The Theory of Composites
The Theory of Composites
复制标题
DOI：
10.1137/1.9781611977486
复制
发表时间：
2002-05
期刊：
影响因子：
--
通讯作者：
G. Milton
中科院分区：
文献类型：
--
作者：
G. Milton
爱因斯坦等人都对复合材料理论做出了贡献。在数学上，它是研究偏微分方程与快速振荡的系数。虽然广泛的研究超过100年，爆炸的想法在过去的四十年（特别是在过去的二十年），大大增加了我们的理解之间的关系的组成材料的性能，复合材料的底层微观结构，和整体有效（电，热，弹性）模量，支配宏观行为。这一复兴已被技术需要，以提高我们的知识基础的复合材料，由先进的基本数学理论的均匀化，由发现新的变分原理，由认识到如何重要的主题是解决结构优化问题，并实现连接的数学问题的拟凸化。这本书调查这些令人兴奋的发展在数学的前沿，并提出了许多新的成果。
Einstein, have contributed to the theory of composite materials. Mathematically, it is the study of partial differential equations with rapid oscillations in their coefficients. Although extensively studied for more than 100 years, an explosion of ideas in the last four decades (and particularly in the last two decades) has dramatically increased our understanding of the relationship between the properties of the constituent materials, the underlying microstructure of a composite, and the overall effective (electrical, thermal, elastic) moduli that govern the macroscopic behavior. This renaissance has been fueled by the technological need for improving our knowledge base of composites, by the advance of the underlying mathematical theory of homogenization, by the discovery of new variational principles, by the recognition of how important the subject is to solving structural optimization problems, and by the realization of the connection with the mathematical problem of quasiconvexification. This book surveys these exciting developments at the frontier of mathematics and presents many new results.