A two-step optimization method is proposed for the efficient multiscale design of heterogeneous materials whose nonlinear macroscopic response is driven by volumetric and interfacial damage taking place at the microstructural level. The Eigendeformation-based reduced-order Homogenization Method (EHM) is used in a reduced-order design phase, allowing for a preliminary design that combines multiple initial configurations with a gradient-based optimization method. The preliminary design is then adopted to initialize a high-fidelity optimization phase based on the Interface-Enriched Generalized Finite Element Method (IGFEM) to arrive at the final design. The analytic sensitivities of EHM with respect to nonlinear material properties are derived to drive the gradient-based algorithm. Several multiscale optimization problems of increasing complexity are presented to illustrate the efficiency of the proposed method using an objective function based on stress error relative to a desired stress–strain response.

提出了一种两步优化方法，用于异质材料的有效多尺度设计，其非线性宏观响应由微观结构水平上发生的体积和界面损伤驱动。基于特征变形的降阶均质化方法(EHM) 用于降阶设计阶段，允许将多个初始配置与基于梯度的优化方法相结合的初步设计。然后采用初步设计来初始化基于富界面广义有限元法 (IGFEM) 的高保真优化阶段，以达到最终设计。EHM 对非线性材料的解析灵敏度导出属性以驱动基于梯度的算法。提出了几个复杂度增加的多尺度优化问题，以说明所提出的方法的效率，该方法使用基于相对于所需应力-应变响应的应力误差的目标函数。