldiphenylamine with π-conjugated linear acenes (naphthalenes, anthracenes, tetracenes, and pentacenes) serving as the electron donor and nitro (NO2 ) groups serving as the electron acceptor were designed to investigate the relationships between the nonlinear optical (NLO) responses and the spirality in the frameworks. A parameter denoted as D was defined to describe the extent of the spiral framework. The D value reached its maximum if the number of NO2 groups was equal to the number of fused benzene rings contained in the linear acene. A longer 4-nitrophenyldiphenylamine chain led to a larger D value and, further, to a larger first hyperpolarizability. Different from traditional NLO materials with charge transfer occurring in the one-dimensional direction, charge transfer in 2-2, 3-3, 4-4, and 5-5 occur in three-dimensional directions due to the attractive spiral frameworks, and this is of great importance in the design of NLO materials. The origin of such an enhancement in the NLO properties of these spiral frameworks was explained with the aid of molecular orbital analysis. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Elastic wave propagation in adaptive honeycomb-based materials with high connectivity
Zhu, Zhi-Wei; Deng, Zi-Chen
2016-08-01
Beam-type periodic materials with high connectivity have displayed unique band gap behaviors analogous to locally resonant band gaps in acoustic metamaterials. In this study, structurally square re-entrant honeycomb, one highly connected lattice configuration featuring eight folded beams connected at each joint, is introduced to be the host structure of a smart material to tailor the elastic wave propagation. Finite length piezoelectric patches connected with negative capacitance shunting circuits are arranged on the beam surfaces, providing active adjustment via altering the parameters of shunting circuits. The characteristics of band structure of this smart structured material are investigated through the application of finite element method in conjunction with the Bloch theorem. Results demonstrate that the variation of internally resonant band gaps induced by the alteration of the piezoelectric patches to those positions and mechanical properties, can be precisely estimated by simple heuristic models proposed according to deformation characteristics of standing wave modes. This founding could promote the practical implementation of the highly connected honeycombs in the adaptive control to elastic wave.
CRACK PROPAGATION IN POLYCRYSTALLINE ELASTIC-VISCOPLASTIC MATERIALS USING COHESIVE ZONE MODELS
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Cohesive zone model was used to simulate two-dimensional plane strain crack propagation at the grain level model including grain boundary zones. Simulated results show that the original crack-tip may not be separated firstly in an elastic-viscoplastic polycrystals. The grain interior's material properties (e.g. strain rate sensitivity) characterize the competitions between plastic and cohesive energy dissipation mechanisms.The higher the strain rate sensitivity is, the larger amount of the external work is transformed into plastic dissipation energy than into cohesive energy, which delays the cohesive zone rupturing. With the strain rate sensitivity decreased, the material property tends to approach the elastic-plastic responses. In this case, the plastic dissipation energy decreases and the cohesive dissipation energy increases which accelerates the cohesive zones debonding. Increasing the cohesive strength or the critical separation displacement will reduce the stress triaxiality at grain interiors and grain boundaries. Enhancing the cohesive zones ductility can improve the matrix materials resistance to void damage.
An existence result for a model of complete damage in elastic materials with reversible evolution
Bonetti, Elena; Freddi, Francesco; Segatti, Antonio
2016-07-01
In this paper, we consider a model describing evolution of damage in elastic materials, in which stiffness completely degenerates once the material is fully damaged. The model is written by using a phase transition approach, with respect to the damage parameter. In particular, a source of damage is represented by a quadratic form involving deformations, which vanishes in the case of complete damage. Hence, an internal constraint is ensured by a maximal monotone operator. The evolution of damage is considered "reversible", in the sense that the material may repair itself. We can prove an existence result for a suitable weak formulation of the problem, rewritten in terms of a new variable (an internal stress). Some numerical simulations are presented in agreement with the mathematical analysis of the system.
An existence result for a model of complete damage in elastic materials with reversible evolution
Bonetti, Elena; Freddi, Francesco; Segatti, Antonio
2017-01-01
In this paper, we consider a model describing evolution of damage in elastic materials, in which stiffness completely degenerates once the material is fully damaged. The model is written by using a phase transition approach, with respect to the damage parameter. In particular, a source of damage is represented by a quadratic form involving deformations, which vanishes in the case of complete damage. Hence, an internal constraint is ensured by a maximal monotone operator. The evolution of damage is considered "reversible", in the sense that the material may repair itself. We can prove an existence result for a suitable weak formulation of the problem, rewritten in terms of a new variable (an internal stress). Some numerical simulations are presented in agreement with the mathematical analysis of the system.
Mode III interfacial crack in the presence of couple stress elastic materials
Piccolroaz, Andrea; Radi, Enrico
2010-01-01
In this paper we are concerned with the problem of a crack lying at the interface between dissimilar materials with microstructure undergoing antiplane deformations. The micropolar behaviour of the materials is described by the theory of couple stress elasticity developed by Koiter (1964). This constitutive model includes the characteristic lengths in bending and torsion and thus it is able to account for the underlying microstructure of the two materials. We perform an asymptotic analysis to investigate the behaviour of the solution near the crack tip. It turns out that the stress singularity at the crack tip is strongly influenced by the microstructural parameters and it may or may not show oscillatory behaviour depending on the ratio between the characteristic lengths.
Standard test method for linear-elastic plane-strain fracture toughness KIc of metallic materials
American Society for Testing and Materials. Philadelphia
2013-01-01
1.1 This test method covers the determination of fracture toughness (KIc) of metallic materials under predominantly linear-elastic, plane-strain conditions using fatigue precracked specimens having a thickness of 1.6 mm (0.063 in.) or greater subjected to slowly, or in special (elective) cases rapidly, increasing crack-displacement force. Details of test apparatus, specimen configuration, and experimental procedure are given in the Annexes. Note 1—Plane-strain fracture toughness tests of thinner materials that are sufficiently brittle (see 7.1) can be made using other types of specimens (1). There is no standard test method for such thin materials. 1.2 This test method is divided into two parts. The first part gives general recommendations and requirements for KIc testing. The second part consists of Annexes that give specific information on displacement gage and loading fixture design, special requirements for individual specimen configurations, and detailed procedures for fatigue precracking. Additional a...
Wang, Neng; Xia, Shuman
2017-01-01
A combined modeling and experimental effort is made in this work to examine the cohesive fracture mechanisms of heterogeneous elastic solids. A two-phase laminated composite, which mimics the key microstructural features of many tough engineering and biological materials, is selected as a model material system. Theoretical and finite element analyses with cohesive zone modeling are performed to study the effective fracture resistance of the heterogeneous material associated with unstable crack propagation and arrest. A crack-tip-position controlled algorithm is implemented in the finite element analysis to overcome the inherent instability issues resulting from crack pinning and depinning at local heterogeneities. Systematic parametric studies are carried out to investigate the effects of various material and geometrical parameters, including the modulus mismatch ratio, phase volume fraction, cohesive zone size, and cohesive law shape. Concurrently, a novel stereolithography-based three-dimensional (3D) printing system is developed and used for fabricating heterogeneous test specimens with well-controlled structural and material properties. Fracture testing of the specimens is performed using the tapered double-cantilever beam (TDCB) test method. With optimal material and geometrical parameters, heterogeneous TDCB specimens are shown to exhibit enhanced effective fracture energy and effective fracture toughness than their homogeneous counterparts, which is in good agreement with the modeling predictions. The integrative computational and experimental study presented here provides a fundamental mechanistic understanding of the fracture mechanisms in brittle heterogeneous materials and sheds light on the rational design of tough materials through patterned heterogeneities.
Evaluation of elastic modulus and hardness of highly inhomogeneous materials by nanoindentation
Epshtein, Svetlana A.; Borodich, Feodor M.; Bull, Steve J.
2015-04-01
The experimental and numerical techniques for evaluation of mechanical properties of highly inhomogeneous materials are discussed. The techniques are applied to coal as an example of such a material. Characterization of coals is a very difficult task because they are composed of a number of distinct organic entities called macerals and some amount of inorganic substances along with internal pores and cracks. It is argued that to avoid the influence of the pores and cracks, the samples of the materials have to be prepared as very thin and very smooth sections, and the depth-sensing nanoindentation (DSNI) techniques has to be employed rather than the conventional microindentation. It is shown that the use of the modern nanoindentation techniques integrated with transmitted light microscopy is very effective for evaluation of elastic modulus and hardness of coal macerals. However, because the thin sections are glued to the substrate and the glue thickness is approximately equal to the thickness of the section, the conventional DSNI techniques show the effective properties of the section/substrate system rather than the properties of the material. As the first approximation, it is proposed to describe the sample/substrate system using the classic exponential weight function for the dependence of the equivalent elastic contact modulus on the depth of indentation. This simple approach allows us to extract the contact modulus of the material constitutes from the data measured on a region occupied by a specific component of the material. The proposed approach is demonstrated on application to the experimental data obtained by Berkovich nanoindentation with varying maximum depth of indentation.
Li, Bing-Xuan; Wei, Yong; Huang, Cheng-Hui; Zhuang, Feng-Jiang; Zhang, Ge; Guo, Guo-Cong
2014-01-01
In the present paper the authors report a research on testing the nonlinear optical performance of optical materials in visible and infrared band. Based on the second order nonlinear optic principle and the photoelectric signal detection technology, the authors have proposed a new testing scheme in which a infrared OPO laser and a method for separating the beams arising from frequency matching and the light produced by other optical effects were used. The OPO laser is adopted as light source to avoid the error of measurement caused by absorption because the double frequency signal of the material is in the transmittance band Our research work includes testing system composition, operational principle and experimental method. The experimental results of KTP, KDP, AGS tested by this method were presented. In the experiment several new infrared non-linear materials were found. This method possesses the merits of good stability and reliability, high sensitivity, simple operation and good reproducibility, which can effectively make qualitative and semi-quantitative test for optical material's nonlinear optical properties from visible to infrared. This work provides an important test -method for the research on second order nonlinear optical materials in visible, infrared and ultraviolet bands.
Bazan, Carlos; Hawkins, Trevor; Torres-Barba, David; Blomgren, Peter; Paolini, Paul
2011-08-22
We are exploring the viability of a novel approach to cardiocyte contractility assessment based on biomechanical properties of the cardiac cells, energy conservation principles, and information content measures. We define our measure of cell contraction as being the distance between the shapes of the contracting cell, assessed by the minimum total energy of the domain deformation (warping) of one cell shape into another. To guarantee a meaningful vis-à-vis correspondence between the two shapes, we employ both a data fidelity term and a regularization term. The data fidelity term is based on nonlinear features of the shapes while the regularization term enforces the compatibility between the shape deformations and that of a hyper-elastic material. We tested the proposed approach by assessing the contractile responses in isolated adult rat cardiocytes and contrasted these measurements against two different methods for contractility assessment in the literature. Our results show good qualitative and quantitative agreements with these methods as far as frequency, pacing, and overall behavior of the contractions are concerned. We hypothesize that the proposed methodology, once appropriately developed and customized, can provide a framework for computational cardiac cell biomechanics that can be used to integrate both theory and experiment. For example, besides giving a good assessment of contractile response of the cardiocyte, since the excitation process of the cell is a closed system, this methodology can be employed in an attempt to infer statistically significant model parameters for the constitutive equations of the cardiocytes.
Nonlinear wave mixing and susceptibility properties of negative refractive index materials.
Chowdhury, Aref; Tataronis, John A
2007-01-01
We present an analysis of second-order and third-order nonlinear susceptibilities and wave-mixing properties of negative refractive index materials. We show that the nonlinear susceptibilities for noncentrosymmetric and centrosymmetric media may be positive or negative and away from resonance depending on the frequency of interest relative to the resonant frequencies of the material. Manipulation of the signs of the nonlinear susceptibilities is important in the field of optics, particularly for solitons and compensation of nonlinear effects. We also show that three- and four-wave mixing can be naturally phase matched in the material.
Material nonlinear analysis via mixed-iterative finite element method
Sutjahjo, Edhi; Chamis, Christos C.
1992-01-01
The performance of elastic-plastic mixed-iterative analysis is examined through a set of convergence studies. Membrane and bending behaviors are tested using 4-node quadrilateral finite elements. The membrane result is excellent, which indicates the implementation of elastic-plastic mixed-iterative analysis is appropriate. On the other hand, further research to improve bending performance of the method seems to be warranted.
Zhang, Rui; Schweizer, Kenneth S
2012-04-21
We generalize the microscopic naïve mode coupling and nonlinear Langevin equation theories of the coupled translation-rotation dynamics of dense suspensions of uniaxial colloids to treat the effect of applied stress on shear elasticity, cooperative cage escape, structural relaxation, and dynamic and static yielding. The key concept is a stress-dependent dynamic free energy surface that quantifies the center-of-mass force and torque on a moving colloid. The consequences of variable particle aspect ratio and volume fraction, and the role of plastic versus double glasses, are established in the context of dense, glass-forming suspensions of hard-core dicolloids. For low aspect ratios, the theory provides a microscopic basis for the recently observed phenomenon of double yielding as a consequence of stress-driven sequential unlocking of caging constraints via reduction of the distinct entropic barriers associated with the rotational and translational degrees of freedom. The existence, and breadth in volume fraction, of the double yielding phenomena is predicted to generally depend on both the degree of particle anisotropy and experimental probing frequency, and as a consequence typically occurs only over a window of (high) volume fractions where there is strong decoupling of rotational and translational activated relaxation. At high enough concentrations, a return to single yielding is predicted. For large aspect ratio dicolloids, rotation and translation are always strongly coupled in the activated barrier hopping event, and hence for all stresses only a single yielding process is predicted.
Georgievskii, D. V.
