Relativistic Anelasticity

TL;DR

This paper develops a relativistic continuum mechanics framework that models anelastic behaviors like viscoelasticity and plasticity within General Relativity, using a four-dimensional body-time complex and a relativistic Eshelby tensor.

Contribution

It introduces a novel formulation of continuum mechanics in relativistic settings that incorporates anelastic effects through a structured four-dimensional approach.

Findings

The framework successfully models viscoelastic and plastic behaviors relativistically.

The approach is illustrated with an example of an anelastic fluid.

A relativistic Eshelby tensor is proposed for material inhomogeneity evolution.

Abstract

A formulation of Continuum Mechanics within the context of General Relativity is presented that allows for the incorporation of certain types of anelastic material behaviour, such as viscoelasticity and plasticity. The approach is based on the concept of a four-dimensional body-time complex structured as a principal bundle. The anelastic response is regarded as the result of a continuous distribution of inhomogeneities, whose evolution is dictated by a suggested relativistic version of the Eshelby tensor. The role played by various groups is emphasized throughout the presentation and illustrated by means of the example of an anelastic fluid.