Showing papers in "Acta Mechanica in 2009"

Pulse propagation in a linear and nonlinear diatomic periodic chain: effects of acoustic frequency band-gap

Abstract: One-dimensional nonlinear phononic crystals have been assembled from periodic diatomic chains of stainless steel cylinders alternated with Polytetrafluoroethylene spheres. This system allows dramatic changes of behavior (from linear to strongly nonlinear) by application of compressive forces practically without changes of geometry of the system. The relevance of classical acoustic band-gap, characteristic for chain with linear interaction forces and derived from the dispersion relation of the linearized system, on the transformation of single and multiple pulses in linear, nonlinear and strongly nonlinear regimes are investigated with numerical calculations and experiments. The limiting frequencies of the acoustic band-gap for investigated system with given precompression force are within the audible frequency range (20–20,000 Hz) and can be tuned by varying the particle’s material properties, mass and initial compression. In the linear elastic chain the presence of the acoustic band-gap was apparent through fast transformation of incoming pulses within very short distances from the chain entrance. It is interesting that pulses with relatively large amplitude (nonlinear elastic chain) exhibit qualitatively similar behavior indicating relevance of the acoustic band gap also for transformation of nonlinear signals. The effects of an in situ band-gap created by a mean dynamic compression are observed in the strongly nonlinear wave regime.

Spherical and acicular representation of hydrates in a micromechanical model for cement paste: prediction of early-age elasticity and strength

Abstract: Early-age stiffness and strength evolution of cement paste is studied in the framework of continuum micromechanics. Based on the self-consistent scheme, elastic and strength properties are upscaled from the scale of several micrometers up to the scale of several hundreds or thousands of micrometers. Four material phases are considered: clinker, hydration products, water and air. We assign a spherical geometry to clinker grains and pores, while we investigate both spherical and acicular (needle-type) shapes as geometrical representation of the micrometer-sized hydration products. As regards macroscopic poromechanical boundary conditions, two extreme cases are considered: drained conditions and sealed conditions, respectively. These choices allow for studying the influence of (i) the morphological representation of hydrates, and of (ii) the bulk stiffness of water, on the micromechanical prediction of early-age behavior of cement paste, including setting and the hydration-dependent evolutions of both elastic stiffness and uniaxial compressive strength. The newly proposed strength model is based on a von Mises-type elastic limit criterion for individual hydrates. Corresponding deviatoric stress peaks within hydrates are estimated through quadratic stress averages. In this way, the micromechanical strength criterion is formulated in terms of macroscopic loading (stresses or strains, respectively). Model-predicted elasticity and strength evolutions are compared with data from experimental testing of cement pastes with water–cement ratios ranging from 0.35 to 0.60. Satisfactory agreement between model predictions and experiments allows for two conclusions: the morphology of hydrates significantly influences micromechanics-based elastic stiffness estimates of cement paste particularly at very early ages, whereas elastic properties of mature cement paste can be estimated reliably on the basis of both spherical or acicular shaped hydrates. The development of a reliable strength model, however, requires consideration of hydrates as non-spherical particles, no matter what age of cement paste is considered.

Generalized wave equation in nonlocal elasticity

Abstract: We study the motion of a one-dimensional continuum whose deformation is described by a strain measure of nonlocal type. In particular, we use the Caputo fractional derivatives and a linear relation between stress and strain measure to obtain an integro-differential equation of motion. This equation is solved in the space of tempered distributions by using the Fourier and Laplace transforms. The properties of the solution are examined and compared with the classical case.

