When modelling discontinuities (interfaces) using the finite element method, the standard approach is to use a conforming finite-element mesh in which the mesh matches the interfaces. However, this approach can prove cumbersome if the geometry is complex, in particular in 3D. In this work, we develop an efficient technique for a non-conforming finite-element treatment of weak discontinuities by using laminated microstructures. The approach is inspired by the so-called composite voxel technique that has been developed for FFT-based spectral solvers in computational homogenization. The idea behind the method is rather simple. Each finite element that is cut by an interface is treated as a simple laminate with the volume fraction of the phases and the lamination orientation determined in terms of the actual geometrical arrangement of the interface within the element. The approach is illustrated by several computational examples relevant to the micromechanics of heterogeneous materials. Elastic and elastic-plastic materials at small and finite strain are considered in the examples. The performance of the proposed method is compared to two alternative, simple methods showing that the new approach is in most cases superior to them while maintaining the simplicity.

翻译：在采用有限元方法模拟不连续界面时，标准做法是使用与界面匹配的协调有限元网格。然而，当几何形状复杂时（尤其在三维问题中），该方法可能显得繁琐。本研究通过利用层压微结构，开发了一种高效的非协调有限元处理弱不连续技术。该方法受计算均质化中基于FFT的谱求解器所采用的复合体素技术启发，其核心思想较为简洁：每个被界面切割的有限单元被视为简单层压复合材料，其中相的体积分数和层压方向由界面在单元内的实际几何排布确定。通过多个与异质材料微观力学相关的计算实例验证了该方法的有效性，实例中考虑了小应变和有限应变下的弹性及弹塑性材料。将该方法与两种替代简单方法进行性能对比，结果表明，新方法在保持简洁性的同时，在多数情况下具有显著优越性。