2007-06-01
Material functions are necessary element of the constitutive relations determining any model of continuum. These functions can be defined as a collection of objects from which the operator of constitutive relations can be reconstructed completely. The material functions are found in test experiments and show the differences between a given medium and other media in the framework of the same model [1]. The "test experiment theory" is an important part of modern experimental mechanics. Just as in any experiment, from determining the viscosity coefficient by using the rotational viscosimeters to constructing the yield surface by using machines combined loading, the material functions are determined with an unavoidable error. For example, experimenters know that, in experiments with arbitrary accuracy, the moduli of elasticity can only be measured with an unimprovable tolerance of about 7%. Starting already from [2], the investigators' attention has been repeatedly drawn to the fact that it is necessary to take into account this tolerance in determining the material constants, functions, and functionals in problems of mechanics and especially in analyzing the stability of deformation processes. Mathematically, this means that problems of stability under perturbations of the initial data, external constantly acting forces, domain boundaries, etc. should be supplemented with the assumption that the material functions have unknown perturbations of a certain class [3]. The variations of material functions in the framework of the linearized stability theory were considered in [2, 4, 5]. In what follows, we study isotropic tensor functions in the most general case of scalar and tensor nonlinearity. These functions are assigned the meaning of constitutive relations between the stress and strain rate tensors in continuum. These constitutive relations contain scalar material functions of invariants on which, as follows from the above, some variations proportional to a small
Doyle, Heather; Lohfeld, Stefan; McHugh, Peter
2014-03-01
This study assesses the ability of finite element (FE) models to capture the mechanical behaviour of sintered orthopaedic scaffold materials. Individual scaffold struts were fabricated from a 50:50 wt% poly-ε-caprolactone (PCL)/β-tricalcium phosphate (β-TCP) blend, using selective laser sintering. The tensile elastic modulus of single struts was determined experimentally. High resolution FE models of single struts were generated from micro-CT scans (28.8 μm resolution) and an effective strut elastic modulus was calculated from tensile loading simulations. Three material assignment methods were employed: (1) homogeneous PCL elastic constants, (2) composite PCL/β-TCP elastic constants based on rule of mixtures, and (3) heterogeneous distribution of micromechanically-determined elastic constants. In comparison with experimental results, the use of homogeneous PCL properties gave a good estimate of strut modulus; however it is not sufficiently representative of the real material as it neglects the β-TCP phase. The rule of mixtures method significantly overestimated strut modulus, while there was no significant difference between strut modulus evaluated using the micromechanically-determined elastic constants and experimentally evaluated strut modulus. These results indicate that the multi-scale approach of linking micromechanical modelling of the sintered scaffold material with macroscale modelling gives an accurate prediction of the mechanical behaviour of the sintered structure.
Composite structures for the enhancement of nonlinear optical materials.
Neeves, A E; Birnboim, M H
1988-12-01
Calculations of the nonlinear optical behavior are developed for model composites consisting of nanospheres with a metallic core and a nonlinear shell suspended in a nonlinear medium. The concept for the enhancement of optical phase conjugation from all these nonlinear regions is that the optical field can be concentrated both inside and in the neighborhood of the metallic core, aided by surface-mediated plasmon resonance. Calculations for gold cores and aluminum cores indicate that phase-conjugate reflectivity enhancements of 10(8) may be possible.
Inclusion Tuning of Nonlinear Optical Materials: KTP (Potassium Titanyl Phosphate) Isomorphs
1988-06-01
o OFCE OF NAVAL RESEARCH Contract N00014-87-K-0457 V R&T Code 4134015-01 0) Technical. Report No. 23 "Inclusion Tuning of Nonlinear Optical Materials : KIP...bry block nuum.ber) see attached #11 Inclusion Tuning of Nonlinear Optical Materials : KTP Isomorphs * Q1 UISTRISUTION/AVAII..ASILITY 00 ABSTRACT 21
Eye/Sensor Protection against Laser Irradiation Organic Nonlinear Optical Materials
1989-06-12
Recent developments in organic nonlinear optical materials for application to eye and sensor protection are reviewed. This compendium includes a...noteworthy organic third-order nonlinear optical materials is included as an appendix. Lasers are playing an important and increasing role in modern
The Synthesis of Third—order Optical Nonlinear Organic Polyheterocyclic Materials
Institute of Scientific and Technical Information of China (English)
JianRongGAO; LuBaiCHENG; 等
2002-01-01
Synthesis of the third-order nonlinear materials:bis (1,4-dihydroxynaphthalene) tetrathiafulvalene and bis (1,4-dialkoxylnaphthalene) tetrathiafulvalene has been achieved in four steps, starting from 2,3-dichloro-1,4-naphthaquinone. The materials exhibit larger third-order nonlinear optical susceptibilities χ.
Effects of acceleration rate on Rayleigh-Taylor instability in elastic-plastic materials
Banerjee, Arindam; Polavarapu, Rinosh
2016-11-01
The effect of acceleration rate in the elastic-plastic transition stage of Rayleigh-Taylor instability in an accelerated non-Newtonian material is investigated experimentally using a rotating wheel experiment. A non-Newtonian material (mayonnaise) was accelerated at different rates by varying the angular acceleration of a rotating wheel and growth patterns of single mode perturbations with different combinations of amplitude and wavelength were analyzed. Experiments were run at two different acceleration rates to compare with experiments presented in prior years at APS DFD meetings and the peak amplitude responses are captured using a high-speed camera. Similar to the instability acceleration, the elastic-plastic transition acceleration is found to be increasing with increase in acceleration rate for a given amplitude and wavelength. The experimental results will be compared to various analytical strength models and prior experimental studies using Newtonian fluids. Authors acknowledge funding support from Los Alamos National Lab subcontract(370333) and DOE-SSAA Grant (DE-NA0001975).
Steady-state propagation of a Mode III crack in couple stress elastic materials
Mishuris, G; Radi, E
2012-01-01
This paper is concerned with the problem of a semi-infinite crack steadily propagating in an elastic solid with microstructures subject to antiplane loading applied on the crack surfaces. The loading is moving with the same constant velocity as that of the crack tip. We assume subsonic regime, that is the crack velocity is smaller than the shear wave velocity. The material behaviour is described by the indeterminate theory of couple stress elasticity developed by Koiter. This constitutive model includes the characteristic lengths in bending and torsion and thus it is able to account for the underlying microstructure of the material as well as for the strong size effects arising at small scales and observed when the representative scale of the deformation field becomes comparable with the length scale of the microstructure, such as the grain size in a polycrystalline or granular aggregate. The present analysis confirms and extends earlier results on the static case by including the effects of crack velocity an...
Guerquin, B
2015-09-01
Improving the understanding of the adaptation to stress of urinary continence. A transversal analysis between physics of materials and the female anatomy. Laws of physics of the materials and of their viscoelastic behavior are applied to the anatomy of the anterior vaginal wall. The anterior vaginal wall may be divided into two segments of different viscoelastic behavior, the vertical segment below the urethra and the horizontal segment below the bladder. If the urethra gets crushed on the first segment according to the hammock theory, the crushing of the bladder on the second segment is, on the other hand, damped by its important elasticity. The importance of this elasticity evokes an unknown function: damping under the bladder that moderates and delays the increase of intravesical pressure. This damping function below the bladder is increased in the cystocele, which is therefore a continence factor; on the other hand, it is impaired in obesity, which is therefore a factor of SUI. It is necessary to include in the theory of stress continence, the notion of a damping function below the bladder. Copyright © 2015 Elsevier Masson SAS. All rights reserved.
Kim, Jong-Min; Lee, Hyun-Boo; Chang, Yoon-Suk; Choi, Jae-Boong; Kim, Young-Jin; Ji, Kum-Young
2010-05-01
Recently, the reliability assurance of lead-free solder to prevent environmental contamination is quite important issue for chip-scale packaging. Although lots of efforts have been devoted to the solder undergone drop, shear and creep loads, there was a little research on IMC due primarily to its thickness restriction and geometric irregularity. However, the IMC is known as the weakest layer governing failures of the solder joint. The present work is to characterize realistic material properties of the IMC for ENEPIG process. Lee's modified reverse algorithm was adopted to determine elastic-plastic stress-strain curve and so forth, after examining several methods, which requires inherently elastic data. In this context, a series of nano-indentation tests as well as corresponding simulations were carried out by changing indentation depths from 200 to 400 nm and strain rates from 0.05 to 0.10 1/s. It would be conclude that effect of strain rate is relatively small and IMC layer should be more than 5 times of indentation depth when using the recommended method, which are applicable to generate realistic material properties for further diverse structural integrity simulations.
Computational Modeling of Ultrafast Pulse Propagation in Nonlinear Optical Materials
Goorjian, Peter M.; Agrawal, Govind P.; Kwak, Dochan (Technical Monitor)
1996-01-01
There is an emerging technology of photonic (or optoelectronic) integrated circuits (PICs or OEICs). In PICs, optical and electronic components are grown together on the same chip. rib build such devices and subsystems, one needs to model the entire chip. Accurate computer modeling of electromagnetic wave propagation in semiconductors is necessary for the successful development of PICs. More specifically, these computer codes would enable the modeling of such devices, including their subsystems, such as semiconductor lasers and semiconductor amplifiers in which there is femtosecond pulse propagation. Here, the computer simulations are made by solving the full vector, nonlinear, Maxwell's equations, coupled with the semiconductor Bloch equations, without any approximations. The carrier is retained in the description of the optical pulse, (i.e. the envelope approximation is not made in the Maxwell's equations), and the rotating wave approximation is not made in the Bloch equations. These coupled equations are solved to simulate the propagation of femtosecond optical pulses in semiconductor materials. The simulations describe the dynamics of the optical pulses, as well as the interband and intraband.
Thermally Stable Heterocyclic Imines as New Potential Nonlinear Optical Materials
Nesterov, Volodymyr V.; Antipin, Mikhail Y.; Nesterov, Vladimir N.; Moore, Craig E.; Cardelino, Beatriz H.; Timofeeva, Tatiana V.
2004-01-01
In the course of a search for new thermostable acentric nonlinear optical crystalline materials, several heterocyclic imine derivatives were designed, with the general structure D-pi-A(D'). Introduction of a donor amino group (D') into the acceptor moiety was expected to bring H-bonds into their crystal structures, and so to elevate their melting points and assist in an acentric molecular packing. Six heterocycle-containing compounds of this type were prepared, single crystals were grown for five of them, and these crystals were characterized by X-ray analysis. A significant melting temperature elevation was found for all of the synthesized compounds. Three of the compounds were also found to crystallize in acentric space groups. One of the acentric compounds is built as a three-dimensional H-bonded molecular network. In the other two compounds, with very similar molecular structure, the molecules form one-dimensional H-bonded head-to-head associates (chains). These chains are parallel in two different crystallographic directions and form very unusual interpenetrating chain patterns in an acentric crystal. Two of the compounds crystallized with centrosymmetric molecular packing.
Analysis of nonlinear optical properties in donor–acceptor materials
Energy Technology Data Exchange (ETDEWEB)
Day, Paul N. [Air Force Research Laboratory, Wright-Patterson Air Force Base, Ohio 45433 (United States); General Dynamics Information Technology, Inc., Dayton, Ohio 45431 (United States); Pachter, Ruth [Air Force Research Laboratory, Wright-Patterson Air Force Base, Ohio 45433 (United States); Nguyen, Kiet A. [Air Force Research Laboratory, Wright-Patterson Air Force Base, Ohio 45433 (United States); UES, Inc., Dayton, Ohio 45432 (United States)
2014-05-14
Time-dependent density functional theory has been used to calculate nonlinear optical (NLO) properties, including the first and second hyperpolarizabilities as well as the two-photon absorption cross-section, for the donor-acceptor molecules p-nitroaniline and dimethylamino nitrostilbene, and for respective materials attached to a gold dimer. The CAMB3LYP, B3LYP, PBE0, and PBE exchange-correlation functionals all had fair but variable performance when compared to higher-level theory and to experiment. The CAMB3LYP functional had the best performance on these compounds of the functionals tested. However, our comprehensive analysis has shown that quantitative prediction of hyperpolarizabilities is still a challenge, hampered by inadequate functionals, basis sets, and solvation models, requiring further experimental characterization. Attachment of the Au{sub 2}S group to molecules already known for their relatively large NLO properties was found to further enhance the response. While our calculations show a modest enhancement for the first hyperpolarizability, the enhancement of the second hyperpolarizability is predicted to be more than an order of magnitude.
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
An expansion theory of spherical cavities in strain-softening materials with different moduli of tension and compression was presented. For geomaterials, two controlling parameters were introduced to take into account the different moduli and strain-softening properties. By means of elastic theory with different moduli and stress-softening models, g. eneral solutions calculating Tresca and Mohr-Coulomb materials' stress and displacement fields of expansion of spherical cavity were derived. The effects caused by different elastic moduli in tensile and compression and strain-softening rates on stress and displacement fields and development of plastic zone of expansion of cavity were analyzed. The results show that the ultimate expansion pressure,stress and displacement fields and development of plastic zone vary with the different elastic moduli and strain-softening properties. If classical elastic theory is adopted and strain-softening properties are neglected, rather large errors may be the result.
Moussawi, Ali
2015-02-24
Summary: The post-treatment of (3D) displacement fields for the identification of spatially varying elastic material parameters is a large inverse problem that remains out of reach for massive 3D structures. We explore here the potential of the constitutive compatibility method for tackling such an inverse problem, provided an appropriate domain decomposition technique is introduced. In the method described here, the statically admissible stress field that can be related through the known constitutive symmetry to the kinematic observations is sought through minimization of an objective function, which measures the violation of constitutive compatibility. After this stress reconstruction, the local material parameters are identified with the given kinematic observations using the constitutive equation. Here, we first adapt this method to solve 3D identification problems and then implement it within a domain decomposition framework which allows for reduced computational load when handling larger problems.
Florentin, Éric
2011-08-09
The constitutive equation gap method (CEGM) is a well-known concept which, until now, has been used mainly for the verification of finite element simulations. Recently, CEGM-based functional has been proposed to identify local elastic parameters based on experimental full-field measurement. From a technical point of view, this approach requires to quickly describe a space of statically admissible stress fields. We present here the technical insights, inspired from previous works in verification, that leads to the construction of such a space. Then, the identification strategy is implemented and the obtained results are compared with the actual material parameters for numerically generated benchmarks. The quality of the identification technique is demonstrated that makes it a valuable tool for interactive design as a way to validate local material properties. © 2011 Springer-Verlag.
