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Large-scale 3D martensitic microstructure evolution problems are studiedusing a finite-element discretization of a finite-strain phase-field model. Themodel admits an arbitrary crystallography of transformation and arbitraryelastic anisotropy of the phases, and incorporates Hencky-type elasticity, apenalty-regularized double-obstacle potential, and viscous dissipation. Thefinite-element discretization of the model is performed in Firedrake and relieson the PETSc solver library. The large systems of linear equations arising areefficiently solved using GMRES and a geometric multigrid preconditioner with acarefully chosen relaxation. The modeling capabilities are illustrated througha 3D simulation of the microstructure evolution in a pseudoelastic CuAlNisingle crystal during nano-indentation, with all six orthorhombic martensitevariants taken into account. Robustness and a good parallel scaling performancehave been demonstrated, with the problem size reaching 150 million degrees offreedom.

Phase-field modeling of multivariant martensitic transformation at finite-strain: computational aspects and large-scale finite-element simulations