Symmetry classes and harmonic decomposition for photoelasticity tensors

Coordinate-free Characterization of the Symmetry Classes of Elasticity Tensors

“…In accordance with this definition, there are eight symmetry classes, as shown by Forte and Vianello [10], Chadwick et al [5], Ting [22], Bóna et al [4]. Another definition of the symmetry class has been proposed by Hou and Del Piero [26] and discussed by Forte and Vianello [11]; this definition results in ten symmetry classes.…”

Symmetry classes for odd‐order tensors

“…In the present situation, tensor spaces will be decomposed into O(3)-invariant spaces. Such a decomposition has been widely used in the mechanical community for studying anisotropic elasticity [5,6,14,15] and is often referred to as the harmonic decomposition. In order to present our results in self-contained way, basic definitions of the harmonic decomposition are summed up here.…”

“…If, for a representation ρ on E, the only G-invariant spaces are the proper ones, the representation will be said to be irreducible. For a compact Lie group, the 15 In the following G will always represent a compact real Lie group, so this specification will mostly be omitted.…”

Décomposition harmonique des tenseurs – Méthode spectrale

“…Ce tenseur correspond physiquement à celui de l'effet Kerr [11]. Le s.-e.-v des tenseurs photoélastiques à la structure suivante :…”

“…17) ce qui correspond au spectre de la décomposition harmonique effectuée dans [11]. Le même calcul effectué par la méthode de Spencer aurait été beaucoup plus compliqué à mener.…”