导电复合材料和弹性复合材料的最佳三材料车轮组合
Optimal Three-Material Wheel Assemblage of Conducting and Elastic Composites
摘要：
我们描述了一种新型的三种材料的微观结构，我们称之为车轮组装，对应于极端的导电性和极端的体积模量的复合材料制成的两种材料和一个理想的材料。有效电导率和匹配层压板的精确下限在（Cherkaev，2009）中找到，各向异性复合材料的精确下限在（Cherkaev，Zhang，2011）中找到。在这里，我们展示了不同的优化结构，概括了经典的Hashin-Shtrikman涂层球（圆）。它们由圆形内含物组成，内含物包含一个实心中心圆（轮毂）和周围环中的径向尖峰，（对于最佳材料的较大体积分数）充满它的环形空间。对于最小传导率的对偶问题，相同的车轮组合是最佳的由两种材料和理想导体制成的复合材料的电阻率（绝缘体）的最大有效体积模量问题和对偶最小问题。
英文摘要：
We describe a new type of three material microstructures which we call wheel assemblages, that correspond to extremal conductivity and extremal bulk modulus for a composite made of two materials and an ideal material. The exact lower bounds for effective conductivity and matching laminates was found in (Cherkaev, 2009) and for anisotropic composites, in (Cherkaev, Zhang, 2011). Here, we show different optimal structures that generalize the classical Hashin-Shtrikman coated spheres (circles). They consist of circular inclusions which contain a solid central circle (hub) and radial spikes in a surrounding annulus, and (for larger volume fractions of the best material) an annulus filled with it. The same wheel assemblages are optimal for the pair of dual problems of minimal conductivity (resistivity) of a composite made from two materials and an ideal conductor (insulator), in the problem of maximal effective bulk modulus of elastic composites made from two linear elastic material and void, and the dual minimum problem.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
