Adapted and objective Voigt representations in anisotropic nonlinear elasticity

We present a theoretical framework for anisotropic nonlinear elasticity based on the decomposition of strain and stress tensors on a tensorial basis adapted to the local anisotropy of the material. The definition of a local orthogonal basis for the space of second-order symmetric tensors allows the expression of a generic constitutive prescription as a vector field on a six-dimensional space, in which each of the six components represents an independent and objective material function. The presence of local anisotropies is reflected on material symmetries, and we consider the corresponding restrictions on material functions for some important crystal classes and for transversely isotropic and isotropic materials. This formalism aims at a clear and mechanically motivated organisation of the degrees of freedom involved in describing nonlinear elasticity, to facilitate the experimental identification of material functions for their constitutive characterisation.