Integration algorithms for planar anisotropic shells with isotropic and kinematic hardening at finite strains

Abstract

AbstractAn elasto‐plastic formulation at finite strains was considered with isotropic and kinematic hardening and anisotropic yield functions. In order to find a simple but thermomechanically consistent continuum mechanical basis for stress integration algorithms of shell problems, evolution equations of the plastic strain rate and internal variables were derived. This was performed in the stress‐free intermediate configuration with the Mandel stress and corresponding back stress tensors. The resulting relations were then transformed into the current configuration and restricted to small elastic strains. For an algorithmic treatment of this material formulation for shell problems, the kinematic hardening was reformulated in stress‐related terms to obtain a set of equations for planar anisotropic elasto‐plastic materials. Finally, an updated iterative treatment for the elasto‐plastic shell at finite strains was derived utilizing the cutting plane algorithm. Copyright © 2003 John Wiley & Sons, Ltd.