THE ISOTROPIC MATERIAL CLOSEST TO A GIVEN ANISOTROPIC MATERIAL
THE ISOTROPIC MATERIAL CLOSEST TO A GIVEN ANISOTROPIC MATERIAL
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DOI：
10.2140/jomms.2006.1.223
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发表时间：
2006-02-01
影响因子：
0.9
通讯作者：
Norris, Andrew N.
中科院分区：
文献类型：
--
作者：
Norris, Andrew N.
最接近给定各向异性弹性张量的各向同性弹性模量使用弹性距离的三种定义来定义：标准Frobenius（欧几里得）范数，张量的黎曼距离和对数欧几里得范数。最接近模对于黎曼范数和对数欧几里德范数是唯一的，与是否考虑刚度或柔度的差异无关。给出了立方体材料的最接近体模量和剪切模量的显式表达式，并描述了一种求解任意各向异性材料的最接近体模量和剪切模量的算法。该方法通过应用于各种材料来说明，这些材料根据它们与各向同性的距离进行排序。
The isotropic elastic moduli closest to a given anisotropic elasticity tensor are defined using three definitions of elastic distance: the standard Frobenius (Euclidean) norm, the Riemannian distance for tensors, and the log-Euclidean norm. The closest moduli are unique for the Riemannian and the log-Euclidean norms, independent of whether the difference in stiffness or compliance is considered. Explicit expressions for the closest bulk and shear moduli are presented for cubic materials, and an algorithm is described for finding them for materials with arbitrary anisotropy. The method is illustrated by application to a variety of materials, which are ranked according to their distance from isotropy.