论文标题
2D耦合定律的最小协变量基础计算
Computation of minimal covariants bases for 2D coupled constitutive laws
论文作者
论文摘要
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对称）织物张量长达十二阶。解释和动机的协变量的概念扩展了不变性的概念。对于应用程序，它似乎更有用。详细说明了获得这些结果所需的所有工具，并制定了清洁算法以在各向同性情况下达到最小性。不变的和协变量首先以复杂的形式，然后以张力形式表达，这要归功于提供的明确的翻译公式。提出的方法还适用于任何$ n $ n $ upirentional构型张量。
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.
