On the representation of fourth and higher order anisotropic elasticity tensors in generalized continuum models
Résumé
The classification of all fourth order anisotropic tensor classes for classical linear elasticity is well known. We review the mathematical procedure behind this classification and extend it to fourth order elasticity tensors acting on non-symmetric matrices. These tensors naturally appear in generalised continuum models. Based on tensor-symmetrization we provide the most general form of these tensors for the case of orthotropic, transversely isotropic, cubic and isotropic materials. We give a self-contained presentation and provide a detailed calculation for simple examples.
Mots clés
representation theory group action character elasticity tensor material symmetries relaxed micromorphic model generalized continua AMS 2010 subject classification: 20C (representation theory of groups) 58D19 (group actions and symmetry properties) 20C15 (ordinary representations and characters) 74A30 (nonsimple materials) 74A60 (micromechanical theories) 74B05 (classical linear elasticity) 74M25 (micromechanics) 74Q15 (effective constitutive equations)
representation theory
group action
character
elasticity tensor
material symmetries
relaxed micromorphic model
generalized continua AMS 2010 subject classification: 20C (representation theory of groups)
58D19 (group actions and symmetry properties)
20C15 (ordinary representations and characters)
74A30 (nonsimple materials)
74A60 (micromechanical theories)
74B05 (classical linear elasticity)
74M25 (micromechanics)
74Q15 (effective constitutive equations)
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