Finite element implementation of state variable-based viscoplasticity models

Implementation of state variable-based viscoplasticity models is made in a general purpose finite element code for structural applications of metals deformed at elevated temperature. Two constitutive models, i.e. Walker's and Robinson's models, are studied in conjunction with two implicit integration methods: the trapezoidal rule with Newton-Raphson iterations and an asymptotic integration algorithm. A comparison is made between the two integration methods, and the latter method appears to be computationally more appealing in terms of numerical accuracy and CPU time. However, in order to make the asymptotic algorithm robust, it is necessary to include a self-adaptive scheme with subincremental step control and error checking of the Jacobian matrix at the integration points. Four examples are given to illustrate the numerical aspects of the integration methods tested.