Explicit integration method with time step control for viscoplasticity and creep

Abstract

Constitutive equations for viscoplasticity and creep are expressed in terms of stress components, temperature and internal variables. The resulting set of ordinary differential equations of the first order under the guise of the finite element method is integrated by the Euler forward scheme with automatic subincrementation. The time step length is set on the basis of a posteriori error estimate. Testing examples were computed, including benchmark problems introduced by Zienkiewicz and Cormeau. In every case a perfect match between the converged step length and the Cormeau formula for the critical time step was observed.