A continuum mechanics based derivation of Reissner’s large-displacement finite-strain beam theory: the case of plane deformations of originally straight Bernoulli–Euler beams

Abstract: In the present paper, we present a continuum mechanics based derivation of Reissner’s equations for large-displacements and finite-strains of beams, where we restrict ourselves to the case of plane deformations of originally straight Bernoulli–Euler beams. For the latter case of extensible elastica, we succeed in attaching a continuum mechanics meaning to the stress resultants and to all of the generalized strains, which were originally introduced by Reissner at the beam-theory level. Our derivations thus circumvent the problem of needing to determine constitutive relations between stress resultants and generalized strains by physical experiments. Instead, constitutive relations at the stress–strain level can be utilized. Subsequently, this is exemplarily shown for a linear relation between Biot stress and Biot strain, which leads to linear constitutive relations at the beam-theory level, and for a linear relation between the second Piola–Kirchhoff stress and the Green strain, which gives non-linear constitutive relations at the beam theory level. A simple inverse method for analytically constructing solutions of Reissner’s non-linear relations is shortly pointed out in Appendix I.

Vibration characteristics of FGM circular cylindrical shells using wave propagation approach

Abstract: In this paper, the wave propagation approach is employed to study the vibration characteristics of functionally graded material circular cylindrical shells. Axial modal dependence is approximated by exponential functions. This is a very simple and easily applicable technique. This avoids a large amount of algebraic manipulations. A theoretical analysis of shell natural frequencies are conducted for various boundary conditions. Validity and accuracy of the present method are confirmed by comparing the present results with those available in the literature. A good agreement is observed between the two sets of the results.

More clarity on the concept of material frame-indifference in classical continuum mechanics

Abstract: There was and still is a considerable amount of confusion in the community of classical continuum mechanics on the concept of material frame-indifference. An extensive review is presented which will point out and try to resolve various misconceptions that still accompany the literature of material frame-indifference. With the tools of differential geometry a precise terminology is developed ending in a consequent mathematical framework, in which not only the concept of material frame-indifference can be formulated naturally, but showing advantages that go beyond all conventional considerations on invariance used so far in classical continuum mechanics. As an exemplification the Navier-Stokes equations and the corresponding Reynolds averaged equations are written in a general covariant form within Newtonian mechanics.

Dynamic analysis of two-dimensional functionally graded thick hollow cylinder with finite length under impact loading

Abstract: In this paper a thick hollow cylinder with finite length made of two-dimensional functionally graded material (2D-FGM) and subjected to impact internal pressure is considered. The axisymmetric conditions are assumed for the 2D-FG cylinder. The finite element method with graded material properties within each element is used to model the structure, and the Newmark direct integration method is implemented to solve the time dependent equations. The time histories of displacements, stresses and 2D wave propagation are investigated for various values of volume fraction exponents. Also the effects of mechanical properties distribution in radial and axial direction on the time responses of the FG cylinder as well as the stress distribution are studied and compared with a cylinder made of 1D-FGM. The achieved results show that using 2D-FGM leads to a more flexible design. To verify the presented method and data, the results are compared to published data.

On the bending of viscoelastic plates made of polymer foams

Abstract: Considering the viscoelastic behavior of polymer foams a new plate theory based on the direct approach is introduced and applied to plates composed of functionally graded materials (FGM). The governing two-dimensional equations are formulated for a deformable surface, the viscoelastic stiffness parameters are identified assuming linear-viscoelastic material behavior. The material properties are changing in the thickness direction. Solving some problems of the global structural analysis it will be demonstrated that in some cases the results significantly differ from the results based on the Kirchhoff-type theory.

Extremum and variational principles for elastic and inelastic media with fractal geometries

Abstract: This paper further continues the recently begun extension of continuum mechanics and thermodynamics to fractal porous media which are specified by a mass (or spatial) fractal dimension D, a surface fractal dimension d, and a resolution lengthscale R. The focus is on pre-fractal media (i.e., those with lower and upper cut-offs) through a theory based on dimensional regularization, in which D is also the order of fractional integrals employed to state global balance laws. In effect, the global forms of governing equations may be cast in forms involving conventional (integer-order) integrals, while the local forms are expressed through partial differential equations with derivatives of integer order but containing coefficients involving D, d and R. Here we first generalize the principles of virtual work, virtual displacement and virtual stresses, which in turn allow us to extend the minimum energy theorems of elasticity theory. Next, we generalize the extremum principles of elasto-plastic and rigid-plastic bodies. In all the cases, the derived relations depend explicitly on D, d and R, and, upon setting D = 3 and d = 2, they reduce to conventional forms of governing equations for continuous media with Euclidean geometries.

