Phase-field modeling of multivariant martensitic transformation at finite-strain: computational aspects and large-scale finite-element simulations. (English) Zbl 1506.74242
Summary: 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.
MSC:
| 74N15 | Analysis of microstructure in solids |
| 74S05 | Finite element methods applied to problems in solid mechanics |
Keywords:
phase-field method; finite-element method; large-scale simulations; shape memory alloys; nano-indentationReferences:
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