We formulate necessary and sufficient conditions for a unit vector $\pmb{\nu }$ to generate a plane or axial symmetry of a constitutive tensor. For the elasticity tensor, these conditions consist of two polynomial equations of degree lower than four in the components of $\pmb{\nu }$ . Compared to Cowin–Mehrabadi conditions, this is an improvement, since these equations involve only the normal vector $\pmb{\nu }$ to the plane symmetry (and no vector perpendicular to $\pmb{\nu }$ ). Similar reduced algebraic conditions are obtained for linear piezo-electricity and for totally symmetric tensors up to order 6.

中文翻译：

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关于确定线弹性和压电中的平面和轴对称性

我们为单位向量 $\pmb{\nu }$ 制定必要和充分条件，以生成本构张量的平面或轴对称。对于弹性张量，这些条件由 $\pmb{\nu }$ 的分量中的阶数小于 4 的两个多项式方程组成。与 Cowin-Mehrabadi 条件相比，这是一个改进，因为这些方程只涉及平面对称的法向量 $\pmb{\nu }$（没有垂直于 $\pmb{\nu }$ 的向量）。对于线性压电和高达 6 阶的完全对称张量，可以获得类似的简化代数条件。