Consistent Return Mapping Algorithm for Plane Stress Elastoplasticity

摘要

An unconditionally stable algorithm for plane stress elastoplasticity is developed, based upon the motion of elastic predictor return mapping (plastic corrector). Enforcement of the consistency condition is shown to reduce to the solution of a simple nonlinear equation. Consistent elastoplastic tangent moduli are obtained by exact linearization of the algorithm. Use of these moduli is essential in order to preserve the asymptotic rate of quadratic convergence of Newton methods. An exact solution for constant strain rate over the typical time step is derived. On the basis of this solution the accuracy of the algorithm is assessed by means of iso-error maps. The excellent performance of the algorithm for large time steps is illustrated in numerical experiments. (ERA citation 11:023277)