2020/11/30 by K. Tůma, Karel Tůma, M. Rezaee-Hajidehi +5 · 19 citations
Engineering · Materials Science · Mathematics · Physics and Astronomy · #Aluminum Alloy Microstructure Properties #Applied mathematics #Classical mechanics #Discretization #Finite element method #Finite strain theory #Linear system #Mathematical analysis #Mathematical optimization #Mathematics #Metallurgy and Material Forming #Multigrid method #Partial differential equation #Physics #Preconditioner #Solidification and crystal growth phenomena #Solver #Thermodynamics #physics.comp-ph
paper · pdf · doi:10.1016/j.cma.2021.113705
published in Computer Methods in Applied Mechanics and Engineering 377, 113705 (Elsevier BV) · Version accepted at Computer Methods in Applied Mechanics and Engineering. It includes Supplementary Material
openalex created_date 2020/11/23 · openalex publication_date 2021/02/15 · arxiv created 2021/02/18 · arxiv updated 2021/02/19 · openalex updated_date 2026/08/05
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.