A rigorous bound on error in backward-difference elastoplastic time-integration

The finite element analysis of elastoplastic structures requires in general a time-stepping procedure and, in most cases, the integration of the constitutive law within each time-step has to be carried out by numerical integration. The error associated to this numerical integration depends on the degree of non-linearity of the structural response and can be used as an indicator for the adaptive definition of the time-step size. Based on Martin’s and Ortiz theorem on minimum total work, a simple estimate of the integration error associated to a backward-difference scheme for elastoplastic models is derived. It is shown that the proposed estimate is a rigorous upper bound on the error in the case of assigned constant strain rate. Finally, a simple strategy for the automatic definition of the time-step size is proposed. The estimator and the adaptive strategy are validated by application to problems with a perfectly plastic material model.