A pseudoelastic model for the simulation of deformation twinning on the microscale is developed and coupled with a crystal plasticity model for crystallographic slip. The material parameters are adopted to {1012} 1 011 twinning and basal glide in a magnesium alloy. Special attention is drawn to the energy invariance of conjugate twin systems that emerges when twinning is treated elastically. The model is tested in three characteristic FE simulations, namely a simple shear test parallel and inclined to a twin system and an elongation test of a notched band. The slip-twin interaction is studied, as well as the practical implications of the strain energy invariance. Some characteristics of twinning could be reproduced. The most important observations are that the load drop at the twin nucleation, the cusp shape of the twin tip in the absence of slip and the kink patterns that evolve in slip-twin interaction could be simulated.
Convexification by construction of a convex hull.A fundamental work on convexity is given by Ball [9]. Given a nonconvex strain energy, it is reasonable to construct a convex hull, and to use the latter in place of the starting strain energy. Obviously, one looses the nonconvex branches of the strain energy. In this way, the uniqueness of the solution is gained at the cost of a clear assignment of the phases at each material point. Nevertheless, a volume fraction of each phase at each material point can be locally determined by introducing a dependence on the distance between the actual configuration and the stress free configurations of the phases. Talking about volume fractions, one has arrived at a macromodel. Sometimes, the construction of the convex hull is referred to as a relaxation procedure, since it corresponds to the relaxation of the constraint that at each material point only one phase exists. Some recently proposed relaxation procedures are given by Pagano [43], Lambrecht [36], Acerbi [2], Govindjee [25], Schmidt [48], and Peigney [45].