A MODIFIED GENERALIZED MIDPOINT RULE FOR THE INTEGRATION OF RATE-DEPENDENT THERMO-ELASTIC-PLASTIC CONSTITUTIVE-EQUATIONS

The integration algorithm presented here is an extension of the widely used generalized midpoint rule. A simple but very effective method is derived to optimize the location of the collocation point (where plas tic consistency is enforced) in order to achieve high accuracy for vir tually unlimited sizes of the lime step. These optimal locations are i n the interval [Delta t/2, Delta t], which automatically guarantees un conditional stability. The optimal weighting parameter theta is estima ted from two explicit formulas. Hence, there is practically no increas e in computational expense compared to applications of the conventiona l generalized midpoint rule. Furthermore, the method features a specia l formulation of plastic consistency, called a plastic predictor, whic h minimizes the necessary iterations at Gauss-point level. Numerical e xamples demonstrate the efficiency and accuracy of the algorithm for r ate-dependent and rate-independent plasticity including combined kinem atic and isotropic hardening, as well as thermal softening.