Variational Principle Involving the Stress Tensor in Elastodynamics
Classical Physics
2008-07-23 v1 Mathematical Physics
math.MP
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.
Cite
@article{arxiv.0807.3454,
title = {Variational Principle Involving the Stress Tensor in Elastodynamics},
author = {Henri Gouin and Jean-François Debieve},
journal= {arXiv preprint arXiv:0807.3454},
year = {2008}
}
Comments
The decomposition of the stress tensor proposed in this article (1986) for a hyperelastic medium is now widely used in the literature. 16 pages