ABSTRACT
In this paper we present an invariant-free strain energy function that links the commonly used structural tensor approach to anisotropic hyperelasticity with generalised Hooke’s Law for infinitesimal deformations. Herein, a bridge is presented between the modern ‘invariant-free’ hyperelastic strain energy representation that implement orthotropic fourth-order tensors and the conventional approach using scalar invariant measures. It is shown that to form this connection, a set of fourth-order structural tensors must be established. The concept of fourth-order structural tensors is explored in detail in this conference paper, and this leads to a unique decomposition of the Hookean elasticity tensor for infinitesimal deformations. Simply through appropriate selection of finite strain measures the model is naturally extended into the realm of nonlinear elasticity. This invariant-free form of the orthotropic strain energy function is beneficial as it correctly returns isotropic behaviours simply as a result of any apparent material symmetries, and the model preserves consistency with the known Hookean strain energy function in the presence of infinitesimal displacements.
