期刊
MATHEMATICS AND MECHANICS OF COMPLEX SYSTEMS
卷 5, 期 1, 页码 41-94出版社
MATHEMATICAL SCIENCE PUBL
DOI: 10.2140/memocs.2017.5.41
关键词
printed materials; elastic G-closures; metamaterials
类别
资金
- National Science Foundation [DMS1211359]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1211359] Funding Source: National Science Foundation
The set GU(f) of possible effective elastic tensors of composites built from two materials with elasticity tensors C-1 > 0 and C-2 = 0 comprising the set U = {C-1, C-2} and mixed in proportions f and 1 - f is partly characterized. The material with tensor C-2 = 0 corresponds to a material which is void. (For technical reasons C-2 is actually taken to be nonzero and we take the limit C-2 -> 0). Specifically, recalling that GUf is completely characterized through minimums of sums of energies, involving a set of applied strains, and complementary energies, involving a set of applied stresses, we provide descriptions of microgeometries that in appropriate limits achieve the minimums in many cases. In these cases the calculation of the minimum is reduced to a finite-dimensional minimization problem that can be done numerically. Each microgeometry consists of a union of walls in appropriate directions, where the material in the wall is an appropriate p-mode material that is easily compliant to p <= 5 independent applied strains, yet supports any stress in the orthogonal space. Thus the material can easily slip in certain directions along the walls. The region outside the walls contains complementary Avellaneda material, which is a hierarchical laminate that minimizes the sum of complementary energies.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据