Directory of Open Access Journals (Sweden)
Masahiko Kanaoka et al
2007-01-01
Full Text Available Optical mirrors used in extreme ultraviolet lithography systems require a figure accuracy and a roughness of about 0.1 nm rms. In addition, mirror substrates must be low-thermal-expansion materials. Thus, in this study, we processed two low-thermal-expansion materials, ULE [K. Hrdina, B. Hanson, P. Fenn, R. Sabia, Proc. SPIE 4688 (2002 454.] (Corning Inc. and Zerodur [I. Mitra, M.J. Davis, J. Alkemper, Rolf Müller, H. Kohlmann, L. Aschke, E. Mörsen, S. Ritter, H. Hack, W. Pannhorst, Proc. SPIE 4688 (2002 462.] (SCHOTT AG, with elastic emission machining (EEM in order to evaluate the removal properties. Consequently, we successfully calculated the respective removal rates, because removal volumes were found to be proportional to process times in EEM. Moreover, we demonstrated that the surface roughness of Zerodur is reduced to 0.1 nm rms in the spatial wavelength range from 100 μm to 1 mm.
Institute of Scientific and Technical Information of China (English)
Tianhu Hao
2005-01-01
This paper presents an exact solution of the crack tip field in functionally gradient material with exponential variation of elastic constants. The dimensionless Poisson's ratios v0 of the engineering materials (iron, glass... ) are far less than one; therefore, neglecting them, one can simplify the basic equation and the exact solution is easy to obtain.Although the exact solution for the case v0 ≠ 0 is also obtained, it is very complicated and the main result is the same with the case v0 = 0 (it will be dealt with in Appendix Ⅶ).It has been found that the exponential term exp(ax + by) in the constitutive equations becomes exp (ax/2 + by/2 - kr / 2 ) in the exact solution.
Indian Academy of Sciences (India)
D P Acharya; Asit Kumar Mondal
2006-06-01
The object of the present paper is to investigate the propagation of quasi-transverse waves in a nonlinear perfectly conducting nonhomogeneous elastic medium in the presence of a uniform magnetic ﬁeld transverse to the direction of wave propagation. Different types of ﬁgures have been drawn to exhibit the distortion of waves due to the presence of magnetic ﬁeld and the nonhomogeneous nature of the medium. Formation of shocks has also been numerically discussed.
Linear and nonlinear elastic properties of dense granular packings: a DEM exploration
Directory of Open Access Journals (Sweden)
Lemrich Laure
2017-01-01
Full Text Available Discrete Element Method modeling is used to study the frequency spectrum of particle motion in dense 3D packings of glass beads with Hertz-Mindlin contacts. Frequency sweeps show a dependency of the resonant frequencies on the drive amplitude and confining stress on the system, showing material changes in the system. The amplitude dependency of the second thickness mode 3λ/4 as identified by the internal strain field scales as f ∝ σ1/6 while the confining stress dependency scales as f ∝ σ 2/3, as predicted by Hertzian theory.
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Some theoretical methods have been reported to deal with nonlinear problems of composite materials but the accuracy is not so good. In the meantime, a lot of nonlinear problems are difficult to be managed by the theoretical methods. The present study aims to use the developed method, the random microstructure finite element method, to deal with these nonlinear problems. In this paper, the random microstructure finite element method is used to deal with all three kinds of nonlinear property problems of composite materials. The analyzed results suggest that the influences of the nonlinear phenomena on the effective properties of composite materials are significant and the random microstructure finite element method is an efficient tool to investigate the nonlinear problems.
Nonlocal description of X waves in quadratic nonlinear materials
DEFF Research Database (Denmark)
Larsen, Peter Ulrik Vingaard; Sørensen, Mads Peter; Bang, Ole
2006-01-01
We study localized light bullets and X-waves in quadratic media and show how the notion of nonlocality can provide an alternative simple physical picture of both types of multi-dimensional nonlinear waves. For X-waves we show that a local cascading limit in terms of a nonlinear Schrodinger equation...
Hosseinzadeh, M; Ghoreishi, M; Narooei, K
2016-06-01
In this study, the hyperelastic models of demineralized and deproteinized bovine cortical femur bone were investigated and appropriate models were developed. Using uniaxial compression test data, the strain energy versus stretch was calculated and the appropriate hyperelastic strain energy functions were fitted on data in order to calculate the material parameters. To obtain the mechanical behavior in other loading conditions, the hyperelastic strain energy equations were investigated for pure shear and equi-biaxial tension loadings. The results showed the Mooney-Rivlin and Ogden models cannot predict the mechanical response of demineralized and deproteinized bovine cortical femur bone accurately, while the general exponential-exponential and general exponential-power law models have a good agreement with the experimental results. To investigate the sensitivity of the hyperelastic models, a variation of 10% in material parameters was performed and the results indicated an acceptable stability for the general exponential-exponential and general exponential-power law models. Finally, the uniaxial tension and compression of cortical femur bone were studied using the finite element method in VUMAT user subroutine of ABAQUS software and the computed stress-stretch curves were shown a good agreement with the experimental data.
Argatov, I
2015-01-01
An indentation testing method, which utilizes lateral contact of a long cylindrical indenter, is developed for a thin transversely isotropic incompressible elastic film deposited onto a smooth rigid substrate. It is assumed that the material symmetry plane is orthogonal to the substrate surface, and the film thickness is small compared to the cylinder indenter length. The presented testing methodology is based on a least squares best fit of the first-order asymptotic model to the depth-sensing indentation data for recovering three independent elastic moduli which characterize an incompressible transversely isotropic material. The case of a weakly compressible material, which is important for biological tissues, is also discussed.
Enakoutsa, Koffi
2015-06-01
Recently, the works by Toupin, Mindlin, Sokolowski and Germain have been developed following two research streams. In the first one, higher-order gradient continuum models were developed based on the Cauchy tetrahedron argument (see, e.g., dell'Isola and Seppecher in Comptes Rendus de l Academie de Sciences 17 Serie IIb: Mecanique, Physique, Chimie, Astronomie 321:303-308, 1995, Meccanica 32:33-52 1997, Zeitschrift fr Angewandte Mathematik und Physik 63(6):1119-1141, 2012). In the second one, the structure of higher-order gradient models is developed with a view to the applications. In particular in the model of linear isotropic solids proposed by Dell'Isola, Sciarra and Vidoli (DSV), the main constitutive equation is obtained for the case of second gradient models. This model introduces in addition to the two well-known Lame's elastic constants five constitutive constants. The practical applications of this model remain in its infancy since the issue of determining the new moduli it introduces is not yet completely addressed. Also, analytical solutions of simple boundary value problems that can be helpful to grasp some of the physical foundations of this model are missing. This paper aims to address these two issues by providing the analytical solutions for two model problems, a spherical shell subjected to axisymmetric loading conditions and the circular bending of a beam in plane strain, both the beam and the shell obeying the DSV second gradient isotropic elastic model. The solution of the circular bending of a beam has served to grasp some of the physical soundness of the model. A framework based on homogenization under inhomogeneous boundary conditions is also suggested to determine the unknown constitutive constants, which are provided in the particular case of elastic porous heterogeneous materials.
Energy Technology Data Exchange (ETDEWEB)
Torello, David [GW Woodruff School of Mechanical Engineering, Georgia Tech (United States); Kim, Jin-Yeon [School of Civil and Environmental Engineering, Georgia Tech (United States); Qu, Jianmin [Department of Civil and Environmental Engineering, Northwestern University (United States); Jacobs, Laurence J. [School of Civil and Environmental Engineering, Georgia Tech and GW Woodruff School of Mechanical Engineering, Georgia Tech (United States)
2015-03-31
This research considers the effects of diffraction, attenuation, and the nonlinearity of generating sources on measurements of nonlinear ultrasonic Rayleigh wave propagation. A new theoretical framework for correcting measurements made with air-coupled and contact piezoelectric receivers for the aforementioned effects is provided based on analytical models and experimental considerations. A method for extracting the nonlinearity parameter β{sub 11} is proposed based on a nonlinear least squares curve-fitting algorithm that is tailored for Rayleigh wave measurements. Quantitative experiments are conducted to confirm the predictions for the nonlinearity of the piezoelectric source and to demonstrate the effectiveness of the curve-fitting procedure. These experiments are conducted on aluminum 2024 and 7075 specimens and a β{sub 11}{sup 7075}/β{sub 11}{sup 2024} measure of 1.363 agrees well with previous literature and earlier work.
Data-driven non-linear elasticity: constitutive manifold construction and problem discretization
Ibañez, Ruben; Borzacchiello, Domenico; Aguado, Jose Vicente; Abisset-Chavanne, Emmanuelle; Cueto, Elias; Ladeveze, Pierre; Chinesta, Francisco
2017-07-01
The use of constitutive equations calibrated from data has been implemented into standard numerical solvers for successfully addressing a variety problems encountered in simulation-based engineering sciences (SBES). However, the complexity remains constantly increasing due to the need of increasingly detailed models as well as the use of engineered materials. Data-Driven simulation constitutes a potential change of paradigm in SBES. Standard simulation in computational mechanics is based on the use of two very different types of equations. The first one, of axiomatic character, is related to balance laws (momentum, mass, energy,\\ldots ), whereas the second one consists of models that scientists have extracted from collected, either natural or synthetic, data. Data-driven (or data-intensive) simulation consists of directly linking experimental data to computers in order to perform numerical simulations. These simulations will employ laws, universally recognized as epistemic, while minimizing the need of explicit, often phenomenological, models. The main drawback of such an approach is the large amount of required data, some of them inaccessible from the nowadays testing facilities. Such difficulty can be circumvented in many cases, and in any case alleviated, by considering complex tests, collecting as many data as possible and then using a data-driven inverse approach in order to generate the whole constitutive manifold from few complex experimental tests, as discussed in the present work.
Rubin, M. B.; Vorobiev, O.; Vitali, E.
2016-07-01
A large deformation thermomechanical model is developed for shock loading of a material that can exhibit elastic and inelastic anisotropy. Use is made of evolution equations for a triad of microstructural vectors mathbf{m}i (hbox {i}=1,2,3) which model elastic deformations and directions of anisotropy. Specific constitutive equations are presented for a material with orthotropic elastic response. The rate of inelasticity depends on an orthotropic yield function that can be used to model weak fault planes with failure in shear and which exhibits a smooth transition to isotropic response at high compression. Moreover, a robust, strongly objective numerical algorithm is proposed for both rate-independent and rate-dependent response. The predictions of the continuum model are examined by comparison with exact steady-state solutions. Also, the constitutive equations are used to obtain a simplified continuum model of jointed rock which is compared with high fidelity numerical solutions that model a persistent system of joints explicitly in the rock medium.
High-accuracy acoustic detection of nonclassical component of material nonlinearity.
Haupert, Sylvain; Renaud, Guillaume; Rivière, Jacques; Talmant, Maryline; Johnson, Paul A; Laugier, Pascal
2011-11-01
The aim is to assess the nonclassical component of material nonlinearity in several classes of materials with weak, intermediate, and high nonlinear properties. In this contribution, an optimized nonlinear resonant ultrasound spectroscopy (NRUS) measuring and data processing protocol applied to small samples is described. The protocol is used to overcome the effects of environmental condition changes that take place during an experiment, and that may mask the intrinsic nonlinearity. External temperature fluctuation is identified as a primary source of measurement contamination. For instance, a variation of 0.1 °C produced a frequency variation of 0.01%, which is similar to the expected nonlinear frequency shift for weakly nonlinear materials. In order to overcome environmental effects, the reference frequency measurements are repeated before each excitation level and then used to compute nonlinear parameters. Using this approach, relative resonant frequency shifts of 10(-5) can be measured, which is below the limit of 10(-4) often considered as the limit of NRUS sensitivity under common experimental conditions. Due to enhanced sensitivity resulting from the correction procedure applied in this work, nonclassical nonlinearity in materials that before have been assumed to only be classically nonlinear in past work (steel, brass, and aluminum) is reported.
Durgesh, B. H.; Alkheraif, A. A.; Al Sharawy, M.; Varrela, J.; Vallittu, P. K.
2016-01-01
The aim of this study was to investigate the magnitude of debonding stress of an orthodontic bracket bonded to the enamel with resin systems having different elastic properties. For the same purpose, sixty human premolars were randomly divided into four groups according to the adhesive system used for bonding brackets: G Fix flowable resin (GFI) with Everstick NET (ESN), GFI, G Aenial Universal Flow (GAU) with ESN, and GAU. The brackets were stressed in the occlusogingival direction on a universal testing machine. The values of debonding load and displacement were determined at the point of debonding. The elastic modulus of the tested materials was determined using nanoindentation. An analysis of variance showed a significant difference in the loads required to debond the bracket among the groups tested. The GAU group had the highest elastic modulus, followed by the GFI and ESN groups. ARI (Adhesive Remnant Index) scores demonstrated more remnants of the adhesive material on the bracket surface with adhesives having a higher elastic modulus. Taking into consideration results of the present in-vitro study, it can be concluded that the incorporation of a glass-fiber-reinforced composite resin (FRC) with a low elastic modulus between the orthodontic bracket and enamel increases the debonding force and strain more than with adhesive systems having a higher elastic modulus.
Mozafari, E.; Shulumba, N.; Steneteg, P.; Alling, B.; Abrikosov, Igor A.