Variational principles for generalized dynamical theory of thermopiezoelectricity

Abstract: The universal thermodynamic variational principle proposed in the previous papers for nonlinear dielectrics is extended to the thermopiezoelectricity and it is used as a fundamental physical principle to derive the simple complete governing equations of the generalized dynamical theory of thermopiezoelectricity in this paper. In the generalized dynamical theory it is assumed that the acceleration of the temperature needs the extra increment of the heat and the inertial entropy is proposed.

A hierarchy of avalanche models on arbitrary topography

Abstract: We use the non-Cartesian, topography-based equations of mass and momentum balance for gravity driven frictional flows of Luca et al. (Math. Mod. Meth. Appl. Sci. 19, 127–171 (2009)) to motivate a study on various approximations of avalanche models for single-phase granular materials. By introducing scaling approximations we develop a hierarchy of model equations which differ by degrees in shallowness, basal curvature, peculiarity of constitutive formulation (non-Newtonian viscous fluids, Savage–Hutter model) and velocity profile parametrization. An interesting result is that differences due to the constitutive behaviour are largely eliminated by scaling approximations. Emphasis is on avalanche flows; however, most equations presented here can be used in the dynamics of other thin films on arbitrary surfaces.

Green’s function and Eshelby’s tensor based on a simplified strain gradient elasticity theory

Abstract: The Eshelby problem of an infinite homogeneous isotropic elastic material containing an inclusion is analytically solved using a simplified strain gradient elasticity theory that involves one material length scale parameter in addition to two classical elastic constants. The Green’s function in the simplified strain gradient elasticity theory is first obtained in terms of elementary functions by applying Fourier transforms, which reduce to the Green’s function in classical elasticity when the strain gradient effect is not considered. The Eshelby tensor is then derived in a general form for an inclusion of arbitrary shape, which consists of a classical part and a gradient part. The former contains Poisson’s ratio only, while the latter includes the length scale parameter additionally, thereby enabling the interpretation of the size effect. By applying the general form of the Eshelby tensor derived, the explicit expressions of the Eshelby tensor for the special case of a spherical inclusion are obtained. The numerical results quantitatively show that the components of the new Eshelby tensor for the spherical inclusion vary with both the position and the inclusion size, unlike their counterparts based on classical elasticity. It is found that when the inclusion radius is small, the contribution of the gradient part is significantly large and thus should not be ignored. For homogenization applications, the volume average of this newly obtained Eshelby tensor over the spherical inclusion is derived in a closed form. It is observed that the components of the averaged Eshelby tensor change with the inclusion size: the smaller the inclusion radius, the smaller the components. Also, these components are seen to approach from below the values of their counterparts based on classical elasticity when the inclusion size becomes sufficiently large.

Transversely isotropic non-linear electro-active elastomers

Abstract: Electro-active or electro-sensitive elastomers are ‘smart materials’, which are composed of a rubber-like basis material filled with electro-active particles, and as a result, their properties are able to change significantly by the application of electric fields. In this paper, we provide the theoretical basis of the non-linear properties for a special class of these materials, namely, the transversely isotropic electro-active elastomers, whose characteristic is that during the curing process, due to the presence of an external applied field, the electro-active particles are aligned in a preferred direction. The theory is applied to some boundary value problems. As well as this, a linear approximation is obtained from the general non-linear formulation, which is compared with the results of the classical theory for piezoelectric materials.

