Conditions for Strong Ellipticity of Anisotropic Elastic Materials
Conditions for Strong Ellipticity of Anisotropic Elastic Materials
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DOI：
10.1007/s10659-009-9205-5
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发表时间：
2009-05
影响因子：
2
通讯作者：
Deren Han;Hui-hui Dai;L. Qi
中科院分区：
文献类型：
--
作者：
Deren Han;Hui-hui Dai;L. Qi
本文给出了各向异性弹性材料强椭圆性条件的充分必要条件。我们首先观察到强椭圆性条件成立当且仅当二阶张量函数对任何单位向量都是正定的。然后，我们进一步将这个条件与三个二阶张量、三个四阶张量和一个六阶张量的秩一正定性联系起来。特别是，我们认为条件强椭圆的菱形类，我们需要检查的copositivity三个二阶张量和正定性的六阶张量。一个直接的方法来验证我们的条件。
In this paper, we derive necessary and sufficient conditions for the strong ellipticity condition of anisotropic elastic materials. We first observe that the strong ellipticity condition holds if and only if a second order tensor function is positive definite for any unit vectors. Then we further link this condition to the rank-one positive definiteness of three second-order tensors, three fourth-order tensors and a sixth-order tensor. In particular, we consider conditions of strong ellipticity of the rhombic classes, for which we need to check the copositivity of three second-order tensors and the positive definiteness of a sixth-order tensor. A direct method is presented to verify our conditions.