Artificially designed composite materials consist of microstructures, that exhibit various thermal properties depending on their shapes, such as anisotropic thermal conductivity. One of the representative applications of such composite materials for thermal control is the thermal cloak. This study proposed a topology optimization method based on a level set method for a heat conduction problem to optimally design composite materials that achieve a thermal cloak. The homogenization method was introduced to evaluate its effective thermal conductivity coefficient. Then, we formulated a multiscale topology optimization method for the composite materials in the framework of the homogenization method, where the microstructures were optimized to minimize objective functions defined using the macroscopic temperature field. We presented examples of optimal structures in a two-dimensional problem and discussed the validity of the obtained structures.

翻译：人工设计的复合材料由微观结构构成，这些微观结构具有各向异性导热系数等随形状变化的热性能。此类复合材料在热控制领域的代表性应用之一是热隐身罩。本研究提出了一种基于水平集方法的热传导拓扑优化方法，以优化设计能够实现热隐身罩的复合材料。引入均匀化方法来评估其等效导热系数。随后，在均匀化方法的框架下，我们建立了一种针对复合材料的多尺度拓扑优化方法，其中微观结构被优化以最小化由宏观温度场定义的目标函数。我们给出了二维问题中优化结构的示例，并讨论了所得结构的有效性。