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

✍ Scribed by Giuseppe Cocchetti; Umberto Perego

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 581 KB
• Volume: 192
• Category: Article
• ISSN: 0045-7825
• DOI: 10.1016/s0045-7825(03)00396-7

✦ Synopsis

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 MartinÕs 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.