This article deals with damage computation of heterogeneous structures containing locally periodic micro-structures. Such heterogeneous structure is extremely expensive to simulate using classical finite element methods, as the level of discretisation required to capture the micro-structural effects is too fine. The simulation time becomes even higher when dealing with highly non-linear material behaviour, e.g. damage, plasticity and such others. Therefore, a multi-scale strategy is proposed here that facilitates the simulation of non-linear heterogeneous material behaviour in a manner that is computationally feasible. Based on the asymptotic homogenisation theory, this multi-scale technique explores the micro–macro behaviour for elasto-(visco)plasticity coupled with damage. The theory inherently segregates the heterogeneous continua into a macroscopic homogeneous structure and an underlying heterogeneous microscopic periodic unit cell. Several heterogeneous structures have been simulated using the multi-scale method along with a one-dimensional verification with respect to a reference solution. Additionally, a reduced order modelling is used to prevent large memory requirement for storing micro-structural quantities of interest.

中文翻译：

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基于渐近理论和模型约简的弹粘塑性耦合损伤数值均匀化

本文涉及包含局部周期性微结构的异质结构的损伤计算。使用经典有限元方法模拟这种异质结构非常昂贵，因为捕捉微观结构效应所需的离散化水平太精细了。在处理高度非线性的材料行为（例如损坏、塑性等）时，模拟时间会变得更长。因此，这里提出了一种多尺度策略，以在计算上可行的方式促进非线性异质材料行为的模拟。基于渐近均质化理论，这种多尺度技术探索了弹（粘）塑性与损伤相结合的微观-宏观行为。该理论固有地将异质连续体分离为宏观均质结构和潜在的异质微观周期性晶胞。已经使用多尺度方法以及相对于参考解决方案的一维验证模拟了几种异构结构。此外，使用降阶建模来防止存储感兴趣的微结构量需要大量内存。