Accelerated initial stiffness schemes for elastoplasticity

Iterative methods for the solution of non-linear finite element equations a re generally based on variants of the Newton-Raphson method. When they are stable, full Newton-Raphson schemes usually converge rapidly but may be exp ensive for some types of problems (for example, when the tangent stiffness matrix is unsymmetric). Initial stiffness schemes, on the other hand, are e xtremely robust but may require large numbers of iterations for cases where the plastic zone is extensive. In most geomechanics applications it is gen erally preferable to use a tangent stiffness scheme, but there are situatio ns in which initial stiffness schemes are very useful. These situations inc lude problems where a nonassociated flow rule is used or where the zone of plastic yielding is highly localized. This paper surveys the performance of several single-parameter techniques f or accelerating the convergence of the initial stiffness scheme. Some simpl e but effective modifications to these procedures are also proposed. In par ticular, a modified version of Thomas' acceleration scheme is developed whi ch has a good rate of convergence, Previously published results on the perf ormance of various acceleration algorithms for initial stiffness iteration are rare and have been restricted to relatively simple yield criteria and s imple 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 (C) 20 00 John Wiley & Sons, Ltd.