On the representation of energy and momentum in elasticity

In order to clarify common assumptions on the form of energy and momentum i n elasticity, a generalized conservation format is proposed for finite elas ticity, in which total energy and momentum are not specified a priori. Velo city, stress, and total energy are assumed to depend constitutively on defo rmation gradient and momentum in a manner restricted by a dissipation princ iple and certain mild invariance requirements. Under these assumptions, rep resentations are obtained for energy and momentum, demonstrating that (i) t he total energy splits into separate internal and kinetic contributions, an d (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.