Transversely isotropic linear elastic material model

Abstract

In this article, a linear elastic constitutive model for transversely isotropic material is derived based on the invariant theory and expressed in a coordinate-invariant form. For a transversely isotropic elastic solid, the strain energy or correspondingly the complementary strain energy depends on five invariants: three invariants of the stress tensor (or strain) and two combined invariants of the structural tensor and strain tensor (or stress).