A simplified calculation for the elatic constants of arbitrarily oriented single crystals
A simplified calculation for the elatic constants of arbitrarily oriented single crystals
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任意取向单晶弹性常数的简化计算
DOI：
10.1107/s0365110x56003144
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发表时间：
1956
期刊：
影响因子：
--
通讯作者：
S. Zirinsky
中科院分区：
文献类型：
--
作者：
D. S. Lieberman;S. Zirinsky
提出了一种简单、完全通用且易于记忆的方案，用于解决涉及弹性常数从一个正交坐标系到相对于第一个正交坐标系旋转的另一个坐标系的变换的问题。由于应力分量可以表示为二阶张量的元素，并且应变分量（如果定义正确）同样可以表示为二阶张量的元素，因此连接应力和应变的弹性常数必定是四阶张量的元素。该方法依赖于四阶张量的同时收缩和连接两个轴系的方向余弦的二次积。应用所得到的“变换矩阵”而不是传统方法，将步骤数减少到最少，同时相应地减少了计算中出错的机会。典型例子表明，时间和劳动力的节省是相当可观的。
A simple, competely general, and easily remembered scheme is presented for solving problems involving the transformation of elastic constants from one orthogonal coordinate system to another rotated with respect to the first. Since the components of stress can be expressed as the elements of a second rank tensor, and the components of strain (if properly defined) can likewise be expressed as the elements of a second rank tensor, the elastic constants connecting stress and strain must be the elements of a fourth rank tensor. The method depends upon the simultaneous contraction of the fourth rank tensor and the quadratic products of the direction cosines connecting the two axis systems. The application of the resultant'transformation matrix', instead of the conventional methods, reduces the number of steps to a minimum with a corresponding reduction in the chance for errors in the computation. The saving in time and labor is considerable, as is shown by typical examples.