Monolithic and partitioned coupling schemes for thermo-viscoplasticity

In this article we investigate a fully, thermo-mechanically coupled viscoplasticity model in view of various numerical aspects. First, we develop the entire system of differential-algebraic equations resulting from the spatially discretized principle of virtual displacements, the principle of virtual temperatures, and the evolution equations of the internal variables provided by the constitutive model. In the time-integration step this system is solved both using a fully monolithic approach based on a Backward-Euler scheme in combination with the Multilevel-Newton algorithm as well as a partitioned approach solving the fully coupled system. The latter is treated by means of a combination of a Backward-Euler method and an accelerated Gauss-Seidel/Multilevel-Newton scheme to solve the resulting system of algebraic equations within each time-integration step. Additionally, we consider a specific treatment of the interpolation between different meshes within the partitioned approach. This is shown for p-version finite elements based on hierarchical shape functions. Finally, it turns out that the specific constitutive model of small-strain thermo-viscoplasticity, which is based on the decomposition into kinematic hardening and energy storing strains, yields a problem-adapted stress algorithm. This allows to reduce the stress algorithm on Gauss-point level to the solution of one scalar equation. Numerical examples serve to elucidate the behavior and properties of the proposed methods.