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Computation of minimal covariants bases for 2D coupled constitutive laws

Abstract : 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.
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Contributor : Boris Kolev <>
Submitted on : Thursday, July 2, 2020 - 8:58:47 PM
Last modification on : Saturday, October 10, 2020 - 3:26:00 AM
Long-term archiving on: : Thursday, September 24, 2020 - 6:17:15 AM


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  • HAL Id : hal-02888267, version 1
  • ARXIV : 2007.01576


Boris Desmorat, Marc Olive, Nicolas Auffray, Rodrigue Desmorat, Boris Kolev. Computation of minimal covariants bases for 2D coupled constitutive laws. 2020. ⟨hal-02888267⟩



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