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

Abstract

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

Version accepted at Computer Methods in Applied Mechanics and Engineering. It includes Supplementary Material