On the Representation of Energy and Momentum in Elasticity
Abstract
In order to clarify common assumptions on the form of energy and momentum in elasticity, a generalized conservation format is proposed for finite elasticity, in which total energy and momentum are not specified a priori. Velocity, stress, and total energy are assumed to depend constitutively on deformation gradient and momentum in a manner restricted by a dissipation principle and certain mild invariance requirements. Under these assumptions, representations are obtained for energy and momentum, demonstrating that (i) the total energy splits into separate internal and kinetic contributions, and (ii) the momentum is linear in the velocity. It is further shown that, if the stress response is strongly elliptic, the classical specifications for kinetic energy and momentum are sufficient to give elasticity the standard format of a quasilinear hyperbolic system.
Keywords
Cite
@article{arxiv.math-ph/9907018,
title = {On the Representation of Energy and Momentum in Elasticity},
author = {P. Podio-Guidugli and S. Sellers and G. Vergara Caffarelli},
journal= {arXiv preprint arXiv:math-ph/9907018},
year = {2007}
}
Comments
14 pages, to appear in Mathematical Models and Methods in Applied Sciences