A variational principle for non-linear elastodynamics and its application to the hybrid stress model

A variational principle is derived for the mixed initial-boundary value problem of non-linear elastodynamics. This principle involves stress quantities only. It is an extension of a similar one derived by Gurtin[1] for linear elastodynamics. The principle is then specialized to the class of semilinear materials, and generalized for the use in the hybrid stress model of finite element analysis. An incremental procedure for the numerical solution is described.