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Mathematics and Mechanics of Solids
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Restricted Invariants on the Space of Elasticity Tensors

Sandra Forte

Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20132 Milano, Italy

Maurizio Vianello

Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20132 Milano, Italy

A linear function defined on the space of elasticity tensors is a restricted invariant under a group of rotations G if it has an invariant restriction to a proper subspace which is larger than the set left fixed by the action of G itself. A necessary and sufficient condition for a function to be a restricted invariant is given using concepts related with isotypic decomposition, Haar integration and G -dependence. The result is applied to characterize isotropic and transversely isotropic restricted invariants.

Key Words: elasticity tensor • invariant anisotropic

This version was published on February 1, 2006

Mathematics and Mechanics of Solids, Vol. 11, No. 1, 48-82 (2006)
DOI: 10.1177/1081286505046483
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