2016-08-01
We present a theoretical scheme to calculate the elastic constants of magnetic materials in the high-temperature paramagnetic state. Our approach is based on a combination of disordered local moments picture and ab initio molecular dynamics (DLM-MD). Moreover, we investigate a possibility to enhance the efficiency of the simulations of elastic properties using the recently introduced method: symmetry imposed force constant temperature-dependent effective potential (SIFC-TDEP). We have chosen cubic paramagnetic CrN as a model system. This is done due to its technological importance and its demonstrated strong coupling between magnetic and lattice degrees of freedom. We have studied the temperature-dependent single-crystal and polycrystalline elastic constants of paramagentic CrN up to 1200 K. The obtained results at T = 300 K agree well with the experimental values of polycrystalline elastic constants as well as the Poisson ratio at room temperature. We observe that the Young's modulus is strongly dependent on temperature, decreasing by ˜14 % from T = 300 K to 1200 K. In addition we have studied the elastic anisotropy of CrN as a function of temperature and we observe that CrN becomes substantially more isotropic as the temperature increases. We demonstrate that the use of Birch law may lead to substantial errors for calculations of temperature induced changes of elastic moduli. The proposed methodology can be used for accurate predictions of mechanical properties of magnetic materials at temperatures above their magnetic order-disorder phase transition.
Elastic airtight container for the compaction of air-sensitive materials.
Shoulders, W Taylor; Locke, Richard; Gaume, Romain M
2016-06-01
We report on the design and fabrication of a simple and versatile elastic canister for the compaction and hot-pressing of air-sensitive materials. This device consists of a heated double-ended floating die assembly, enclosed in a compressible stainless steel bellows that allows the action of an external hydraulic press in a uniaxial motion. The enclosure is fitted with vacuum, gas, and electrical feedthroughs to allow for atmosphere control, heating, and in situ process monitoring. The overall chamber is compact enough to be portable and transferrable into and out of a standard laboratory glovebox, thus eliminating the problem of exposing samples to ambient atmosphere during loading and unloading. Our design has been tested up to 600 °C and 7500 kg-force applied load, conditions within which transparent ceramics of anhydrous halides can be produced.
Institute of Scientific and Technical Information of China (English)
程昌钧; 任九生
2003-01-01
The finite deformation and stress analyses for a transversely isotropic rectangularplate with voids and made of hyper-elastic material with the generalized neo-Hookean strainenergy function under a uniaxial extension are studied. The deformation functions of plateswith voids that are symmetrically distributed in a certain manner are given and the functionsare expressed by two parameters by solving the differential equations. The solution may beapproximately obtained from the minimum potential energy principle. Thus, the analyticsolutions of the deformation and stress of the plate are obtained. The growth of the void.s andthe distribution of stresses along the voids are analyzed and the influences of the degree ofanisotropy, the size of the voids and the distance between the voids are discussed. Thecharacteristics of the growth of the voids and the distribution of stresses of the plates with onevoid, three or five voids are obtained and compared.
Elasticity and Anelasticity of Materials from Time-Resolved X-ray Diffraction
Sinogeikin, S. V.; Smith, J.; Lin, C.; Bai, L.; Rod, E.; Shen, G.
2014-12-01
Recent advances in synchrotron sources, x-ray optics, area detectors, and sample environment control have enabled many time-resolved experimental techniques for studying materials at extreme pressure and temperature conditions. The High Pressure Collaborative Access Team (HPCAT) at the Advanced Photon Source has made a sustained effort to develop and assemble a powerful collection of high-pressure apparatus for time-resolved research, and considerable time has been invested in developing techniques for collecting high-quality time-resolved x-ray scattering data. In this talk we will outline recently developed capabilities at HPCAT for studying elasticity and anelasticity of minerals using fast compression and cyclic compression-decompression. A few recent studies will be highlighted. For example, with fast x-ray area detectors having millisecond time resolution, accurate thermal equations of state of materials at temperatures up to 1000K and megabar pressures can be collected in a matter of seconds using membrane-driven diamond anvil cells (DAC), yielding unprecedented time and pressure resolution of true isotherms. Short duration of the experiments eliminates temperature variation during the experiments and in general allows volume measurements at higher pressures and temperatures. Alternatively, high-frequency (kilohertz range) radial diffraction measurements in a panoramic DAC combined with fast, precise cyclic loading/unloading by piezo drive could provide the short time scale necessary for studying rheology of minerals from the elastic response and lattice relaxation as a function of pressure, temperature and strain rate. Finally, we consider some possible future applications for time-resolved high-pressure, high-temperature research of mantle minerals.
Finding the Next Deep-Ultraviolet Nonlinear Optical Material: NH4B4O6F.
Shi, Guoqiang; Wang, Ying; Zhang, Fangfang; Zhang, Bingbing; Yang, Zhihua; Hou, Xueling; Pan, Shilie; Poeppelmeier, Kenneth R
2017-08-09
Nonlinear optical materials are essential for the development of solid-state lasers. KBe2BO3F2 (KBBF) is a unique nonlinear optical material for generation of deep-ultraviolet coherent light; however, its industrial application is limited. Here, we report a new material NH4B4O6F, which exhibits a wide deep-ultraviolet transparent range and suitable birefringence that enables frequency doubling below 200 nm. NH4B4O6F possesses large nonlinear coefficients about 2.5 times that of KBBF. In addition, it is easy to grow bulk crystals and does not contain toxic elements.
Investigation of nonlinear optical properties of various organic materials by the Z-scan method
Ganeev, R. A.; Boltaev, G. S.; Tugushev, R. I.; Usmanov, T.
2012-06-01
We have studied the nonlinear optical properties of various organic materials (vegetable oil, juice, wine, cognac, Coca-Cola and Fanta drinks, Nescafé coffee, tea, gasoline, clock oil, glycerol, and polyphenyl ether) that are used in everyday life. Their nonlinearities have been studied by the Z-scan method in the near-IR and visible spectral ranges. We have shown that the majority of samples possess a nonlinear absorption; however, some of the studied materials show a strong saturated absorption and nonlinear refraction. Red wine and glycerol proved to be the most interesting materials. For these samples, we have observed a change in the sign of the nonlinear absorption with increasing laser intensity, which was attributed to the competition between two-photon absorption and saturated absorption.
A review of recent theoretical studies in nonlinear crystals: towards the design of new materials
Luppi, Eleonora; Véniard, Valérie
2016-12-01
Nonlinear optics is an important and exciting field of fundamental and applied research, with applications in many different disciplines such as physics chemistry, material science and biology. In the recent years, nonlinear optical phenomena started to be also widely used in technological applications for optoelectronics and photovoltaics. This coincided with an important experimental and theoretical search for new materials with an efficient and exploitable nonlinear optical response. Here, starting from the discovery of nonlinear optics, we review the most important theoretical formalisms developed to understand, interpret and predict the nonlinear optical phenomena. We show the different level of approximation of the many-electrons interactions that these formalisms can describe which are fundamental in the interpretation of the experiments. The impact of the theory is then analyzed on different classes of new materials particularly studied in these years: silicon bulk to nano, compound semiconductors, graphene, transition metal dichalcogenide, hexagonal boron nitride and borate crystals.
Mechanics of extended continua: modeling and simulation of elastic microstretch materials
Kirchner, N.; Steinmann, P.
2007-09-01
The investigation of microstretch and micromorphic continua (which are prominent examples of so-called extended continua) dates back to Eringens pioneering works in the mid 1960, cf. (Eringen in Mechanics of micromorphic materials. Springer, Berlin Heidelberg New York, pp 131-138, 1966; Eringen in Int J Eng Sci 8:819-828; Eringen in Microcontinuum field theories. Springer, Berlin Heidelberg New York, 1999). Here, we re-derive the governing equations of microstretch continua in a variational setting, providing a natural framework within which numerical implementations of the model equations by means of the finite element method can be obtained straightforwardly. In the application of Dirichlets principle, the postulation of an appropriate form of the Helmholtz free energy turns out to be crucial to the derivation of the balance laws and constitutive relations for microstretch continua. At present, the material parameters involved in the free energy have been assigned fixed values throughout all numerical simulations—this simplification is addressed in detail as the influence of those parameters must not be underestimated. Since only few numerical results demonstrating elastic microstretch material behavior in engineering applications are available, the focus is here on the presentation of numerical results for simple twodimensional test specimens subjected to a plane strain condition and uniaxial tension. Confidence in the simulations for microstretch materials is gained by showing that they exhibit a “downward-compatibility” to Cosserat continuum formulation: by switching off all stretch-related effects, the governing set of equations reduces to the one used for polar materials. Further, certain material parameters can be chosen to act as penalty parameters, forcing stretch-related contributions to an almost negligible range in a full microstretch model so that numerical results obtained for a polar model can be obtained as a limiting case from the full
A thermodynamic framework for thermo-chemo-elastic interactions in chemically active materials
Zhang, XiaoLong; Zhong, Zheng
2017-08-01
In this paper, a general thermodynamic framework is developed to describe the thermo-chemo-mechanical interactions in elastic solids undergoing mechanical deformation, imbibition of diffusive chemical species, chemical reactions and heat exchanges. Fully coupled constitutive relations and evolving laws for irreversible fluxes are provided based on entropy imbalance and stoichiometry that governs reactions. The framework manifests itself with a special feature that the change of Helmholtz free energy is attributed to separate contributions of the diffusion-swelling process and chemical reaction-dilation process. Both the extent of reaction and the concentrations of diffusive species are taken as independent state variables, which describe the reaction-activated responses with underlying variation of microstructures and properties of a material in an explicit way. A specialized isothermal formulation for isotropic materials is proposed that can properly account for volumetric constraints from material incompressibility under chemo-mechanical loadings, in which inhomogeneous deformation is associated with reaction and diffusion under various kinetic time scales. This framework can be easily applied to model the transient volumetric swelling of a solid caused by imbibition of external chemical species and simultaneous chemical dilation arising from reactions between the diffusing species and the solid.
The Synthesis of Third-order Optical Nonlinear Organic Polyheterocyclic Materials
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
Synthesis of the third-order nonlinear materials: bis (l,4-dihydroxynaphthalene)tetrathiafulvalene and bis (1,4-dialkoxylnaphthalene) tetrathiafulvalene has been achieved in four steps, starting from 2,3-dichloro-l,4-naphthaquinone. The matcrials exhibit larger third-order nonlinear optical susceptibilities X(3).
Exact solutions of optical pulse propagation in nonlinear meta-materials
Nanda, Lipsa
2017-01-01
An analytical and simulation based method has been used to exactly solve the nonlinear wave propagation in bulk media exhibiting frequency dependent dielectric susceptibility and magnetic permeability. The method has been further extended to investigate the intensity distribution in a nonlinear meta-material with negative refractive index where both ɛ and μ are dispersive and negative in nature.
Institute of Scientific and Technical Information of China (English)
Xiang Li; Serge Cescotto; Barbara Rossi
2009-01-01
The natural neighbour method can be considered as one of many variants of the meshless methods. In the present paper, a new approach based on the Fraeijs de Veubeke (FdV) functional, which is initially developed for linear elasticity, is extended to the case of geometrically linear but materially non-linear solids. The new approach provides an original treatment to two classical problems: the numerical evaluation of the integrals over the domain A and the enforcement of boundary conditions of the type ui = uion Su. In the absence of body forces (Fi = 0), it will be shown that the calculation of integrals of the type fA .dA can be avoided and that boundary conditions of the type ui = ui on Su can be imposed in the average sense in general and exactly if ui is linear between two contour nodes, which is obviously the case for ui = 0.
Bednarcyk, Brett A.; Arnold, Steven M.
2012-01-01
A framework for the multiscale design and analysis of composite materials and structures is presented. The ImMAC software suite, developed at NASA Glenn Research Center, embeds efficient, nonlinear micromechanics capabilities within higher scale structural analysis methods such as finite element analysis. The result is an integrated, multiscale tool that relates global loading to the constituent scale, captures nonlinearities at this scale, and homogenizes local nonlinearities to predict their effects at the structural scale. Example applications of the multiscale framework are presented for the stochastic progressive failure of a SiC/Ti composite tensile specimen and the effects of microstructural variations on the nonlinear response of woven polymer matrix composites.
Self-Assembly of Nanocomposite Nonlinear Optical Materials for Photonic Devices Project
National Aeronautics and Space Administration — This program targets the development of new highly anisotropic nonlinear optical nanocomposite materials for NASA and non-NASA applications in advanced photonic and...
Erofeev, V. I.; Leontieva, A. V.; Malkhanov, A. O.
2017-06-01
Within the framework of self consistent dynamic problems, the impact of dislocations and point defects on the spatial localization of nonlinear acoustic waves propagating in materials has been studied.
Renaud, Guillaume; Talmant, Maryline; Marrelec, Guillaume
2016-10-01
The nonlinear elasticity of solids at the microstrain level has been recently studied by applying dynamic acousto-elastic testing. It is the analog of conventional quasi-static acousto-elastic experiments but the strain-dependence (or stress-dependence) of ultrasonic wave-speed is measured with an applied strain ranging from 10-7 to 10-5 and produced by a stationary elastic wave. In conventional quasi-static acousto-elastic experiments, the strain is applied in a quasi-static manner; it exceeds 10-4 and can reach 10-2. In this work, we apply dynamic acousto-elastic testing to measure the third-order elastic constants of two isotropic materials: polymethyl methacrylate and dry Berea sandstone. The peak amplitude of the dynamic applied strain is 8 × 10-6. The method is shown to be particularly suitable for materials exhibiting large elastic nonlinearity like sandstones, since the measurement is performed in the domain of validity of the third-order hyperelastic model. In contrast, conventional quasi-static acousto-elastic experiments in such materials are often performed outside the domain of validity of the third-order hyperelastic model and the stress-dependence of the ultrasonic wave-speed must be extrapolated at zero stress, leading to approximate values of the third-order elastic constants. The uncertainty of the evaluation of the third-order elastic constants is assessed by repeating multiple times the measurements and with Monte-Carlo simulations. The obtained values of the Murnaghan third-order elastic constants are l = -73 GPa ± 9%, m = -34 GPa ± 9%, and n = -61 GPa ± 10% for polymethyl methacrylate, and l = -17 000 GPa ± 20%, m = -11 000 GPa ± 10%, and n = -30 000 GPa ± 20% for dry Berea sandstone.
