Publications [#56650] of Tod A Laursen

Papers Published

1. Laursen, T.A. and Meng, X.N., A new solution procedures for application of energy-conserving algorithms to general constitutive models in nonlinear elastodynamics, Computer Methods in Applied Mechanics and Engineering, vol. 190 no. 46-47 (2001), pp. 6309 - 6322 [S0045-7825(01)00257-2]
   (last updated on 2007/04/06)

   Abstract:
   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. © 2001 Elsevier Science B.V. All rights reserved.

   Keywords:
   Nonlinear equations;Algorithms;Mathematical models;