论文标题
上限估计到立方或正性弹性的距离
Upper bounds estimates of the distance to cubic or orthotropic elasticity
论文作者
论文摘要
我们解决了问题，而不是确定的问题（通常需要数值方法），而是对原始弹性张量与立方对称性和正交相关的距离进行准确的分析估计。我们指出，没有一个二级张量，它们携带可能的Cubic/Orthotropic坐标系统的原始张量。由于（确切的）立方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。我们扩展到立方对称性和矫形器，Klimeš最近提出的有关横向各向同性的技术：在分析上求解一个辅助二次最小化问题，其溶液是二阶张量，它含有可能立方坐标系统。提供了数值示例，我们在其上评估了与立方或正性对称性距离的不同上限估计的准确性。
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.
