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

Large-scale 3D martensitic microstructure evolution problems are studied using a finite-element discretization of finite-strain phase-field model. The model admits an arbitrary crystallography transformation and elastic anisotropy the phases, incorporates Hencky-type elasticity, penalty-regularized double-obstacle potential, viscous dissipation. is performed in Firedrake relies on PETSc solver library. large systems linear equations arising efficiently solved GMRES geometric multigrid preconditioner with carefully chosen relaxation. modeling capabilities illustrated through simulation pseudoelastic CuAlNi single crystal during nano-indentation, all six orthorhombic martensite variants taken into account. Robustness good parallel scaling performance have been demonstrated, problem size reaching 150 million degrees freedom.