Accelerated initial sti ! ness schemes for elastoplasticity

Iterative methods for the solution of non-linear "nite element equations are generally based on variants of the Newton}Raphson method. When they are stable, full Newton}Raphson schemes usually converge rapidly but may be expensive for some types of problems (for example, when the tangent sti!ness matrix is unsymmetric). Initial sti!ness schemes, on the other hand, are extremely robust but may require large numbers of iterations for cases where the plastic zone is extensive. In most geomechanics applications it is generally preferable to use a tangent sti!ness scheme, but there are situations in which initial sti!ness schemes are very useful. These situations include problems where a nonassociated #ow rule is used or where the zone of plastic yielding is highly localized. This paper surveys the performance of several single-parameter techniques for accelerating the convergence of the initial sti!ness scheme. Some simple but e!ective modi"cations to these procedures are also proposed. In particular, a modi"ed version of Thomas' acceleration scheme is developed which has a good rate of convergence. Previously published results on the performance of various acceleration algorithms for initial sti!ness iteration are rare and have been restricted to relatively simple yield criteria and simple problems. In this study, detailed numerical results are presented for the expansion of a thick cylinder, the collapse of a rigid strip footing, and the failure of a vertical cut. These analyses use the Mohr}Coulomb and Tresca yield criteria which are popular in soil mechanics. Copyright ( 2000 John Wiley & Sons, Ltd.