Effect of magnetic field and initial stress on the propagation of interface waves in transversely isotropic perfectly conducting media

Abstract: Elasto-dynamical equations for transversely isotropic solids have been employed to investigate the general theory of transversely isotropic magneto-elastic interface waves in conducting media under initial hydrostatic tension or compression. Particular cases of interface waves such as Rayleigh, Love and Stoneley waves have been investigated in details. In all cases, the wave velocity equations have been deduced which are in complete agreement with the corresponding results of classical surface waves of the same types where magnetic fields and initial stresses are absent. Results obtained in this paper may be considered as more general and important in the sense that the corresponding results of classical surface waves due to Rayleigh, Love and Stoneley can readily be deduced from our results as special cases. Numerical calculations and graphs have been presented in the case of Love waves and conclusions are drawn.

Reduction of thermal stresses by composition optimization of two-dimensional functionally graded materials

Abstract: Reduction of the thermal stresses in machine elements that are subjected to severe thermal loadings was achieved by developing two-dimensional functionally graded materials, 2D-FGM In the current investigation, composition optimization for ZrO2/6061-T6/Ti-6Al-4V 2D-FGM, under a severe thermal loading cycle that consists of heating followed by cooling, was carried out based on the minimization of temperatures and thermal and residual stresses to achieve better reduction of the thermal stresses From the current investigation it was found that the optimum composition based on the minimum value of the maximum temperature for ZrO2/6061-T6/Ti-6Al-4V 2D-FGM was achieved for m x = 01 and m y = 01, while the optimum composition based on the minimum value of the maximum normalized equivalent stresses for ZrO2/6061-T6/Ti-6Al-4V 2D-FGM was achieved for m x = 01 and m y = 5, where m x and m y are the composition variation parameters in x- and y-directions, respectively Also, the obtained optimum composition of ZrO2/6061-T6/Ti-6Al-4V 2D-FGM can stand well with the adopted severe thermal loading without any plastic deformation or residual stresses, where the maximum value of the normalized equivalent stresses during the heating stage was 08 and the maximum value of the normalized equivalent stresses during the cooling stage was 024

Hamiltonian dynamic analysis of an axially translating beam featuring time-variant velocity

Abstract: A dynamic analysis is presented for an axially translating cantilever beam simulating the spacecraft antenna featuring time-variant velocity. The extended Hamilton’s principle is employed to formulate the governing partial differential equations of motion for an axially translating Bernoulli–Euler beam. Further, the assumed modes method and the separation of variables are utilized to solve the resulting equation of motion. Attention is focused on assessing the coupling effects between the axial translation motion and the flexural deformation during the beam extension or retraction operations upon the vibratory motion of a beam with an arbitrarily varying length under a prescribed time-variant velocity field. A number of numerical simulations are also presented to illustrate the qualitative features of the underlying mechanical vibration of an axially extending or contracting flexible beam. In general, the transverse beam vibration is stabilized during extension and unstabilized during retraction. The axial acceleration of a translating beam does not affect the transverse vibratory system stabilization.

Mechanics of microtubules modeled as orthotropic elastic shells with transverse shearing

Abstract: Microtubules are hollow cylindrical filaments of the eukaryotic cytoskeleton characterized by extremely low shear modulus. In this paper, an orthotropic elastic shell model with transverse shearing is developed to study the effects of transverse shearing on shell-like mechanics of microtubules. The study is based on a detailed comparison between four elastic beam and shell models with and without transverse shearing. It is shown that the length-dependent flexural rigidity of microtubules predicted by the present orthotropic shell model with transverse shearing is in good agreement with known experimental data and is consistently close to that given by the Timoshenko-beam model. Our results show that transverse shearing is essential for shell-like deformation of microtubules when the axial wave-length is not extremely long (compared to the diameter of microtubules which is ~25 nm) or the circumferential wave-number is larger than unity. In particular, transverse shearing is found to significantly lower the critical pressure for buckling of a long microtubule under radial pressure and leads to an even better agreement with recently observed experimental data. These results suggest that the 2D orthotropic shell model with transverse shearing is suitable to study the shell-like mechanics of microtubules for short axial wave-length and circumferential wave-number exceeding unity.

