  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.
