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.