Failure of cemented granular materials under simple compression: experiments and numerical simulations

Abstract: We investigate the strength and failure properties of a model cemented granular material under simple compressive deformation. The particles are lightweight expanded clay aggregate beads coated by a controlled volume fraction of silicone. The beads are mixed with a joint seal paste (the matrix) and molded to obtain dense cemented granular samples of cylindrical shape. Several samples are prepared for different volume fractions of the matrix, controlling the porosity, and silicone coating upon which depends the effective particle–matrix adhesion. Interestingly, the compressive strength is found to be an affine function of the product of the matrix volume fraction and effective particle–matrix adhesion. On the other hand, it is shown that particle damage occurs beyond a critical value of the contact debonding energy. The experiments suggest three regimes of crack propagation corresponding to no particle damage, particle abrasion and particle fragmentation, respectively, depending on the matrix volume fraction and effective particle–matrix adhesion. We also use a sub-particle lattice discretization method to simulate cemented granular materials in two dimensions. The numerical results for crack regimes and the compressive strength are in excellent agreement with the experiments.

Effect of fiber orientation on the non-affine deformation of random fiber networks

Abstract: The study of fiber networks is essential in understanding the mechanical properties of many polymeric and biological materials. These systems deform non-affinely, i.e. the local deformation is different than the applied far-field. The degree of non-affinity increases with decreasing scale of observation. Here, we show that this relationship is a power law with a scaling exponent independent of the type of applied load. Preferential fiber orientation influences non-affinity in a significant way: this parameter generally increases upon increasing orientation. However, some components of non-affinity, such as that associated with the normal strain in the direction of the preferential fiber orientation, decrease. In random networks, the nature of the far-field has little influence on the level of non-affinity. This is not the case in oriented networks.

Analysis of thermoelastic response in a functionally graded spherically isotropic hollow sphere based on Green–Lindsay theory

Abstract: This paper is concerned with the investigation of thermoelastic displacements and stresses in a functionally graded spherically isotropic hollow sphere due to prescribed temperature in the context of the linear theory of generalized thermoelasticity with two relaxation time parameters (Green and Lindsay theory). Both the surfaces of the body are free from radial stresses, and the inner surface is subjected to a time-dependent thermal shock whereas the outer one is maintained at constant temperature. The basic equations have been written in the form of a vector-matrix differential equation in the Laplace transform domain which is then solved by an eigenvalue approach. The numerical inversion of the transforms is carried out using a method of Bellman et al. The displacements and stresses are computed and presented graphically. It is found that the variation of the thermophysical properties of a material as well as the thickness of the body strongly influence the response to loading. A comparative study with the corresponding homogeneous material has also been made. The solution of the problem of a spherically isotropic infinite medium containing a spherical cavity has been derived theoretically by tending the outer radius to infinity, as a particular case.

Elastodynamic theory of framed structures and reverberation-ray matrix analysis

Abstract: Based on one-dimensional theory of elastodynamics, the vibration and wave propagation in members of a framed structure are analyzed by the recently developed method of reverberation-ray matrix. Unidirectional traveling wave solutions for axial, torsional, and two flexural waves in six modes that are reverberated in structural members through repeated reflection and multiple scattering by joints of the structure are expressed in matrix form with two sets of unknown amplitude coefficients. From joint coupling equations and from compatibility conditions of displacements in dual coordinates of each member, the two sets of unknowns are determined in terms of a reverberation-ray matrix for given source excitations at joints. Free and forced wave motion in steady-state response can all be evaluated from the matrix solutions, and transient response is determined in one more step of Fourier inverse transform. The method is particularly effective to determine the early time transient response through Neumann series expansion of the inverse transformed solution with a special numerical algorithm.

Anisotropy and symmetry in porous media convection

Abstract: The linear and nonlinear stability analysis of the motionless state (conduction solution) and of a vertical throughflow in an anisotropic porous medium is performed. In particular, the effect of a nonhomogeneous porosity and a constant anisotropic thermal diffusivity have been taken into account.

