A simple framework for full-network hyperelasticity and anisotropic damage

A formulation of a constitutive behaviour law is proposed for hyperelastic materials, such that damage induced anisotropy can be accounted for continuously. The full-network approach with directional damage is adopted as a starting point. The full-network law with elementary strain energy density based on the inverse Langevin is chosen as a reference law which is cast into the proposed framework. This continuum formalism is then rewritten using spherical harmonics to capture damage directionality. The proposed formalism allows for an efficient (and systematic) expansion of complex non-linear anisotropic constitutive laws. A low order truncated expression of the resulting behaviour is shown to reproduce accurately the stress-strain curves of the exact behaviour laws.