Consistent Tangent Moduli for a Class of Viscoplasticity

Abstract

Consistent (algorithmic) tangent moduli for the generalized Duvaut‐Lions viscoplasticity model are derived in this work. The derivations are based on consistent linearization of the residual functions associated with two alternative unconditionally stable constitutive integration algorithms; namely, the implicit backward Euler and the “full integration” algorithms. This “consistent linearization” procedure is equally applicable to the Perzyna‐type viscoplasticity formulations. In particular, the von Mises isotropic/kinematic hardening viscoplasticity model is chosen as a model problem for demonstration. Consistent viscoplastic tangent moduli for other choices of (single or multiple) loading surfaces can be derived in a similar fashion provided that consistent elastoplastic (inviscid) tangent moduli are available. It is noted that since continuum tangent moduli do not exist at all for viscoplasticity, use of the proposed consistent tangent moduli is not only desirable but necessary in the Newton‐type finite‐element computations. In addition, due to the difference in the two constitutive integration algorithms used, the corresponding consistent tangent moduli are not the same even when time steps are small. Numerical examples are also presented to illustrate the remarkable quadratic performance of the proposed consistent tangent moduli for the generalized Duvaut‐Lions viscoplasticity model.