Related papers: Thermodynamic consistency of third grade finite st…
We study the nonlinear elastic response of a two-dimensional material to a localized boundary force, with the particular goal of understanding the differences observed between isotropic granular materials and those with hexagonal…
In this paper, we use the Green-Naghdi theory of thermomechanics of continua to derive a nonlinear theory of thermoelasticity with microtemperatures of type III. This theory permits propagation of both thermal and microtemperatures waves at…
Computational studies of the thermodynamic properties of materials at the mesoscopic and macroscopic scales -- involving lengths and times of at least $\mu$m and $\mu$s, respectively -- rely on a coarse-graining approximation such that only…
The present work is concerned with the propagation of electro-magneto-thermoelastic plane waves of assigned frequency in a homogeneous isotropic and finitely conducting elastic medium permeated by a primary uniform external magnetic field.…
We present a phenomenological time-dependent Ginzburg-Landau theory of nonlinear plastic deformations in solids. Because the problem is very complex, we first give models in one and two dimensions without vacancies and interstitials, where…
Depinning of two-dimensional liquid ridges and three-dimensional drops on an inclined substrate is studied within the lubrication approximation. The structures are pinned to wetting heterogeneities arising from variations of the strength of…
A large variety of materials, widely encountered both in engineering applications and in the biological realm, are characterised by a non-vanishing internal stress distribution, even in the absence of external deformations or applied…
A theory is developed for evaluation of nonlinear elastic moduli of composite materials with nonlinear inclusions dispersed in another nonlinear material (matrix). We elaborate a method aimed for determination of elastic parameters of a…
We develop a formalism for computing the non-linear response of interacting integrable systems. Our results are asymptotically exact in the hydrodynamic limit where perturbing fields vary sufficiently slowly in space and time. We show that…
Motivated by the recent experimental and analytical developments enabling high-fidelity material characterization of (heterogeneous) sheet-like solid specimens, we seek to elucidate the constitutive behavior of linear viscoelastic solids…
We study a mathematical model for deformation of glued elastic bodies in 2D or 3D, which is a linear elasticity system with adhesive force on the glued surface. We reveal a variational structure of the model and prove the unique existence…
The linear dispersion relation for longwave surface perturbations, as derived by Levine et al. Phys. Rev. B 75, 205312 (2007) is extended to include a smooth surface energy anisotropy function with a variable anisotropy strength (from weak…
This paper shows nonlinear stability of homogeneous states in second-order hyperbolic systems of partial differential equations that model the dynamics of dissipative relativistic fluids, by checking a dissipativity criterion formulated…
Analytical method for the second-order homogenization of two-phase composites within Mindlin-Toupin strain gradient elasticity theory is proposed. Direct approach and self-consistent approximation are used to reduce the homogenization…
The three-dimensional elastic-plastic deformation is considered. The catastrophe theory underlies the construction of this process model. It was shown that the variety of stable states consists on elastic states and can be depicted as a…
We develop a theory of the effective disorder temperature in glass-forming materials driven away from thermodynamic equilibrium by external forces. Our basic premise is that the slow configurational degrees of freedom of such materials are…
A linear stability analysis of the hydrodynamic equations with respect to the homogeneous cooling state is performed to study the conditions for stability of a suspension of solid particles immersed in a viscous gas. The dissipation in such…
Distributed-order time-fractional wave equations appear in the modeling of wave propagation in viscoelastic media. The material characteristics of the medium are modeled through constitutive functions or distributions in the…
A Landau-Ginsburg-Devonshire-type nonlinear phenomenological theory is presented, which enables the thermodynamic description of dense laminar polydomain states in epitaxial ferroelectric thin films. The theory explicitly takes into account…
An unconstrained, non-linearly elastic, semi-infinite solid is maintained in a state of large static plane strain. A power-law relation between the pre-stretches is assumed and it is shown that this assumption is well-motivated physically…