A quasi-static boundary value problem in multi-surface elastoplasticity: Part 2 - Numerical solution

Multi-yield elastoplasticity models a material with more than one plastic state and hence allows for refined approximation of irreversible deformations. Aspects of the mathematical modelling and a proof of unique existence of weak solutions can be found in part I of this paper (Math. Models Methods Appl. Sci. 2004). In this part II we establish a canonical time-space discretization of the evolution problem and present various algorithms for the solving really discrete problems. Based on a global Newton-Raphson solver, we carefully study and solve elementwise inner iterations. Numerical examples illustrate the model and its flexibility to allow for refined hysteresis curves.