Benchmark tests based on the Couette viscometer—II: Thermo-elasto-plastic solid behaviour in small and large strains

The Couette viscometer is a well-known problem of fluid mechanics, well-suited for the verification of numerical methods. The aim of this work is to extend the classical steady state mechanical solution obtained in fluid mechanics and to use the extended solutions to assess new finite elements. Part I was devoted to the case of laminar flow of incompressible fluids with inertia effects and thermomechanical coupling. The present Part II focuses on solid-type nonlinear behaviours; we address the cases of elastic–plastic and thermo-elastic–plastic von Mises materials, both in small and large strains. The extended solutions permit to assess a new formulation of a mixed P1+/P1 finite element in solid mechanics, in a temperature/velocity/pressure formulation coupled with an implicit (backward) Euler algorithm in time. The verification evidences a good behaviour of the solid finite element.