P. Podio-Guidugli, S. Sellers, G. Vergara Caffarelli
ON THE REPRESENTATION OF 
ENERGY AND MOMENTUM IN ELASTICITY
(55K, LaTex2e)

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