Variational Principle Involving the Stress Tensor in Elastodynamics

TL;DR

This paper extends a classical variational principle from fluid mechanics to thermo-elastic bodies undergoing large deformations, using potentials and replacing pressure with the stress tensor trace.

Contribution

It introduces a novel variational formulation for thermo-elastic dynamics involving the stress tensor, applicable to large deformation motions.

Findings

Derived new equations of motion using potentials

Replaced pressure term with stress tensor trace

Extended classical fluid variational principles to thermo-elastic solids

Abstract

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 continuous medium is stationary. The present study extends this principle to the dynamics of large deformations for isentropic motions in thermo-elastic bodies: we use a new way of writing the equations of motion in terms of potentials and we substitute the trace of the stress tensor for the pressure term.