Motivated by recent advances in manufacturing, the design of materials is the focal point of interest in the material research community. One of the critical challenges in this field is finding optimal material microstructure for a desired macroscopic response. This work presents a computational method for the mesoscale‐level design of particulate composites for an optimal macroscale‐level response. The method relies on a custom shape optimization scheme to find the extrema of a nonlinear cost function subject to a set of constraints. Three key “modules” constitute the method: multiscale modeling, sensitivity analysis, and optimization. Multiscale modeling relies on a classical homogenization method and a nonlinear NURBS‐based generalized finite element scheme to efficiently and accurately compute the structural response of particulate composites using a nonconformal discretization. A three‐parameter isotropic damage law is used to model microstructure‐level failure. An analytical sensitivity method is developed to compute the derivatives of the cost/constraint functions with respect to the design variables that control the microstructure's geometry. The derivation uncovers subtle but essential new terms contributing to the sensitivity of finite element shape functions and their spatial derivatives. Several structural problems are solved to demonstrate the applicability, performance, and accuracy of the method for the design of particulate composites with a desired macroscopic nonlinear stress‐strain response.

中文翻译：

---

使用欧拉形状优化方案的非线性材料多尺度设计

受制造业最新进展的推动，材料设计是材料研究界关注的焦点。该领域的关键挑战之一是为所需的宏观响应找到最佳的材料微观结构。这项工作为微粒复合材料的中尺度级设计提供了一种计算方法，以实现最佳的宏观尺度级响应。该方法依赖于自定义形状优化方案来找到受一组约束约束的非线性成本函数的极值。该方法由三个关键的“模块”组成：多尺度建模，灵敏度分析和优化。多尺度建模依赖于经典的均质化方法和基于NURBS的非线性广义有限元方案，可以通过非保形离散有效而准确地计算颗粒复合材料的结构响应。使用三参数各向同性破坏定律对微观结构级别的破坏进行建模。开发了一种分析灵敏度方法来计算成本/约束函数相对于控制微结构几何形状的设计变量的导数。该推导发现了一些微妙但必不可少的新术语，这些术语对有限元形状函数及其空间导数的敏感性做出了贡献。解决了几个结构性问题，以证明其适用性，性能，