We construct weak solutions to the 3D hypoviscous incompressible elastodynamics with finite kinetic energy which was unknown in literatures. Our result holds for fractional hypoviscosity (−Δ)θ, where 0≤θ<1. The proof consists of a convex integration scheme new building blocks 2D intermittency and suitable temporal correctors, are motivated by inherent geometric structure viscoelastic equations.

The paper deals with elastic wave propagating in a layer on half-space induced by vertical force. focus is the effect of sliding contact along interface and its comparative study perfect one. effective boundary conditions substituting presence are derived. leading order term these corresponds to inertia layer, whereas next correction involves plate waves coating. Analysis associated dispersion ...

We consider a variational scheme developed in [10] that approximates the equations describing the dynamics of three dimensional motions for isotropic elastic materials; these form a system of conservation laws. We establish the convergence of the time-continuous interpolates constructed in the scheme to a smooth solution of the elastodynamics system by adapting the relative entropy method to th...

In the present paper, the redial harmonic vibrations of hollow cylinders of orthotropic material as affected by the angular velocity are discussed on the basis of the linear theory of elasticity. The one-dimensional equation of elastodynamics has been solved in terms of radial displacement. Three different boundary conditions, the free, fixed and mixed ones are considered. The determination of ...

We give an overview on existence results in nonlinear peridynamics, a nonlocal elasticity theory, and compare these results with those known for classical nonlinear elastodynamics. We conclude that even though peridynamics was developed in the beginning of the current century, it is possible to obtain stronger results under equal or even less restrictive assumptions on the stress. Etienne Emmri...

This paper is concerned with developing methods for the propagation of linear waves in several space dimensions. The methods are time-reversible, and hence free from numerical dissipation. They are based on bicharacteristic forms of the governing equations, and are made possible by adopting forms of staggered storage that depend on the precise equations under consideration. Analysis is presente...

Electromagnetic circuits are the electromagnetic analog at fixed frequency of mass-spring networks in elastodynamics. By interchanging the roles of ε and μ in electromagnetic circuits one obtains magnetoelectric circuits. Here we show that by introducing tetrahedral connectors having ε = μ = 0 one can join electromagnetic and magnetoelectric circuits to obtain hybrid circuits. Their response is...