Numerical treatment of a finite strain viscoplasticity model based on a double multiplicative split

Abstract

A viscoplastic material model of overstress type is analyzed. The model is based on the kinematic assumption of a double multiplicative split in order to simulate a nonlinear kinematic hardening. We investigate theoretically and numerically two implicit time-stepping methods, which were used lately in engineering literature to integrate the evolution equations in the context of multiplicative plasticity/viscoplasticity. A common feature of both methods is that the plastic incompressibility constraint is exactly satisfied. Moreover, we show that both methods preserve the symmetry of internal variables, which is inherent to the problem. According to testing results, both methods are equivalent regarding robustness, accuracy, and computational efficiency.

On the simulation of plastic forming under consideration of thermal effects

“…where ðM ÀT Þ Ã ð N Þ ¼ Mð N ÞM T for all M: A detailed motivation for these transformations can be found in [7]: the relations can be derived from the concept of dual variables proposed by Haupt and Tsakmakis. ByR R and N N we denote the driving forces for the inelastic flow and the flow on the microstructural level, respectively (cf.…”

“…ByR R and N N we denote the driving forces for the inelastic flow and the flow on the microstructural level, respectively (cf. [7]):…”

“…Now we formally postulate the following potential relations for stresses, backstresses, isotropic hardening R, and entropy f (cf. [3,7]):…”

“…After some computations (similar computations can be found, for instance, in [3,7]), we obtain the first inequality in the form as follows: Bild 2. Zusammenfassung von multiplikativen Zerlegungen des Deformationsgradienten in Form eines kommutativen Diagramms (vgl.…”

“…In this paper we present a straight-forward generalization of the material model presented in [7]. Note that the material parameters of the resulting thermo-mechanical model (like the yield stress, viscosity etc.)…”