Spontaneous emission and nonlinear effects in photonic bandgap materials
Fogel, Ishella S.; Bendickson, Jon M.; Tocci, Michael D.; Bloemer, Mark J.; Scalora, Michael; Bowden, Charles M.; Dowling, Jonathan P.
1998-03-01
We summarize and review our theoretical and experimental work on spontaneous emission and nonlinear effects in one-dimensional, photonic bandgap (PBG) structures. We present a new result: a method for calculating the normal-mode solutions - and hence the spontaneous emission of embedded emitters - in an arbitrary, linear, lossless, one-dimensional, PBG structure.
Physical Models of Hysteretic Nonlinear Elasticity of Rock%岩石滞后非线性弹性响应的物理模型
Institute of Scientific and Technical Information of China (English)
任隽; 陈东柏; 戴王强; 陈运平; 潘纪顺
2011-01-01
Several physical models of hysteretic nonlinear elasticity of rock are introduced. The Hertz grain contact model is a typical model with multi-scale and hysteretic behavior, which predicts strong nonlinearity in rocks. The soft adhesion system almost determines the mechanical properties of rock, and the fluid in the system has great contribution to nonlinear response. However, how the adhesion system and the pore fluid affect the nonlinear response remains unclear. The GL model based on metal dislocation is a physical model, which is a pioneering microscope model in hysteretic dynamic behaviour. The PM model is a phenomenological model based on mesoscopic elastic units in rock, which is important in understanding the mechanism and extent of hysteretic nonlinearity in rocks.%介绍了岩石滞后非线性弹性的几个物理模型.赫兹颗粒接触模型是具有多尺度和滞后特性的经典模型,它预测了岩石中强烈的非线性；软的粘结系统几乎决定了岩石的力学性质,粘结系统中的流体对非线性响应的贡献特别显著,但是目前还没有搞清楚粘结系统和孔隙流体究竟是如何影响非线性响应的；GL模型是一个基于金属位错的物理模型,这是滞后动力行为方面一个开拓性的微观模型；PM模型是一个基于岩石细观尺度的唯象模型,它对理解岩石滞后非线性的机制和尺度是很重要的.
On the influence of strain rate in acousto-elasticity : experimental results for Berea sandstone
Riviere, J. V.; Candela, T.; Scuderi, M.; Marone, C.; Guyer, R. A.; Johnson, P. A.
2013-12-01
Elastic nonlinear effects are pervasive in the Earth, including during strong ground motion, tidal forcing and earthquake slip processes. We study elastic nonlinear effects in the laboratory with the goal of developing new methods to probe elastic changes in the Earth, and to characterize and understand their origins. Here we report on nonlinear, frequency dispersion effects by applying a method termed dynamic acousto-elasticity (DAE), analogous to quasi-static acousto-elasticity. DAE allows one to obtain the elastic behavior over the entire dynamic cycle, detailing the full nonlinear behavior under tension and compression, including hysteresis and memory effects. We perform DAE on samples of Berea sandstone subject to 0.5 MPa uniaxial and biaxial loading conditions with oscillating loads at frequencies from 0.001 to 10 Hz and amplitudes of a few 100 kPa. We compare results to DAE measurements made in the kHz range. We observe that the average decrease in modulus due to nonlinear material softening increases with frequency, suggesting a frequency and/or a strain rate dependence. Previous quasi-static measurements (Claytor et al., GRL 2009) show that stress-strain nonlinear hysteretic behavior disappears when the experiment is performed at a very low strain-rate, implying that a rate dependent nonlinear elastic model would be useful (Gusev et al., PRB 2004). Our results also suggest that when elastic nonlinear Earth processes are studied, stress forcing frequency is an important consideration, and may lead to unexpected behaviors.
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.
Non-Linear Optical Studies of IR Materials with Infrared Femtosecond Laser
2016-12-15
AFRL-RD-PS- AFRL-RD-PS- TR-2016-0055 TR-2016-0055 NON-LINEAR OPTICAL STUDIES OF IR MATERIALS WITH INFRARED FEMTOSECOND LASER Enam...ANDREAS SCHMITT-SODY, DR-III ERIN PETTYJOHN, DR-III Program Manager Deputy Chief, High Power Electromagnetics Division This...TITLE AND SUBTITLE Non-Linear Optical Studies of IR Materials with Infrared Femtosecond Laser 5a. CONTRACT NUMBER 5b. GRANT NUMBER FA9451-14-1
Hybrid Nonlinear Optical Materials for Applications in Power Limiting and Photorefractive Devices
2010-03-01
Final 3. DATES COVERED (From - To) 04/01/2007 to 11/30/2009 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER FA9550-07-1-0307 Hybrid Nonlinear Optical Materials for...Hybrid Nonlinear Optical Materials for Applications in Power Limiting and Photorefractive devices Prime Contract: FA95500710307
Zaitsev, V Yu; Gusev, V E; Zaytsev, Yu V
2005-08-01
Self-action and effects mutually induced by oscillations interacting in hysteretic media are investigated analytically and numerically. Special attention is paid to non-simplex processes for which presence of intermediate extrema results in appearance of minor nested loops inside the main hysteretic stress-strain loop. Non-simplex regimes are typical of interaction of excitations having different frequencies and amplitudes, but comparable strain rates. It is found that, due to transition between the regimes, frequency and amplitude dependencies of the variations in elasticity and dissipation induced by one wave for another one may become non-monotonous. Either additional dissipation or induced transparency may occur in different regimes. The results obtained are important for correct interpretation of experimental data on nonlinear acoustic interactions in rocks and many other microstructured (mesoscopic) solids that are known to exhibit elastic hysteresis and memory properties.
Microcrack Identification in Cement-Based Materials Using Nonlinear Acoustic Waves
Chen, X. J.; Kim, J.-Y.; Qu, J.; Kurtis, K. E.; Wu, S. C.; Jacobs, L. J.
2007-03-01
This paper presents results from tests that use nonlinear acoustic waves to distinguish microcracks in cement-based materials. Portland cement mortar samples prepared with alkali-reactive aggregate were exposed to an aggressive environment to induce cracking were compared to control samples, of the same composition, but which were not exposed to aggressive conditions. Two nonlinear ultrasonic methods were used to characterize the samples, with the aim of identifying the time and extent of microcracking; these techniques were a nonlinear acoustical modulation (NAM) method and a harmonic amplitude relation (HAR) method. These nonlinear acoustic results show that both methods can distinguish damaged samples from undamaged ones, demonstrating the potential of nonlinear acoustic waves to provide a quantitative evaluation of the deterioration of cement-based materials.
Taghizadeh, K.; Kumar, N.; Magnanimo, V.; Luding, S.
2015-09-01
Understanding the mechanical stiffness of closely packed, dense granular systems is of interest in many fields, such as soil mechanics, material science and physics. The main difficulty arises due to discreteness and disorder in granular materials at the microscopic scale which requires a multi-scale approach. The Discrete Element Method (DEM) is a powerful tool to inspect the influence of the microscopic contact properties of its individual constituents on the bulk behavior of granular assemblies. In this study, the isotropic deformation mode of polydisperse packings of frictionless and frictional spheres are modeled by using DEM, to investigate the effective stiffness of the granular assembly. At various volume fractions, for every sample, we determine the stress and fabric incremental response that result from the application of strain-probes. As we are interested first in the reversible, elastic response, the amplitude of the applied perturbations has to be small enough to avoid opening and closing of too many contacts, which would lead to irreversible rearrangements in the sample. Counterintuitively, with increasing inter-particle contact friction, the bulk modulus decreases systematically with the coefficient of friction for samples with the same volume fraction. We explain this by the difference in microstructure (isotropic fabric) the samples get when compressed to the same density.
Smith, Brent
2002-01-01
Describes the laws of thermodynamics as a supplement to an introductory thermodynamics undergraduate course. Uses rubber-elastic materials (REM) which have strong analogies to the concept of ideal gas. Provides examples of the analogies between ideal gas and REM and mathematical analogies. (YDS)
Smith, Brent
2002-01-01
Describes equations of state as a supplement to an introductory thermodynamics undergraduate course. Uses rubber-elastic materials (REM) which have strong analogies to the concept of an ideal gas and explains the molar basis of REM. Provides examples of the analogies between ideal gas and REM and mathematical analogies. (Contains 22 references.)…
Smith, Brent
2002-01-01
Describes the laws of thermodynamics as a supplement to an introductory thermodynamics undergraduate course. Uses rubber-elastic materials (REM) which have strong analogies to the concept of ideal gas. Provides examples of the analogies between ideal gas and REM and mathematical analogies. (YDS)
Smith, Brent
2002-01-01
Describes equations of state as a supplement to an introductory thermodynamics undergraduate course. Uses rubber-elastic materials (REM) which have strong analogies to the concept of an ideal gas and explains the molar basis of REM. Provides examples of the analogies between ideal gas and REM and mathematical analogies. (Contains 22 references.)…
Martin, D A
2015-01-01
We study evolution equations and stationary homogeneous solutions for electric and magnetic field amplitudes in a ring cavity with flat mirrors. The cavity is filled with a positive or negative refraction index material with third order Kerr-like electric nonlinearities and also magnetic nonlinearities, which can be relevant in metamaterials. We consider the degree of freedom of polarization in the incident beam. It is found that considering a magnetic nonlinearity increases the variety of possible qualitatively different solutions. A classification of solutions is proposed in terms of the number of bifurcations. The analysis can be useful for the implementation of optical switching or memory storage using ring cavities with non linear materials.
Schweizer, Kenneth S.; Sussman, Daniel M.
2016-12-01
We employ a first-principles-based, force-level approach to construct the anharmonic tube confinement field for entangled fluids of rigid needles, and also for chains described at the primitive-path (PP) level in two limiting situations where chain stretch is assumed to either be completely equilibrated or unrelaxed. The influence of shear and extensional deformation and polymer orientation is determined in a nonlinear elastic limit where dissipative relaxation processes are intentionally neglected. For needles and PP-level chains, a self-consistent analysis of transverse polymer harmonic dynamical fluctuations predicts that deformation-induced orientation leads to tube weakening or widening. In contrast, for deformed polymers in which chain stretch does not relax, we find tube strengthening or compression. For all three systems, a finite maximum transverse entanglement force localizing the polymers in effective tubes is predicted. The conditions when this entanglement force can be overcome by an externally applied force associated with macroscopic deformation can be crisply defined in the nonlinear elastic limit, and the possibility of a "microscopic absolute yielding" event destroying the tube confinement can be analyzed. For needles and contour-relaxed PP chains, this force imbalance occurs at a stress of order the equilibrium shear modulus and a strain of order unity, corresponding to a mechanically fragile entanglement tube field. However, for unrelaxed stretched chains, tube compression stabilizes transverse polymer confinement, and there appears to be no force imbalance. These results collectively suggest that the crossover from elastic to irreversible viscous response requires chain retraction to initiate disentanglement. We qualitatively discuss comparisons with existing phenomenological models for nonlinear startup shear, step strain, and creep rheology experiments.
Nonlinear Magnetic Phenomena in Highly Polarized Target Materials
Kiselev, Yu F
2007-01-01
The report introduces and surveys nonlinear magnetic phenomena which have been observed at high nuclear polarizations in polarized targets of the SMC and of the COMPASS collaborations at CERN. Some of these phenomena, namely the frequency modulation eect and the distortion of the NMR line shape, promote the development of the polarized target technique. Others, as the spin-spin cross-relaxation between spin subsystems can be used for the development of quantum statistical physics. New findings bear on an electromagnetic noise and the spectrally resolved radiation from LiD with negatively polarized nuclei detected by low temperature bolometers. These nonlinear phenomena need to be taken into account for achieving the ultimate polarizations.
A donor-nanotube paradigm for nonlinear optical materials.
Xiao, Dequan; Bulat, Felipe A; Yang, Weitao; Beratan, David N
2008-09-01
Studies of the nonlinear electronic response of donor/acceptor substituted nanotubes suggest a behavior that is both surprising and qualitatively distinct from that in conventional conjugated organic species. We find that the carbon nanotubes serve as both electronic bridges and acceptors, leading to a donor-nanotube paradigm for the effective design of large first hyperpolarizabilities. We also find that tuning the donor orientation, relative to the nanotube, can significantly enhance the first hyperpolarizability.
Salamon, P; Eber, N; Seltmann, J; Lehmann, M; Gleeson, J T; Sprunt, S; Jákli, A
2012-06-01
The effect of director pretilt on the twist magnetic Fréedericksz transition of nematics was investigated in a planar cell. The director configuration was calculated as a function of magnetic inductance. The dielectric and optical response of the nematic liquid crystal was numerically modeled. A dielectric measurement method for determining the elastic constant K_{22} is presented. The influence of the conditions for the Mauguin effect is discussed. The theoretical predictions were confirmed by our experiments. Experimental data for all elastic constants of a bent-core nematic material are presented and discussed.
Elastic Response of a Half-Plane to a Bonded Interference-Fit Disc of the Same Material.
