有限应变下多元马氏体相变的相场模拟：计算方面和大规模有限元模拟
Phase-field modeling of multivariant martensitic transformation at finite-strain: computational aspects and large-scale finite-element simulations
摘要：
采用有限应变相场模型的有限元离散化方法研究了大规模三维马氏体组织演化问题。该模型承认任意晶体学的转变和任意弹性各向异性的阶段，并纳入亨奇型弹性，罚正则化的双障碍潜力，和粘性耗散。模型的有限元离散化在Firedrake中进行，并依赖于PETSc求解器库。使用GMRES和几何多重网格预处理器与精心选择的放松，有效地解决了大型系统的线性方程组。的建模能力，说明通过一个3D模拟的微观结构的演变过程中的伪弹性CuAlNi单晶纳米压痕，考虑到所有六个正交马氏体变体。已证明其鲁棒性和良好的并行扩展性能，问题大小达到1.5亿个自由度。
英文摘要：
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.
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