Related papers: Realizing the Willis equations with pre-stresses

Metamaterials whose momentum is constitutively coupled with their strain show promise in wave manipulation for engineering purposes and are called Willis materials. They were discovered using an effective medium theory which shows that…

Viscoelastic stress relaxation is a basic characteristic of soft matter systems such as colloids, gels, and biological networks. Although the Maxwell model of linear viscoelasticity provides a classical description of stress relaxation, the…

We introduce models for viscoelastic materials, both solids and fluids, based on logarithmic stresses to capture the elastic contribution to the material response. The matrix logarithm allows to link the measures of strain, that naturally…

The aim of this review is to highlight the connection between well-established physical and mathematical principles as they pertain to the theory of linear viscoelasticity. We begin by examining the physical foundations of Boltzmann and…

This paper presents the derivation of the homogenized equations that describe the macroscopic mechanical response of elastomers filled with liquid inclusions in the setting of small quasistatic deformations. The derivation is carried out…

The nonlinear hyperbolic system of pde's governing the evolution of the deformation of isotropic hyperelastic materials is considered. In the absence of boundaries and with an additional nonresonance or null condition, the system has global…

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…

Bianisotropy is common in electromagnetics whenever a cross-coupling between electric and magnetic responses exists. However, the analogous concept for elastic waves in solids, termed as Willis coupling, is more challenging to observe. It…

In this paper we construct, by means of a variational formulation, the solutions of a problem of elastodynamics which includes the effect of damage for the elastic material. The result is a wave equation with time dependent operators which…

A theory for the non-local shear stress correlations in supercooled liquids is derived from first principles. It captures the crossover from viscous to elastic dynamics at an idealized liquid to glass transition and explains the emergence…

Elasto-plastic models are among the most successful ways to study the critical properties of the plastic yielding transition of amorphous solids. Typically these models are studied under a condition of constant transition rates from one…

We prove that, when linearized, the governing equations of an incompressible elastic continuum yield Maxwell's equations as corollaries. Through judicious distinction between the referential and local descriptions, the principle of material…

We carry out the homogenization of a fluid-structure interaction problem consisting in the periodic inclusions of a viscous fluid in an elastic body. We get a macrostructure model where the body behaves as a viscoelastic material with a…

We obtain an exact strain consistency equation for full, elastic, and plastic strain characteristics that have a clear physical meaning and are naturally related to stresses. The dynamic equations are represented in a form that does not use…

We present a variational principle governing the quasistatic evolution of a linearized elastoplastic material. In case of linear hardening, the novel characterization allows to recover and partly extend some known results and proves itself…

We investigate the interplay between pre-stress and mechanical properties in random elastic networks. To do this in a controlled fashion, we introduce an algorithm for creating random freestanding frames that support exactly one state of…

By reinforcing the interaction energy of the liquid with respect to the surface using total wetting boundary conditions, the response of liquids to mechanical shear stress is stronger and exhibits at sub-millimeter scale elastic properties.…

In the mechanics of inviscid conservative fluids, it is classical to generate the equations of dynamics by formulating with adequate variables, that the pressure integral calculated in the time-space domain corresponding to the motion of…

The existence and uniqueness of weak solutions is shown for a system related to the Willis model of elastodynamics. Both the whole space case and the case of a bounded smooth domain are studied. To this end the equations are reformulated as…

This work presents a generalized physical interpretation of unconventional dispersion asymmetries associated moving elastic solids. By shifting the notion from systems with time-variant material fields to physically traveling materials, the…