1984-07-01
Library Trans-Australia Airlines, Library Qantas Airways Limited Ansett Airlines of Australia, Library Commonwealth Aircraft Corporation, Library Hawker...throughout. It is to be noted that the analysis is valid only for disc and plate of the same material and where there is no failure of the bond nor...points around the interface. 5. CONCLUSIONS For a bonded interference-fit disc in an elastic half plane of the same material, the present analysis
Tzoneva, Rumiana; Weckwerth, Claudia; Seifert, Barbara; Behl, Marc; Heuchel, Matthias; Tsoneva, Iana; Lendlein, Andreas
2011-01-01
There is a need to create cell- and histocompatible implant materials, which might temporarily replace the mechanical function of a native tissue for regenerative therapies. To match the elastic behavior of the native tissue two different multiblock co-polymers were investigated: PDC, consisting of poly(p-dioxanone) (PPDO)/poly(ε-caprolactone) (PCL), and PDD, based on PPDO/poly((adipinate-alt-1,4-butanediol)-co-(adipinate-alt-ethylene glycol)-co-adipinate-alt-diethylene glycol) (Diorez). PDC is capable of a shapememory effect. Both multiblock co-polymers show an improved elasticity compared to materials applied in established vascular prosthesis. PDD is softer than PDC at 20°C, while PDC maintains its elasticity at 37°C. Thermodynamic characteristics indicate a more polar surface of PDD. Low cell adhesion was found on surfaces with low molar free energy of hysteresis (ΔG) derived from contact angle measurements in wetting and dewetting mode and high cell adhesion on high-ΔG surfaces. An increasing content of PCL in PDC improved cell adhesion and spreading of human umbilical vein endothelial cells. The prothrombotic potential of PDD is higher than PDC. Finally, it is concluded that PDC is a promising material for vascular tissue engineering because of its improved elastic properties, as well as balanced prothrombotic and anti-thrombotic properties with endothelial cells.
DEFF Research Database (Denmark)
Schløer, Signe; Bredmose, Henrik; Bingham, Harry B.
2016-01-01
and nonlinear irregular wave realizations are calculated using the fully nonlinear potential flow wave model OceanWave3D [1]. The linear and nonlinear wave realizations are compared using both a static analysis on a fixed monopile and dynamic calculations with the aeroelastic code Flex5 [2]. The conclusion from...... this analysis is that linear wave theory is generally sufficient for estimating the fatigue loading, but wave nonlinearity is important in determining the ultimate design loads.......The response of an offshore wind turbine tower and its monopile foundation has been investigated when exposed to linear and fully nonlinear irregular waves on four different water depths. The investigation focuses on the consequences of including full nonlinearity in the wave kinematics. The linear...
Energy Technology Data Exchange (ETDEWEB)
Singh, B.N., E-mail: bnsingh@aero.iitkgp.ernet.i [Department of Aerospace Engineering, IIT Kharagpur 721 302, West Bengal (India); Lal, Achchhe [Department of Mechanical Engineering, SVNIT, Surat 395007 (India)
2010-10-15
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{sup 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.
Frequency Response of Synthetic Vocal Fold Models with Linear and Nonlinear Material Properties
Shaw, Stephanie M.; Thomson, Scott L.; Dromey, Christopher; Smith, Simeon
2014-01-01
Purpose The purpose of this study was to create synthetic vocal fold models with nonlinear stress-strain properties and to investigate the effect of linear versus nonlinear material properties on fundamental frequency during anterior-posterior stretching. Method Three materially linear and three materially nonlinear models were created and stretched up to 10 mm in 1 mm increments. Phonation onset pressure (Pon) and fundamental frequency (F0) at Pon were recorded for each length. Measurements were repeated as the models were relaxed in 1 mm increments back to their resting lengths, and tensile tests were conducted to determine the stress-strain responses of linear versus nonlinear models. Results Nonlinear models demonstrated a more substantial frequency response than did linear models and a more predictable pattern of F0 increase with respect to increasing length (although range was inconsistent across models). Pon generally increased with increasing vocal fold length for nonlinear models, whereas for linear models, Pon decreased with increasing length. Conclusions Nonlinear synthetic models appear to more accurately represent the human vocal folds than linear models, especially with respect to F0 response. PMID:22271874
National Aeronautics and Space Administration — The overall goal of the project is to develop reliable reduced order modeling technologies to automatically generate nonlinear, parameter-varying (PV),...
Hu, Ji-Ying; Li, Zhao-Hui; Sun, Yang; Li, Qi-Hu
2016-12-01
Shear-mode piezoelectric materials have been widely used to shunt the damping of vibrations where utilizing surface or interface shear stresses. The thick-shear mode (TSM) elastic constant and the mechanical loss factor can change correspondingly when piezoelectric materials are shunted to different electrical circuits. This phenomenon makes it possible to control the performance of a shear-mode piezoelectric damping system through designing the shunt circuit. However, due to the difficulties in directly measuring the TSM elastic constant and the mechanical loss factor of piezoelectric materials, the relationships between those parameters and the shunt circuits have rarely been investigated. In this paper, a coupling TSM electro-mechanical resonant system is proposed to indirectly measure the variations of the TSM elastic constant and the mechanical loss factor of piezoelectric materials. The main idea is to transform the variations of the TSM elastic constant and the mechanical loss factor into the changes of the easily observed resonant frequency and electrical quality factor of the coupling electro-mechanical resonator. Based on this model, the formular relationships are set up theoretically with Mason equivalent circuit method and they are validated with finite element (FE) analyses. Finally, a prototype of the coupling electro-mechanical resonator is fabricated with two shear-mode PZT5A plates to investigate the TSM elastic constants and the mechanical loss factors of different circuit-shunted cases of the piezoelectric plate. Both the resonant frequency shifts and the bandwidth changes observed in experiments are in good consistence with the theoretical and FE analyses under the same shunt conditions. The proposed coupling resonator and the obtained relationships are validated with but not limited to PZT5A. Project supported by the National Defense Foundation of China (Grant No. 9149A12050414JW02180).
Material and elastic properties of Al-tobermorite in ancient roman seawater concrete
Jackson, Marie D.
2013-05-28
The material characteristics and elastic properties of aluminum-substituted 11 Å tobermorite in the relict lime clasts of 2000-year-old Roman seawater harbor concrete are described with TG-DSC and 29Si MAS NMR studies, along with nanoscale tomography, X-ray microdiffraction, and high-pressure X-ray diffraction synchrotron radiation applications. The crystals have aluminum substitution for silicon in tetrahedral bridging and branching sites and 11.49(3) Å interlayer (002) spacing. With prolonged heating to 350°C, the crystals exhibit normal behavior. The experimentally measured isothermal bulk modulus at zero pressure, K0, 55 ±5 GPa, is less than ab initio and molecular dynamics models for ideal tobermorite with a double-silicate chain structure. Even so, K0, is substantially higher than calcium-aluminum-silicate-hydrate binder (C-A-S-H) in slag concrete. Based on nanoscale tomographic study, the crystal clusters form a well connected solid, despite having about 52% porosity. In the pumiceous cementitious matrix, Al-tobermorite with 11.27 Å interlayer spacing is locally associated with phillipsite, similar to geologic occurrences in basaltic tephra. The ancient concretes provide a sustainable prototype for producing Al-tobermorite in high-performance concretes with natural volcanic pozzolans. © 2013 The American Ceramic Society.
Theoretical and Numerical Study of Nonlinear Phononic Crystals
Guerder, Pierre-Yves
This work is dedicated to the theoretical and numerical study of nonlinear phononic crystals. The studied nonlinearities are those due to the second (quadratic) and third (cubic) order elastic constants of the materials that constitute the crystals. Nonlinear effects are studied by the means of finite element methods, used to simulate the propagation of an elastic wave through the crystals. A first research project concerns the study of a bone structure, namely the dispersion of elastic waves in a structure composed of collagen and hydroxy apatite alternate constituent layers. Simulations showed that it exists a strong link between bones hydration and their ability to dissipate the energy. The second study relates to an elastic resonator. A structure composed of steel inclusions in a silica matrix shows a switch behavior when the cubic nonlinearities of steel are taken into account. This strong nonlinear effect appears when the amplitude of the incident wave reaches a threshold. A full analytical model is provided. The last study demonstrates the design of composite materials with both strong cubic nonlinearities and weak quadratic nonlinearities. The derivation of the mixing laws of the elastic parameters of a nonlinear material inside a linear one is performed up to order three. Equations show a strong amplification of the nonlinear parameters of the material for some concentrations. Numerical simulations allow to conclude that the above mentioned resonator can be produced.
Jiang, Jian-jun; Li, He-ping; Dai, Li-dong; Hu, Hai-ying; Wang, Yan; Zhao, Chao-shuai
2015-09-01
In-situ experimental results on the elastic wave velocity of Earth materials at high pressure and high temperature in combination with data from seismic observation can help to inverse the chemical composition, state and migration of materials in Earth's interior, providing an important approach to explore information of deep earth. Applying the Brillouin scattering into the Diamond Anvil Cell (DAC) to obtain the in situ elastic wave velocities of minerals, is the important approach to investigate elastic properties of Earth's Interior. With the development of DAC technology, on the one hand, the high temperature and high pressure experimental environment to simulate different layers of the earth can be achieved; on the other hand, the optical properties of DAC made many kinds of optical analysis and test methods have been widely applied in this research field. In order to gain the elastic wave velocity under high temperature and high pressure, the accurate experimental pressure and heating temperature of the sample in the cavity should be measured and calibrated first, then the scattering signal needs to dealt with, using the Brillouin frequency shift to calculate the velocity in the sample. Combined with the lattice constants obtained from X ray technique, by a solid elastic theory, all the elastic parameters of minerals can be solved. In this paper, firstly, application of methods based on optical spectrum such as Brillouin and Raman scattering in elasticity study on materials in Earth's interior, and the basic principle and research progress of them in the velocity measurement, pressure and temperature calibration are described in detail. Secondly, principle and scope of application of two common methods of spectral pressure calibration (fluorescence and Raman spectral pressure standard) are analyzed, in addition with introduce of the application of two conventional means of temperature calibration (blackbody radiation and Raman temperature scale) in
Molecular design of porphyrin-based nonlinear optical materials.
Keinan, Shahar; Therien, Michael J; Beratan, David N; Yang, Weitao
2008-11-27
Nonlinear optical chromophores containing (porphyrinato)Zn(II), proquinoid, and (terpyridyl)metal(II) building blocks were optimized in a library containing approximately 10(6) structures using the linear combination of atomic potentials (LCAP) methodology. We report here the library design and molecular property optimizations. Two basic structural types of large beta(0) chromophores were examined: linear and T-shaped motifs. These T-shaped geometries suggest a promising NLO chromophoric architecture for experimental investigation and further support the value of performing LCAP searches in large chemical spaces.
Directory of Open Access Journals (Sweden)
Shahriar Dastjerdi
2016-06-01
Full Text Available Nonlinear bending analysis of orthotropic annular/circular graphene sheets has been studied based on the non-local elasticity theory. The first order shear deformation theory (FSDT is applied in combination with the nonlinear Von-Karman strain field. The obtained differential equations are solved by using two methods, first the differential quadrature method (DQM and a new semi-analytical polynomial method (SAPM which is innovated by the authors. Applying the DQM or SAPM, the differential equations are transformed to nonlinear algebraic equations system. Then the Newton–Raphson iterative scheme is used. First, the obtained results from DQM and SAPM are compared and it is concluded that although the SAPM’s formulation is considerably simpler than DQM, however, the SAPM’s results are so close to DQM. The results are validated with available papers. Finally, the effects of small scale parameter on the results, the comparison between local and non-local theories, and linear to nonlinear analyses are investigated.
Breakdown of elasticity in amorphous solids
Biroli, Giulio; Urbani, Pierfrancesco
2016-12-01
What characterizes a solid is the way that it responds to external stresses. Ordered solids, such as crystals, exhibit an elastic regime followed by a plastic regime, both understood microscopically in terms of lattice distortion and dislocations. For amorphous solids the situation is instead less clear, and the microscopic understanding of the response to deformation and stress is a very active research topic. Several studies have revealed that even in the elastic regime the response is very jerky at low temperature, resembling very much the response of disordered magnetic materials. Here we show that in a very large class of amorphous solids this behaviour emerges upon decreasing temperature, as a phase transition, where standard elastic behaviour breaks down. At the transition all nonlinear elastic moduli diverge and standard elasticity theory no longer holds. Below the transition, the response to deformation becomes history- and time-dependent.
Nonlinear property of the visco-elastic-plastic material in the impact problem
Institute of Scientific and Technical Information of China (English)
HOU Lei; CAI Li
2009-01-01
In this paper a numerical investigation on the non-Newtonian flow problem is conducted, in order to shed further light on the mathematical and virtual test methods in the auto-crash safety analysis. The accurate mathematical prediction would supply ultimate research tool for the passive safety analysis in such a scale.
Creep characterization of gels and nonlinear viscoelastic material model
Ishikawa, Kiyotaka; Fujikawa, Masaki; Makabe, Chobin; Tanaka, Kou
2016-07-01
In this paper, we examine gel creep behavior and develop a material model for useful and simple numerical simulation of this behavior. This study has three stages and aims: (1) gel creep behavior is examined; (2) the material model is determined and the material constants are identified; and (3) the versatility of the material model and the constants are evaluated. The creep behavior is found to be independent of the initial stress level in the present experiment. Thus, the viscoelastic model proposed by Simo is selected, and its material constants are identified using the results of creep tests. Moreover, from the results of numerical calculations and experiments, it is found that the chosen material model has good reproducibility, predictive performance and high versatility.
Directory of Open Access Journals (Sweden)
Lhoucine Boutahar
2016-03-01
Full Text Available Some Functionally Graded Materials contain pores due to the result of processing; this influences their elastic and mechanical properties. Therefore, it may be very useful to examine the vibration behavior of thin Functionally Graded Annular Plates Clamped at both edges including porosities. In the present study, the rule of mixture is modified to take into account the effect of porosity and to approximate the material properties assumed to be graded in the thickness direction of the examined annular plate. A semi-analytical model based on Hamilton’s principle and spectral analysis is adopted using a homogenization procedure to reduce the problem under consideration to that of an equivalent isotropic homogeneous annular plate. The problem is solved by a numerical iterative method. The effects of porosity, material property, and elastic foundations characteristics on the CCFGAP axisymmetric large deflection response are presented and discussed in detail.
