We propose an effective geometrical approach to recover the normal form of a given Elasticity tensor, once we know its symmetry class. In other words, we produce a rotation which brings an Elasticity tensor onto its normal form, given its components in any orthonormal frame, and this for any tensor of any symmetry class. Our methodology relies on the use of specific covariants and on the geometric characterization of each symmetry class using these covariants.

中文翻译：

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恢复弹性张量的范式和对称类

我们提出了一种有效的几何方法来恢复给定弹性张量的正常形式，一旦我们知道它的对称类。换句话说，我们产生一个旋转，将弹性张量带入其正常形式，给定它在任何正交坐标系中的分量，这对于任何对称类的任何张量。我们的方法依赖于特定协变量的使用以及使用这些协变量的每个对称类的几何特征。