A new solution procedure for application of energy-conserving algorithms to general constitutive models in nonlinear elastodynamics Original Research Article

This paper develops a novel solution strategy for temporal discretization of initial value problems in nonlinear elastodynamics, enabling exact energy and momentum conservation for a spatially discretized problem. This new energy–momentum algorithm fits into the general framework established by Simo and Tarnow [Z. Angew Math. Phys. 43 (1992) 757]. However, in contrast to the presentation given in that reference, the current approach extends the critical stress update formula to encompass generic stored energy functions for the hyperelastic continuum, in a manner which also allows for quadratically convergent Newton–Raphson solution of the nonlinear algorithmic equations. Numerical examples using a Neo–Hookean material model are given to illustrate the excellent performance of the proposed scheme. Not only is the new algorithm guaranteed to be second-order accurate and unconditionally stable in the fully nonlinear regime (as are other energy–momentum strategies), but also the approach advocated is demonstrated to be more robust and versatile than its predecessors.