ON A CLASS OF CONSTITUTIVE-EQUATIONS IN VISCOPLASTICITY - FORMULATIONAND COMPUTATIONAL ISSUES

The viscoplastic constitutive model is formulated based on the existen ce of the dissipation potential which embodies the notion of the gauge (Minkowski) function of the convex set. A perturbation method is used for a solution of stiff differential equations characterizing the ass ociated problem of evolution. It relies on a discrete formulation of v iscoplasticity which results from the regularized version of the princ iple of maximum plastic dissipation. The operator split methodology an d the Newton-Raphson method are used to obtain the numerical solution of the discretized equations of evolution. The consistent tangent modu lus is expressed in a closed form as a result of the exact linearizati on of the discretized evolution equations. For several variants of the flow potential function, including some representative stiff function al forms, numerical tests of the integration algorithm based on iso-er ror maps are provided. Finally, a numerical example is presented to il lustrate the robustness and the effectiveness of the proposed approach .