A variational approximation scheme for radial polyconvex elasticity that preserves the positivity of Jacobians

TL;DR

This paper introduces a variational approximation scheme for radial elasticity that ensures energy decrease and prevents matter interpenetration, maintaining physical realism in elastic motion simulations.

Contribution

It develops a novel variational scheme for radial elastic dynamics that guarantees energy dissipation and positivity of Jacobians, ensuring physically realistic solutions.

Findings

The scheme preserves the positivity of Jacobians.

It guarantees energy decrease over time.

The method produces physically realistic elastic motions.

Abstract

We consider the equations describing the dynamics of radial motions for isotropic elastic materials; these form a system of non-homogeneous conservation laws. We construct a variational approximation scheme that decreases the total mechanical energy and at the same time leads to physically realizable motions that avoid interpenetration of matter.