Stable Second-Order Nonlinear Optical Materials Based on Interpenetrating Polymer Networks
1994-03-17
0IJUN93 to 31MAY94 4. 1I1Lk ANDLSUBI1ILIE D. ?-UNUING NUMBERS •’• Stable Second-Order Nonlinear Optical Materials Based On C:N00014-90-J-1148...release and sale; its distribution is unlimited. I Stable Second-Order Nonlinear Optical Materials Based On Interpenetrating Polymer Networks S... Optical Materials Based On Interpenetrating Polymer Networks by S. Marturunkakul, J. I. Chen, L. Li, X. L. Jiang, R. J. Jeng, S. K. Sengupta, J. Kumar
{open_quotes}Quadrupoled{close_quotes} materials for second-order nonlinear optics
Energy Technology Data Exchange (ETDEWEB)
Hubbard, S.F.; Petschek, R.G.; Singer, K.D. [Case Western Reserve Univ., Cleveland, OH (United States). Dept. of Physics] [and others
1997-10-01
We describe a new approach to second-order nonlinear optical materials, namely quadrupoling. This approach is valid in the regime of Kleinman (full permutation) symmetry breaking, and thus requires a two- or three dimensional microscopic nonlinearity at wavelengths away from material resonances. This {open_quotes}quadrupolar{close_quotes} nonlinearity arises from the second rank pseudotensor of the rotationally invariant representation of the second-order nonlinear optical tensor. We have experimentally investigated candidate molecules comprised of chiral camphorquinone derivatives by measuring the scalar invariant associated with the rank two pseudotensor using hyper-Rayleigh scattering. We have found sizable scalar figures of merit for several compounds using light for which the second harmonic wavelengths are greater than 100 nm longer than the absorption peak location. At these wavelengths, the quadrupolar scalar is as large as the polar (EFISH) scalar of p-nitroaniline. Prospects for applications are discussed.
Yu, Weiguo; Jia, Jianhong; Gao, Jianrong; Han, Liang; Li, Yujin
2015-03-01
Six symmetrical ferrocenyl Schiff base materials were synthesized and characterized by UV, 1H NMR, mass spectrometry (MS) and elemental analysis. Their off-resonant third-order nonlinear optical properties were measured using femtosecond laser and degenerate four-wave mixing (DFWM) technique. The third-order nonlinear optical susceptibilities χ(3) were 1.961-6.363 × 10-13 esu. The nonlinear refractive indexes n2 were 3.609-11.716 × 10-12 esu. The second-order hyperpolarizabilities γ of these molecules were 1.967-6.388 × 10-31 esu. The response time were 45.759-73.079 fs. The results indicate that these materials have potential nonlinear optical applications.
Blom, F.C.; Driessen, A.; Hoekstra, Hugo; van Schoot, J.B.P.; van Schoot, Jan B.P.; Popma, T.J.A.
1999-01-01
In the long trajectory from the synthesis of organic nonlinear optical materials to the completed all-optical device it is highly desirable to be able to concentrate already in an early state on only a few promising materials. Third harmonic generation (THG) is a very convenient method as it allows
Blom, Freek C.; Driessen, Alfred; Hoekstra, Hugo J.W.M.; Schoot, van Jan B.P.; Popma, Th.J.A.
1999-01-01
In the long trajectory from the synthesis of organic nonlinear optical materials to the completed all-optical device it is highly desirable to be able to concentrate already in an early state on only a few promising materials. Third harmonic generation (THG) is a very convenient method as it allows
An exact approach to intensity analysis of optical pulses in nonlinear meta-materials
Nanda, Lipsa
2016-05-01
The nonlinear pulse propagation has been analytically studied by solving the nonlinear Schrödinger's equation (NLSE) in bulk media exhibiting frequency dependent dielectric permittivity(ɛ) and magnetic permeability(μ). The exact solutions obtained are shown to be of trigonometric & localized types. The analytical and simulation based method has been further extended to investigate the intensity distribution in a nonlinear meta-material which behaves as a negative refractive medium (NRM), where both ɛ and μ are shown to be dispersive and negative in nature.
Directory of Open Access Journals (Sweden)
Wei Sun
2015-01-01
Full Text Available Due to the material nonlinearity of hard coating, the coated structure produces the nonlinear dynamical behaviors of variable stiffness and damping, which make the modeling of hard-coating composite structure become a challenging task. In this study, the polynomial was adopted to characterize this material nonlinearity and an analytical modeling method was developed for the hard-coating composite plate. Firstly, to relate the hard-coating material parameters obtained by test and the analytical model, the expression of equivalent strain of composite plate was derived. Then, the analytical model of hard-coating composite plate was created by energy method considering the material nonlinearity of hard coating. Next, using the Newton-Raphson method to solve the vibration response and resonant frequencies of composite plate and a specific calculation procedure was also proposed. Finally, a cantilever plate coated with MgO + Al2O3 hard coating was chosen as study case; the vibration response and resonant frequencies of composite plate were calculated using the proposed method. The calculation results were compared with the experiment and general linear calculation, and the correctness of the created model was verified. The study shows the proposed method can still maintain an acceptable precision when the material nonlinearity of hard coating is stronger.
[New formation of elastic fiber material in aortic defects covered with muscle flaps].
Klima, G; Papp, C
1985-01-01
The examination of the coverage of vascular defects with intercostal muscles showed during an observation period of 7 weeks the development of cartilage tissue with thick elastic fiber nettings running between the chondroma.
Ziółkowski, Andrzej
2016-09-01
An apparatus of micromechanics is used to isolate the key ingredients entering macroscopic Gibbs free energy function of a shape memory alloy (SMA) material. A new self-equilibrated eigenstrains influence moduli (SEIM) method is developed for consistent estimation of effective (macroscopic) thermostatic properties of solid materials, which in microscale can be regarded as amalgams of n-phase linear thermoelastic component materials with eigenstrains. The SEIM satisfy the self-consistency conditions, following from elastic reciprocity (Betti) theorem. The method allowed expressing macroscopic coherency energy and elastic complementary energy terms present in the general form of macroscopic Gibbs free energy of SMA materials in the form of semilinear and semiquadratic functions of the phase composition. Consistent SEIM estimates of elastic complementary energy, coherency energy and phase transformation strains corresponding to classical Reuss and Voigt conjectures are explicitly specified. The Voigt explicit relations served as inspiration for working out an original engineering practice-oriented semiexperimental SEIM estimates. They are especially conveniently applicable for an isotropic aggregate (composite) composed of a mixture of n isotropic phases. Using experimental data for NiTi alloy and adopting conjecture that it can be treated as an isotropic aggregate of two isotropic phases, it is shown that the NiTi coherency energy and macroscopic phase strain are practically not influenced by the difference in values of austenite and martensite elastic constants. It is shown that existence of nonzero fluctuating part of phase microeigenstrains field is responsible for building up of so-called stored energy of coherency, which is accumulated in pure martensitic phase after full completion of phase transition. Experimental data for NiTi alloy show that the stored coherency energy cannot be neglected as it considerably influences the characteristic phase transition
Ziółkowski, Andrzej
2017-01-01
An apparatus of micromechanics is used to isolate the key ingredients entering macroscopic Gibbs free energy function of a shape memory alloy (SMA) material. A new self-equilibrated eigenstrains influence moduli (SEIM) method is developed for consistent estimation of effective (macroscopic) thermostatic properties of solid materials, which in microscale can be regarded as amalgams of n-phase linear thermoelastic component materials with eigenstrains. The SEIM satisfy the self-consistency conditions, following from elastic reciprocity (Betti) theorem. The method allowed expressing macroscopic coherency energy and elastic complementary energy terms present in the general form of macroscopic Gibbs free energy of SMA materials in the form of semilinear and semiquadratic functions of the phase composition. Consistent SEIM estimates of elastic complementary energy, coherency energy and phase transformation strains corresponding to classical Reuss and Voigt conjectures are explicitly specified. The Voigt explicit relations served as inspiration for working out an original engineering practice-oriented semiexperimental SEIM estimates. They are especially conveniently applicable for an isotropic aggregate (composite) composed of a mixture of n isotropic phases. Using experimental data for NiTi alloy and adopting conjecture that it can be treated as an isotropic aggregate of two isotropic phases, it is shown that the NiTi coherency energy and macroscopic phase strain are practically not influenced by the difference in values of austenite and martensite elastic constants. It is shown that existence of nonzero fluctuating part of phase microeigenstrains field is responsible for building up of so-called stored energy of coherency, which is accumulated in pure martensitic phase after full completion of phase transition. Experimental data for NiTi alloy show that the stored coherency energy cannot be neglected as it considerably influences the characteristic phase transition
Directory of Open Access Journals (Sweden)
Tieliang Yang
2016-01-01
Full Text Available This paper presents an analytical study for sound radiation of functionally graded materials (FGM plate based on the three-dimensional theory of elasticity. The FGM plate is a mixture of metal and ceramic, and its material properties are assumed to have smooth and continuous variation in the thickness direction according to a power-law distribution in terms of volume fractions of the constituents. Based on the three-dimensional theory of elasticity and state space method, the governing equations with variable coefficients of the FGM plate are derived. The sound radiation of the vibration plate is calculated with Rayleigh integral. Comparisons of the present results with those of solutions in the available literature are made and good agreements are achieved. Finally, some parametric studies are carried out to investigate the sound radiation properties of FGM plates.
Directory of Open Access Journals (Sweden)
Bonić Zoran
2010-01-01
Full Text Available The paper presents application of nonlinear material models in the software package Ansys. The development of the model theory is presented in the paper of the mathematical modeling of material nonlinear problems in structural analysis (part I - theoretical foundations, and here is described incremental-iterative procedure for solving problems of nonlinear material used by this package and an example of modeling of spread footing by using Bilinear-kinematics and Drucker-Prager mode was given. A comparative analysis of the results obtained by these modeling and experimental research of the author was made. Occurrence of the load level that corresponds to plastic deformation was noted, development of deformations with increasing load, as well as the distribution of dilatation in the footing was observed. Comparison of calculated and measured values of reinforcement dilatation shows their very good agreement.
Material and Geometric Nonlinear Analysis of Functionally Graded Plate-Shell Type Structures
Moita, J. S.; Araújo, A. L.; Mota Soares, C. M.; Mota Soares, C. A.; Herskovits, J.
2016-08-01
A nonlinear formulation for general Functionally Graded Material plate-shell type structures is presented. The formulation accounts for geometric and material nonlinear behaviour of these structures. Using the Newton-Raphson incremental-iterative method, the incremental equilibrium path is obtained, and in case of snap-through occurrence the automatic arc-length method is used. This simple and fast element model is a non-conforming triangular flat plate/shell element with 24 degrees of freedom for the generalized displacements. It is benchmarked in the solution of some illustrative plate- shell examples and the results are presented and discussed with numerical alternative models. Benchmark tests with material and geometrically nonlinear behaviour are also proposed.
Wu, Jian-Ying; Cervera, Miguel
2017-04-20
Damage-induced strain softening is of vital importance for the modeling of localized failure in frictional-cohesive materials. This paper addresses strain localization of damaging solids and the resulting consistent frictional-cohesive crack models. As a supplement to the framework recently established for stress-based continuum material models in rate form (Wu and Cervera 2015, 2016), several classical strain-based damage models, expressed usually in total and secant format, are considered. Upon strain localization of such damaging solids, Maxwell's kinematics of a strong (or regularized) discontinuity has to be reproduced by the inelastic damage strains, which are defined by a bounded characteristic tensor and an unbounded scalar related to the damage variable. This kinematic constraint yields a set of nonlinear equations from which the discontinuity orientation and damage-type localized cohesive relations can be derived. It is found that for the "Simó and Ju 1987" isotropic damage model, the localization angles and the resulting cohesive model heavily depend on lateral deformations usually ignored in classical crack models for quasi-brittle solids. To remedy this inconsistency, a modified damage model is proposed. Its strain localization analysis naturally results in a consistent frictional-cohesive crack model of damage type, which can be regularized as a classical smeared crack model. The analytical results are numerically verified by the recently-proposed mixed stabilized finite element method, regarding a singly-perforated plate under uniaxial tension. Remarkably, for all of the damage models discussed in this work, the numerically-obtained localization angles agree almost exactly with the closed-form results. This agreement, on the one hand, consolidates the strain localization analysis based on Maxwell's kinematics and, on the other hand, illustrates versatility of the mixed stabilized finite element method.
Bacigalupo, Andrea; Gambarotta, Luigi
2017-05-01
Dispersive waves in two-dimensional blocky materials with periodic microstructure made up of equal rigid units, having polygonal centro-symmetric shape with mass and gyroscopic inertia, connected with each other through homogeneous linear interfaces, have been analyzed. The acoustic behavior of the resulting discrete Lagrangian model has been obtained through a Floquet-Bloch approach. From the resulting eigenproblem derived by the Euler-Lagrange equations for harmonic wave propagation, two acoustic branches and an optical branch are obtained in the frequency spectrum. A micropolar continuum model to approximate the Lagrangian model has been derived based on a second-order Taylor expansion of the generalized macro-displacement field. The constitutive equations of the equivalent micropolar continuum have been obtained, with the peculiarity that the positive definiteness of the second-order symmetric tensor associated to the curvature vector is not guaranteed and depends both on the ratio between the local tangent and normal stiffness and on the block shape. The same results have been obtained through an extended Hamiltonian derivation of the equations of motion for the equivalent continuum that is related to the Hill-Mandel macro homogeneity condition. Moreover, it is shown that the hermitian matrix governing the eigenproblem of harmonic wave propagation in the micropolar model is exact up to the second order in the norm of the wave vector with respect to the same matrix from the discrete model. To appreciate the acoustic behavior of some relevant blocky materials and to understand the reliability and the validity limits of the micropolar continuum model, some blocky patterns have been analyzed: rhombic and hexagonal assemblages and running bond masonry. From the results obtained in the examples, the obtained micropolar model turns out to be particularly accurate to describe dispersive functions for wavelengths greater than 3-4 times the characteristic dimension of
Energy Technology Data Exchange (ETDEWEB)
Batou, A., E-mail: anas.batou@univ-paris-est.fr [Université Paris-Est, Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-la-Vallee (France); Soize, C., E-mail: christian.soize@univ-paris-est.fr [Université Paris-Est, Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-la-Vallee (France); Brie, N., E-mail: nicolas.brie@edf.fr [EDF R and D, Département AMA, 1 avenue du général De Gaulle, 92140 Clamart (France)
2013-09-15
Highlights: • A ROM of a nonlinear dynamical structure is built with a global displacements basis. • The reduced order model of fuel assemblies is accurate and of very small size. • The shocks between grids of a row of seven fuel assemblies are computed. -- Abstract: We are interested in the construction of a reduced-order computational model for nonlinear complex dynamical structures which are characterized by the presence of numerous local elastic modes in the low-frequency band. This high modal density makes the use of the classical modal analysis method not suitable. Therefore the reduced-order computational model is constructed using a basis of a space of global displacements, which is constructed a priori and which allows the nonlinear dynamical response of the structure observed on the stiff part to be predicted with a good accuracy. The methodology is applied to a complex industrial structure which is made up of a row of seven fuel assemblies with possibility of collisions between grids and which is submitted to a seismic loading.
