A modified generalized midpoint rule for the integration of rate-dependent thermo-elastic-plastic constitutive equations

Abstract

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 plastic consistency is enforced) in order to achieve high accuracy for virtually unlimited sizes of the time step. These optimal locations are in the interval [ Δt 2 , Δt ], which automatically guarantees unconditional stability. The optimal weighting parameter θ is estimated from two explicit formulas. Hence, there is practically no increase in computational expense compared to applications of the conventional generalized midpoint rule. Furthermore, the method features a special formulation of plastic consistency, called a plastic predictor, which minimizes the necessary iterations at Gauss-point level. Numerical examples demonstrate the efficiency and accuracy of the algorithm for rate-dependent and rate-independent plasticity including combined kinematic and isotropic hardening, as well as thermal softening.