NSM analysis of time-dependent nonlinear buoyancy-driven double-diffusive radiative convection flow in non-Darcy geological porous media

Abstract: A network numerical simulator is developed and described to simulate the transient, nonlinear buoyancy-driven double diffusive heat and mass transfer of a viscous, incompressible, gray, absorbing–emitting fluid flowing past an impulsively started moving vertical plate adjacent to a non-Darcian geological porous regime. The governing boundary-layer equations are formulated in an (X *, Y *, t *) coordinate system with appropriate boundary conditions. An algebraic diffusion approximation is used to simplify the radiation heat transfer contribution. The non-dimensionalized transport equations are solved in an (X, Y, t) coordinate system using the network simulation model (NSM) and the computer code, Pspice. A detailed discussion of the network design is provided. The effects of Prandtl number, radiation–conduction parameter (Stark number), thermal Grashof number, species Grashof number, Schmidt number, Darcy number and Forchheimer number on the transient dimensionless velocities (U, V), non-dimensional temperature (T) and dimensionless concentration function (C) are illustrated graphically. Additionally, we have computed plots of U, V, T, C versus time and average Nusselt number and Sherwood number versus X, Y coordinate, for various thermophysical parameters. The model finds applications in geological contamination, geothermal energy systems and radioactive waste-repository near-field thermo-geofluid mechanics.

Responses of viscoelastic polymer composites with temperature and time dependent constituents

Abstract: This study formulates a concurrent micromechanical model for predicting effective responses of fiber reinforced polymer (FRP) composites, whose constituents exhibit thermo-viscoelastic behaviors. The studied FRP composite consists of orthotropic unidirectional fiber and isotropic matrix. The viscoelastic material properties for the fiber and matrix constituents are allowed to change with the temperature field. The composite microstructures are idealized with periodically distributed square fibers in a matrix medium. A unit-cell model, consisting of four fiber and matrix subcells, is generated to obtain effective nonlinear thermo-viscoelastic responses of the composites. A time-integration algorithm is formulated to link two different thermo-viscoelastic constitutive material models at the lowest level (homogeneous fiber and matrix constituents) to the effective material responses at the macro level, and to transfer external mechanical and thermal stimuli to the constituents. This forms a concurrent micromechanical model, which is needed as the material properties of the constituents depend on the temperature field. Consistent tangent stiffness matrices are formulated at the fiber and matrix constituents and also at the effective composite level to improve prediction accuracy. The thermo-viscoelastic responses obtained from the concurrent micromodel are verified with available experimental data. Detailed finite element (FE) models of the FRP microstructures are also generated using 3D continuum elements for several fiber volume fractions. Thermo-viscoelastic responses of the concurrent micromodel are also compared to the ones of the detailed FRP microstructures.

Linearly elastic annular and circular membranes under radial, transverse, and torsional loading. Part I: large unwrinkled axisymmetric deformations

Abstract: Three theories for determination of the equilibrium states of initially flat, linearly elastic, rotationally symmetric, taut membranes are considered: Foppl-von Karman theory, Reissner’s theory, and a new generalization of Reissner’s theory that does not restrict the strains to be small. Attention is focused on annular membranes, but circular membranes are also treated. Large deformations are allowed, and the equilibrium equations are written in terms of transverse, radial, and circumferential displacements. Problems considered include radial stretching, transverse displacement of the inner edge, an adhesive punch pull-off test on a circular blister, transverse pressure, ponding of annular and circular membranes, a vertical distributed load with a vertically sliding outer membrane edge, pull-in (snap-down, jump-to-contact) instability of a MEMS device, torsion of the inner or outer edge of a stretched membrane, and a combination of radial stretching, vertical displacement, and torsion. Results for the three theories are compared. Closed-form solutions are available in a few cases, but usually a shooting method is utilized to obtain numerical solutions for displacements, strains, and stresses. Conditions for the onset of wrinkling are determined. In the second part of this two-part study, small vibrations about equilibrium configurations are analyzed.