2015-03-01
AFRL-RY-WP-TP-2015-0068 GROWTH AND STUDY OF NONLINEAR OPTICAL MATERIALS FOR FREQUENCY CONVERSION DEVICES WITH APPLICATIONS IN DEFENCE AND...2015 Technical Paper 1 August 2013 – 1 August 2014 4. TITLE AND SUBTITLE GROWTH AND STUDY OF NONLINEAR OPTICAL MATERIALS FOR FREQUENCY CONVERSION...SUBJECT TERMS hydride vapor phase epitaxy, nonlinear optical materials , quasi-phase matching 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF
Le Page, Yvon; Saxe, Paul
2002-03-01
A symmetry-general approach for the least-squares, therefore precise, extraction of elastic coefficients for strained materials is reported. It analyzes stresses calculated ab initio for properly selected strains. The problem, its implementation, and its solution strategy all differ radically from a previous energy-strain approach that we published last year, but the normal equations turn out to be amenable to the same constrainment scheme that makes both approaches symmetry general. The symmetry considerations governing the automated selection of appropriately strained models and their Cartesian systems are detailed. The extension to materials under general stress is discussed and implemented. VASP was used for ab initio calculation of stresses. A comprehensive range of examples includes a triclinic material (kyanite) and simple materials with a range of symmetries at zero pressure, MgO under hydrostatic pressure, Ti4As3 under [001] uniaxial strain, and Si under [001] uniaxial stress. The MgO case agrees with recent experimental work including elastic coefficients as well as their first and second derivatives. The curves of elastic coefficients for Si show a gradual increase in the 33 compliance coefficient, leading to a collapse of the material at -11.7 GPa, compared with -12.0 GPa experimentally. Interpretation of results for Be using two approximations [local density (LDA), generalized gradient (GGA)], two approaches (stress strain and energy strain), two potential types (projector augmented wave and ultrasoft), and two quantum engines (VASP and ORESTES) expose the utmost importance of the cell data used for the elastic calculations and the lesser importance of the other factors. For stiffness at relaxed cell data, differences are shown to originate mostly in the considerable overestimation of the residual compressive stresses at x-ray cell data by LDA, resulting in a smaller relaxed cell, thus larger values for diagonal stiffness coefficients. The symmetry
Three-dimensional treatment of nonequilibrium dynamics and higher order elasticity
Lott, Martin; Payan, Cédric; Garnier, Vincent; Vu, Quang A.; Eiras, Jesús N.; Remillieux, Marcel C.; Le Bas, Pierre-Yves; Ulrich, T. J.
2016-04-01
This letter presents a three-dimensional model to describe the complex behavior of nonlinear mesoscopic elastic materials such as rocks and concrete. Assuming isotropy and geometric contraction of principal stress axes under dynamic loading, the expression of elastic wave velocity is derived, based on the second-order elastic constants ( λ , μ ) , third-order elastic constants (l, m, n), and a parameter α of nonclassical nonlinear elasticity resulting from conditioning. We demonstrate that both softening and recovering of the elastic properties under dynamic loading is an isotropic effect related to the strain tensor. The measurement of the conditioning is achieved using three polarized waves. The model allows the evaluation of the third-order elastic constants uncoupled from conditioning and viscoelastic effects. The values obtained are similar to those reported in the literature using quasi-static loading.
On the Prediction of the Nonlinear Absorption in Reverse Saturable Absorbing Materials
Pachter, Ruth; Nguyen, Kiet A.; Day, Paul N.; Kennel, Joshua C.
2001-03-01
In our continuing efforts to design materials that exhibit reverse saturable absorption (RSA), we systematically examine the ability of the time-dependent density functional theory (TDDFT) method using local, nonlocal, and hybrid functionals, to predict the experimental nonlinear absorption for a variety of organic and organometallic molecular systems, including a number of free-base porphyrins, phthalocyanine and their metal complexes. The ground and triplet-triplet excitation energies, as well as the oscillator strengths are calculated, indicating good agreement with experiment. We conclude that the TDDFT approach with a hybrid functional provides good estimates for the nonlinear absorption of RSA materials.
Wave propagation in parallel-plate waveguides filled with nonlinear left-handed material
Institute of Scientific and Technical Information of China (English)
Burhan Zamir; Rashid Ali
2011-01-01
A theoretical investigation of field components for transverse electric mode in the parallel-plate waveguides has been studied. In this analysis two different types of waveguide structures have been discussed, i.e., (a) normal good/perfect conducting parallel-plate waveguide filled with nonlinear left-handed material and (b) high-temperature-superconducting parallel-plate waveguide filled with nonlinear left-handed material. The dispersion relations of transverse electric mode have also been discussed for these two types of waveguide structures.
Deliktaş, Ekin; Teymür, Mevlüt
2017-07-01
In this study, the propagation of shear horizontal (SH) waves in a nonlinear elastic half space covered by a nonlinear elastic layer with a slowly varying interface is examined. The constituent materials are assumed to be homogenous, isotropic, elastic and having different mechanical properties. By employing the method of multiple scales, a nonlinear Schrödinger equation (NLS) with variable coefficients is derived for the nonlinear self-modulation of SH waves. We examine the effects of dispersion, irregularity of the interface and nonlinearity on the propagation characteristics of SH waves.
Chip scale low dimensional materials: optoelectronics & nonlinear optics
Gu, Tingyi
The CMOS foundry infrastructure enables integration of high density, high performance optical transceivers. We developed integrated devices that assemble resonators, waveguide, tapered couplers, pn junction and electrodes. Not only the volume standard manufacture in silicon foundry is promising to low-lost optical components operating at IR and mid-IR range, it also provides a robust platform for revealing new physical phenomenon. The thesis starts from comparison between photonic crystal and micro-ring resonators based on chip routers, showing photonic crystal switches have small footprint, consume low operation power, but its higher linear loss may require extra energy for signal amplification. Different designs are employed in their implementation in optical signal routing on chip. The second part of chapter 2 reviews the graphene based optoelectronic devices, such as modulators, lasers, switches and detectors, potential for group IV optoelectronic integrated circuits (OEIC). In chapter 3, the highly efficient thermal optic control could act as on-chip switches and (transmittance) tunable filters. Local temperature tuning compensates the wavelength differences between two resonances, and separate electrode is used for fine tuning of optical pathways between two resonators. In frequency domain, the two cavity system also serves as an optical analogue of Autler-Towns splitting, where the cavity-cavity resonance detuning is controlled by the length of pathway (phase) between them. The high thermal sensitivity of cavity resonance also effectively reflects the heat distribution around the nanoheaters, and thus derives the thermal conductivity in the planar porous suspended silicon membrane. Chapter 4 & 5 analyze graphene-silicon photonic crystal cavities with high Q and small mode volume. With negligible nonlinear response to the milliwatt laser excitation, the monolithic silicon PhC turns into highly nonlinear after transferring the single layer graphene with
Chortis, Dimitris I
2013-01-01
This book concerns the development of novel finite elements for the structural analysis of composite beams and blades. The introduction of material damping is also an important aspect of composite structures and it is presented here in terms of their static and dynamic behavior. The book thoroughly presents a new shear beam finite element, which entails new blade section mechanics, capable of predicting structural blade coupling due to composite coupling and/or internal section geometry. Theoretical background is further expanded towards the inclusion of nonlinear structural blade models and damping mechanics for composite structures. The models effectively include geometrically nonlinear terms due to large displacements and rotations, improve the modeling accuracy of very large flexible blades, and enable the modeling of rotational stiffening and buckling, as well as, nonlinear structural coupling. Validation simulations on specimen level study the geometric nonlinearities effect on the modal frequencies and...
Comment on "Nonlinear refraction measurements of materials using the moiré deflectometry"
Rashidian Vaziri, M. R.
2015-12-01
In an influential paper Jamshidi-Ghaleh and Mansour [1] (Opt. Commun. 234 (2004) 419), have reported on a new method for measuring the nonlinear refractive index of materials using the rotational moiré deflectometry technique. In the cited work, the authors apply the ray matrix theory for finding the beam deflection angle on the plane of the first grating in the used geometry. To this end, using the parabolic approximation, the exponential term in the beam irradiance is expanded and retaining the first two resultant terms, the nonlinear sample is treated as a thin lens with a position dependent focal length. In this comment, the effective focal length of the nonlinear sample has been rederived in detail using the Gaussian beam theory and it is shown that it must contain a correction factor. The relative error introduced by ignoring this factor can be as large as 73.5-84.4% in determining the nonlinear refractive index of thin samples.
Organic nonlinear optical materials: where we have been and where we are going.
Marder, Seth R
2006-01-14
Nonlinear optical (NLO) materials can be useful for a variety of applications varying from modulation of optical signals facilitated by the electro-optic effect-the effect whereby the refractive index of a material changes in response to an applied electric field-to microfabrication, sensing, imaging, and cancer therapy facilitated by multiphoton absorption, wherein molecules simultaneously absorb two or more photons of light. This short Focus article is a brief personal perspective of some of the key advances in second-order NLO materials and in multiphoton-absorbing materials, and of how and why these advances have led to renewed interest in organic NLO materials.
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.
Fatigue Life Prediction of Metallic Materials Based on the Combined Nonlinear Ultrasonic Parameter
Zhang, Yuhua; Li, Xinxin; Wu, Zhenyong; Huang, Zhenfeng; Mao, Hanling
2017-07-01
The fatigue life prediction of metallic materials is always a tough problem that needs to be solved in the mechanical engineering field because it is very important for the secure service of mechanical components. In this paper, a combined nonlinear ultrasonic parameter based on the collinear wave mixing technique is applied for fatigue life prediction of a metallic material. Sweep experiments are first conducted to explore the influence of driving frequency on the interaction of two driving signals and the fatigue damage of specimens, and the amplitudes of sidebands at the difference frequency and sum frequency are tracked when the driving frequency changes. Then, collinear wave mixing tests are carried out on a pair of cylindrically notched specimens with different fatigue damage to explore the relationship between the fatigue damage and the relative nonlinear parameters. The experimental results show when the fatigue degree is below 65% the relative nonlinear parameter increases quickly, and the growth rate is approximately 130%. If the fatigue degree is above 65%, the increase in the relative nonlinear parameter is slow, which has a close relationship with the microstructure evolution of specimens. A combined nonlinear ultrasonic parameter is proposed to highlight the relationship of the relative nonlinear parameter and fatigue degree of specimens; the fatigue life prediction model is built based on the relationship, and the prediction error is below 3%, which is below the prediction error based on the relative nonlinear parameters at the difference and sum frequencies. Therefore, the combined nonlinear ultrasonic parameter using the collinear wave mixing method can effectively estimate the fatigue degree of specimens, which provides a fast and convenient method for fatigue life prediction.
Fatigue Life Prediction of Metallic Materials Based on the Combined Nonlinear Ultrasonic Parameter
Zhang, Yuhua; Li, Xinxin; Wu, Zhenyong; Huang, Zhenfeng; Mao, Hanling
2017-08-01
The fatigue life prediction of metallic materials is always a tough problem that needs to be solved in the mechanical engineering field because it is very important for the secure service of mechanical components. In this paper, a combined nonlinear ultrasonic parameter based on the collinear wave mixing technique is applied for fatigue life prediction of a metallic material. Sweep experiments are first conducted to explore the influence of driving frequency on the interaction of two driving signals and the fatigue damage of specimens, and the amplitudes of sidebands at the difference frequency and sum frequency are tracked when the driving frequency changes. Then, collinear wave mixing tests are carried out on a pair of cylindrically notched specimens with different fatigue damage to explore the relationship between the fatigue damage and the relative nonlinear parameters. The experimental results show when the fatigue degree is below 65% the relative nonlinear parameter increases quickly, and the growth rate is approximately 130%. If the fatigue degree is above 65%, the increase in the relative nonlinear parameter is slow, which has a close relationship with the microstructure evolution of specimens. A combined nonlinear ultrasonic parameter is proposed to highlight the relationship of the relative nonlinear parameter and fatigue degree of specimens; the fatigue life prediction model is built based on the relationship, and the prediction error is below 3%, which is below the prediction error based on the relative nonlinear parameters at the difference and sum frequencies. Therefore, the combined nonlinear ultrasonic parameter using the collinear wave mixing method can effectively estimate the fatigue degree of specimens, which provides a fast and convenient method for fatigue life prediction.
Energy Technology Data Exchange (ETDEWEB)
Hutula, D.N.
1980-03-01
A finite element procedure is presented for finite deformation analysis of continuum structures with time-dependent anisotropic elastic-plastic material behavior. An updated Lagrangian formulation is used to describe the kinematics of deformation. Anisotropic constitutive relations are referred, at each material point, to a set of three mutually orthogonal axes which rotate as a unit with an angular velocity equal to the spin at the point. The time-history of the solution is generated by using a linear incremental procedure with residual force correction, along with an automatic time step control algorithm which chooses time step sizes to control the accuracy and numerical stability of the solution.