三次或正交各向异性弹性距离的上界估计
Upper bounds estimates of the distance to cubic or orthotropic elasticity
摘要：
我们解决的问题，而不是确定-这通常需要数值方法-但准确的分析估计的原始弹性张量的距离立方对称性和正交各向异性。我们指出，有不是一个，而是几个二阶张量进行可能的立方/正交各向异性坐标系的原始张量。由于（精确）三次弹性张量的所有二阶协变量都是各向同性的，因此仅基于此类协变量的距离估计并不总是准确的。我们扩展到三次对称和正交各向异性的技术最近建议Klimee的横向各向同性：解析求解辅助二次最小化问题，其解决方案是一个二阶张量进行可能的立方坐标系。数值例子，我们评估不同的上限估计的距离立方或正交各向异性对称的准确性。
英文摘要：
We address the problem, not of the determination -- which usually needs numerical methods -- but of an accurate analytical estimation of the distance of a raw elasticity tensor to cubic symmetry and to orthotropy. We point out that there are not one but several secondorder tensors that carry the likely cubic/orthotropic coordinate system of the raw tensor. Since all the second-order covariants of an (exactly) cubic elasticity tensor are isotropic, distance estimates based only on such covariants are not always accurate. We extend to cubic symmetry and to orthotropy the technique recently suggested by Klimeš for transverse isotropy: solving analytically an auxiliary quadratic minimization problem whose solution is a second-order tensor that carries the likely cubic coordinate system. Numerical examples are provided, on which we evaluate the accuracy of different upper bounds estimates of the distance to cubic or orthotropic symmetry.
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