A phase field model for the formation and evolution of martensitic laminate microstructure at finite strains

The extraordinary properties of shape-memory alloys stem from the formation and evolution of their complex microstructure. At lower temperatures, this microstructure typically consists of martensitic laminates with coherent twin boundaries. We suggest a variational-based phase field model at finite strains for the formation and dissipative evolution of such two-variant martensitic twinned laminate microstructures. The starting point is a geometric discussion of the link between sharp interface topologies and their regularisation, which is connected to the notion of Gamma-convergence. To model the energy storage in the two-phase laminates, we propose an interface energy that is coherence-dependent and a bulk energy that vanishes in the interface region, thus allowing for a clear separation of the two contributions. The dissipation related to phase transformation is modelled by use of a dissipation potential that leads to a Ginzburg-Landau type evolution equation for the phase field. We construct distinct rate-type continuous and finite-step-sized incremental variational principles for the proposed dissipative material and demonstrate its modelling capabilities by means of finite element simulations of laminate formation and evolution in martensitic CuAlNi.