报告题目：From Local to Global: Babuska Problem in Composite Materials and the Effective Elasticity Properties

主 讲 人：Haigang Li

单 位：北京师范大学

时 间：12月9日16:00

腾 讯 ID：514-208-950

摘 要：

In a two-phase composite, the study of its effective property is a central topic in material sciences. Especially, in a high-contrast elastic composite media, when inclusions are spaced closely, the stress always concentrates in between inclusions and causes damage initiation. This local concentration phenomenon essentially affects the global properties of the composite. For Babuska problem in linear elasticity, we obtain the blow-up asymptotic expressions of the gradients of solutions to the Lame system with partially infinite coefficients in the narrow region when the distance between inclusions tends to zero, by developing an iteration technique with respect to the energy integral. This result holds for convex inclusions with arbitrary shape and in all dimensions. Recently, we apply it to prove an extended Flaherty-Keller formula on the effective elastic property of a periodic composite with densely packed fibers, which is related to the “Vigdergauz microstructure”, possessing optimality properties in the context of Hashin-Shtrickmann bounds in structural optimization problems.

简 介：

李海刚，北京师范大学教授、博士生导师，主要从事材料科学中的偏微分方程理论研究。在复合材料中的Babuska问题及其相关领域做出一系列深刻原创成果，在Adv. Math.、ARMA、JMPA、JFA等杂志发表论文30余篇。2016年获得教育部霍英东青年教师基金，2018年获得教育部自然科学奖二等奖，2020年入选教育部奖励计划青年学者。