Multiscale design of nonlinear materials using reduced-order modeling
Multiscale design of nonlinear materials using reduced-order modeling
复制标题
DOI：
10.1016/j.cma.2022.115388
复制
发表时间：
2022-09
影响因子：
7.2
通讯作者：
David R. Brandyberry;Xiang Zhang;P. Geubelle
中科院分区：
文献类型：
--
作者：
David R. Brandyberry;Xiang Zhang;P. Geubelle
提出了一种两步优化方法，用于非均质材料的有效多尺度设计，其非线性宏观响应由发生在微观结构水平的体积和界面损伤驱动。基于特征变形的降阶均匀化方法（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。初步设计，然后通过初始化一个高保真优化阶段的基础上，界面丰富的广义有限元法（IGFEM），以达到最终的设计。推导了电磁力模型对非线性材料特性的灵敏度分析公式，以驱动基于梯度的算法。几个多尺度优化问题的复杂性不断增加，以说明所提出的方法使用的目标函数的基础上的应力误差相对于所需的应力-应变响应的效率。
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.