Faber series method for plane problems of an arbitrarily shaped inclusion

Abstract: This paper presents the theoretical and numerical results for the plane problem of an arbitrarily shaped inclusion in an infinite isotropic matrix based on the Faber series method. The key of the method is to express the complex potentials in the arbitrary inclusion in the form of Faber series with unknown coefficients and then substitute them directly into the boundary conditions on the interface. These conditions lead to a set of linear equations containing all the unknown coefficients. Through solving these linear equations, one can obtain the complex potentials both inside the inclusion and in the matrix. Then, numerical results are presented and graphically shown for the cases of an elliptic, square, and triangle inclusions, respectively. It is found that as the stiffness of the inclusion increases, the hoop stress decreases at the rim of the inclusion, while the radial and shear stresses increase. Especially, it is also found that the stresses show the nature of intense fluctuations near the corners of the triangle inclusion, since the inclusion in this case is similar to a wedge.

Constitutive equations for ligament and other soft tissue: evaluation by experiment

Abstract: Ligaments, tendons and other soft tissues are nonlinearly viscoelastic. To discriminate among various constitutive equations which may be used to describe the tissue, appropriate experimental modalities are requisite. Ideally, testing should span physiologic ranges for load (or strain), load history (recovery and reloading), and load onset and duration, and a robust model will fit all data. Methods to expand the experimental window of time for relaxation and creep are presented and evaluated. The role of ramp, relaxation and recovery protocols is studied in the context of viscoelasticity describable by linear, quasi-linear, nonlinear superposition, Schapery, and multiple integral formulations. The advantages associated with testing protocols that expand the time windows for creep or relaxation are presented.

Application and extension of the stochastic linearization by Anh and Di Paola

Abstract: This study deals with the stochastic linearization technique in a new setting. First of all, the usual minimum mean-square difference requirement between the original nonlinear force and its linear counterpart is replaced by the orthogonal condition. Additionally, another recently developed idea of first replacing the nonlinear terms by higher order terms, prior to its ordinary reduction to linear ones, is super-imposed with the above condition. The results are checked on several nonlinear oscillators. In the Atalik and Utku oscillator, instead of 14% error obtained with classical linearization, the error is reduced to about 3%. In the Lutes and Sarkani oscillator the error is reduced from 22.85 to 1.23%, nearly 18-fold. In the latter case the optimal number of “regulation” steps is shown to be 2.

Effective elastic moduli of three-phase composites with randomly located and interacting spherical particles of distinct properties

Abstract: A micromechanical analytical framework is presented to predict effective elastic moduli of three-phase composites containing many randomly dispersed and pairwisely interacting spherical particles. Specifically, the two inhomogeneity phases feature distinct elastic properties. A higher-order structure is proposed based on the probabilistic spatial distribution of spherical particles, the pairwise particle interactions, and the ensemble-volume homogenization method. Two non-equivalent formulations are considered in detail to derive effective elastic moduli with heterogeneous inclusions. As a special case, the effective shear modulus for an incompressible matrix containing randomly dispersed and identical rigid spheres is derived. It is demonstrated that a significant improvement in the singular problem and accuracy is achieved by employing the proposed methodology. Comparisons among our theoretical predictions, available experimental data, and other analytical predictions are rendered. Moreover, numerical examples are implemented to illustrate the potential of the present method.

Rayleigh waves in magneto-electro-elastic half planes

Abstract: This paper investigates Rayleigh waves in magneto-electro-elastic half planes The magneto-electro-elastic materials are assumed to possess hexagonal (6 mm) symmetry Sixteen sets of boundary conditions are considered and the corresponding frequency equations are derived It is found that for any of the 16 sets of boundary conditions, the Rayleigh waves, if exist, are always non-dispersive Numerical results show that both the material coefficients and boundary conditions can significantly influence the Rayleigh wave properties in magneto-electro-elastic half planes