We formulate effective necessary and sufficient conditions to identify the symmetry class of an elasticity tensor, a fourth-order tensor which is the cornerstone of the theory of elasticity and a toy model for linear constitutive laws in physics. The novelty is that these conditions are written using polynomial covariants. As a corollary, we deduce that the symmetry classes are affine algebraic sets, a result which seems to be new. Meanwhile, we have been lead to produce a minimal set of 70 generators for the covariant algebra of a fourth-order harmonic tensor and introduce an original generalized cross-product on totally symmetric tensors. Finally, using these tensorial covariants, we produce a new minimal set of 294 generators for the invariant algebra of the elasticity tensor.

我们制定了有效的必要和充分条件，以识别弹性张量，四阶张量（这是弹性理论的基石）和物理线性本构律的玩具模型的对称类别。新颖的是，这些条件是使用多项式协变量编写的。作为推论，我们推论对称类是仿射代数集，这个结果似乎是新的。同时，我们被引导为四阶谐波张量的协变代数产生最少的70个生成器集，并在完全对称张量上引入原始的广义叉积。最后，使用这些张量协变量，我们为弹性张量的不变代数产生了一组新的最小生成器294个生成器。