We extend the embedded unit cell (EUC) homogenization approach, to efficiently and accurately capture the multiscale solution of a solid with localized domains undergoing plastic yielding. The EUC approach is based on a mathematical homogenization formulation with non-periodic domains, in which the macroscopic and microscopic domain are concurrently coupled. The formulation consists of a theoretical derivation and the development of special boundary conditions representing the variations of the local displacement field across the unit cell boundaries. In particular, we introduce a restraining band surrounding the local domain in order to support the consistency of the solution in the transition layer between the micro and macro scales. The method is neither limited to a specific plasticity model nor to the number of localized features, thereby providing great flexibility in modeling. Several numerical examples illustrate that the proposed approach is accurate compared with direct finite element simulations, yet requires less computational cost.

我们扩展了嵌入式晶胞 (EUC) 均质化方法，以高效准确地捕获具有塑性屈服的局部域的固体的多尺度解。EUC 方法基于具有非周期性域的数学同质化公式，其中宏观域和微观域同时耦合。该公式包括理论推导和特殊边界条件的发展，代表跨单位单元边界的局部位移场的变化。特别是，我们在局部域周围引入了一个约束带，以支持微观和宏观尺度之间过渡层中解的一致性。该方法既不限于特定的可塑性模型，也不限于局部特征的数量，从而为建模提供了极大的灵活性。几个数值例子表明，与直接有限元模拟相比，所提出的方法是准确的，但需要较少的计算成本。