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

This paper develops a novel solution strategy for temporal discretization o f initial value problems in nonlinear elastodynamics, enabling exact energy and momentum conservation for a spatially discretized problem. This new en ergy-momentum algorithm fits into the general framework established by Simo and Tarnow [Z. Angew Math. Phys. 43 (1992) 757). However, in contrast to t he presentation given in that reference, the current approach extends the c ritical stress update formula to encompass generic stored energy functions for the hyperelastic continuum, in a manner which also allows for quadratic ally convergent Newton-Raphson solution of the nonlinear algorithmic equati ons. Numerical examples using a Neo-Hookean material model are given to ill ustrate the excellent performance of the proposed scheme. Not only is the n ew algorithm guaranteed to be second-order accurate and unconditionally sta ble in the fully nonlinear regime (as are other energy-momentum strategies) , but also the approach advocated is demonstrated to be more robust and ver satile than its predecessors. (C) 2001 Elsevier Science B.V. All rights res erved.