Below is the ascii version of the abstract for 99-276.
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P. Podio-Guidugli, S. Sellers, G. Vergara Caffarelli
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