论文标题
有限型在有限型的多变量马氏体变换的相位模型：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
论文作者
论文摘要
大规模3D Martensitic微观结构进化问题是使用有限型晶体相位模型的有限元离散化研究的。该模型接受了这些相的转化和任意弹性各向异性的任意晶体学，并结合了hencky型弹性，惩罚性调节的双嵌入电位和粘性耗散。模型的有限元离散化是在Firedrake中执行的，并依赖于PETSC求解器库。使用GMRE和带有精心选择的松弛的几何多机预科机有效地求解了线性方程的大系统。通过在纳米识别过程中对伪弹性cualni单晶体中微结构演化的3D模拟进行了建模功能，并考虑了所有六个正骨bombic martensite变体。已经证明了稳健性和良好的平行缩放性能，问题大小达到了1.5亿个自由度。
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.
