Energy Splitting Theorems for Materials with Memory

TL;DR

This paper generalizes energy splitting theorems to materials with fading memory and internal variables, showing that total energy can be decomposed into internal and kinetic parts with related inertial forces.

Contribution

It extends previous results on energy decomposition to more complex materials with memory effects and internal variables, providing a unified representation involving a mass tensor.

Findings

Energy can be split into internal and kinetic components for materials with memory.

Kinetic energy and inertial forces are represented using a common mass tensor.

The results unify the treatment of materials with fading memory and internal variables.

Abstract

We extend to materials with fading memory and materials with internal variables a result previously established by one of us for materials with instantaneous memory: the additive decomposability of the total energy into an internal and a kinetic part, and a representation of the latter and the inertial forces in terms of one and the same mass tensor.