A new approach is developed for computational modelling of microstructure evolution problems. The approach combines the phase-field method with the recently-developed laminated element technique (LET) which is a simple and efficient method to model weak discontinuities using nonconforming finite-element meshes. The essence of LET is in treating the elements that are cut by an interface as simple laminates of the two phases, and this idea is here extended to propagating interfaces so that the volume fraction of the phases and the lamination orientation vary accordingly. In the proposed LET-PF approach, the phase-field variable (order parameter), which is governed by an evolution equation of the Ginzburg-Landau type, plays the role of a level-set function that implicitly defines the position of the (sharp) interface. The mechanical equilibrium subproblem is then solved using the semisharp LET technique. Performance of LET-PF is illustrated by numerical examples. In particular, it is shown that, for the problems studied, LET-PF exhibits higher accuracy than the conventional phase-field method so that, for instance, qualitatively correct results can be obtained using a significantly coarser mesh, and thus at a lower computational cost.

翻译：为微观结构演化问题的计算建模开发了一种新方法。该方法将相场法与近期发展的层状单元技术（LET）相结合，后者是一种利用非协调有限元网格模拟弱不连续性的简单高效方法。LET的核心在于将被界面切割的单元视为两相的简单层状复合材料，此处将此概念推广至传播界面，使相的体积分数和层状取向随之相应变化。在所提出的LET-PF方法中，由Ginzburg-Landau型演化方程控制的相场变量（序参量）扮演水平集函数的角色，隐式定义（尖锐）界面的位置。随后利用半尖锐LET技术求解力学平衡子问题。通过数值算例展示了LET-PF的性能。特别地，研究表明，对于所研究的问题，LET-PF比传统相场方法具有更高精度，例如，使用显著较粗的网格即可获得定性正确的结果，从而降低计算成本。