Multiscale Modeling &Simulation, Volume 18, Issue 2, Page 1136-1152, January 2020.
This article combines shape optimization and homogenization techniques by looking for the optimal design of the microstructure in composite materials and of scaffolds. The development of materials with specific properties is of huge practical interest, for example, for medical applications or for the development of lightweight structures in aeronautics. In particular, the optimal design of microstructures leads to fundamental questions for porous media: what is the sensitivity of homogenized coefficients with respect to the shape of the microstructure? We compute Hadamard's shape gradient for the problem of realizing a prescribed effective tensor and demonstrate the applicability and feasibility of our approach through numerical experiments.

中文翻译：

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复合材料和脚手架结构的形状优化

多尺度建模与仿真，第18卷，第2期，第1136-1152页，2020年1月。
本文通过寻找复合材料和支架的微观结构的最佳设计，结合了形状优化和均质化技术。具有特定性能的材料的开发具有巨大的实际意义，例如，用于医疗应用或用于航空领域的轻型结构的开发。特别是，微观结构的优化设计导致了多孔介质的基本问题：相对于微观结构的形状，均质系数的敏感性如何？我们针对实现预定有效张量的问题计算了Hadamard的形状梯度，并通过数值实验证明了该方法的适用性和可行性。