We produce minimal integrity bases for both isotropic and hemitropic invariant algebras (and more generally covariant algebras) of most common bidimensional constitutive tensors and — possibly coupled — laws, including piezoelectricity law, photoelasticity, Eshelby and elasticity tensors, complex viscoelasticity tensor, Hill elasto-plasticity, and (totally symmetric) fabric tensors up to twelfth-order. The concept of covariant, which extends that of invariant is explained and motivated. It appears to be much more useful for applications. All the tools required to obtain these results are explained in detail and a cleaning algorithm is formulated to achieve minimality in the isotropic case. The invariants and covariants are first expressed in complex forms and then in tensorial forms, thanks to explicit translation formulas which are provided. The proposed approach also applies to any $n$-uplet of bidimensional constitutive tensors.

我们为最常见的二维本构张量和可能耦合的定律（包括压电定律、光弹性、Eshelby 和弹性张量、复粘弹性张量、Hill elasto-塑性和（完全对称的）织物张量高达十二阶。解释并激发了协变的概念，它扩展了不变量的概念。它似乎对应用程序更有用。详细解释了获得这些结果所需的所有工具，并制定了清洁算法以实现最小化各向同性的情况。由于提供了明确的转换公式，不变量和协变量首先以复数形式表示，然后以张量形式表示。提议的方法也适用于任何$n$- 二维本构张量的 uplet。