Elastic constants and their admissible values for incompressible and slightly compressible anisotropic materials
Elastic constants and their admissible values for incompressible and slightly compressible anisotropic materials
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DOI：
10.1007/bf01182156
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发表时间：
2002-01-01
期刊：
影响因子：
2.7
通讯作者：
Aksel, N
中科院分区：
文献类型：
--
作者：
Itskov, M;Aksel, N
不可压缩（微可压缩）各向异性材料的本构关系不能（几乎不能）通过广义胡克定律的反演得到，因为在这种情况下对应的柔度张量是奇异的（病态的）。这是由于不可压缩性（轻微可压缩性）条件对弹性常数施加了一些额外的约束。这个问题需要在本文中讨论一个特殊的程序。这个过程的思想是基于柔度张量的谱分解，但导致弹性张量的封闭公式没有显式使用特征值问题的解决方案。材料张量的非负（正）定条件限制了弹性常数属于一个容许值域。对于正交异性和横向各向同性不可压缩以及各向同性可压缩材料，相应的域用图形表示。
Constitutive relations for incompressible (slightly compressible) anisotropic materials cannot (could hardly) be obtained through the inversion of the generalized Hooke's law since the corresponding compliance tensor becomes singular (ill-conditioned) in this case. This is due to the fact that the incompressibility (slight compressibility) condition imposes some additional constraints on the elastic constants. The problem requires a special procedure discussed in the present paper. The idea of this procedure is based on the spectral decomposition of the compliance tensor but leads to a closed formula for the elasticity tensor without explicit using the eigenvalue problem solution. The condition of nonnegative (positive) definiteness of the material tensors restricts the elastic constants to belong to an admissible value domain. For orthotropic and transversely isotropic incompressible as well as isotropically compressible materials the corresponding domains are illustrated graphically.