Conservation Laws for One-Dimensional Finite Elastodynamics

Abstract

The field equations of one - dimensional nonlinear elastodynamics are expressed in terms of appropriate exterior differential forms. By explicitly contructing a closed ideal of the ring generated by these differential forms it is shown that the conservation law structure of the field equations is determined by two scalar functions satisfying a number of linear partial differential equations. The solutions of this set of equations are found and an exhaustive list of the conservation laws are given. The linear case is also studied.