On the representation of fourth and higher order anisotropic elasticity tensors in generalized continuum models

• Published in: Mathematics and mechanics of solids
• Main Authors: Valerio d'Agostino, Marco, Martin, Robert J, Lewintan, Peter, Bernardini, Davide, Danescu, Alexandre, Neff, Patrizio
• Format: Journal Article
• Language: English
• Published: SAGE Publications 2024
• Subjects: Mathematics; Mechanics; Physics; Representation Theory; 20C15 (ordinary representations and characters); 74B05 (classical linear elasticity); relaxed micromorphic model; 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); elasticity tensor; 58D19 (group actions and symmetry properties); material symmetries; character; 74M25 (micromechanics); 74A30 (nonsimple materials); representation theory; 74Q15 (effective constitutive equations); group action; 74A60 (micromechanical theories); generalized continua AMS 2010 subject classification: 20C (representation theory of groups)
• ISSN: 1081-2865

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.