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Topology optimization of multiple anisotropic materials, with application to self-assembling diblock copolymers

机译：多种各向异性材料的拓扑优化及其在自组装二嵌段共聚物中的应用

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摘要

We propose a solution strategy for a multimaterial minimum compliance topology optimization problem, which consists in finding the optimal allocation of a finite number of candidate (possibly anisotropic) materials inside a reference domain, with the aim of maximizing the stiffness of the body. As a relevant and novel application we consider the optimization of self-assembled structures obtained by means of diblock copolymers. Such polymers are a class of self-assembling materials which spontaneously synthesize periodic microstructures at the nanoscale, whose anisotropic features can be exploited to build structures with optimal elastic response, resembling biological tissues exhibiting microstructures, such as bones and wood. For this purpose we present a new generalization of the classical Optimality Criteria algorithm to encompass a wider class of problems, where multiple candidate materials are considered, the orientation of the anisotropic materials is optimized, and the elastic properties of the materials are assumed to depend on a scalar parameter, which is optimized simultaneously to the material allocation and orientation. Well-posedness of the optimization problem and well-definition of the presented algorithm are narrowly treated and proved. The capabilities of the proposed method are assessed through several numerical tests. (C) 2018 Elsevier B.V. All rights reserved.
机译：我们提出了一种针对多材料最小顺应性拓扑优化问题的解决方案策略，该策略包括在参考域内找到有限数量的候选（可能是各向异性的）材料的最优分配，目的是最大化车体的刚度。作为相关且新颖的应用，我们考虑了通过二嵌段共聚物获得的自组装结构的优化。这类聚合物是一类自组装材料，可自发合成纳米级的周期性微结构，其各向异性特征可用于构建具有最佳弹性响应的结构，类似于表现出微结构的生物组织，例如骨骼和木材。为此，我们提出了经典最佳标准算法的新概括，以涵盖更广泛的问题类别，其中考虑了多种候选材料，优化了各向异性材料的方向，并假定材料的弹性特性取决于标量参数，可同时针对材料分配和方向进行优化。优化问题的适定性和所提出算法的良好定义被狭义地对待和证明。通过几种数值测试评估了所提出方法的能力。 （C）2018 Elsevier B.V.保留所有权利。

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