A general framework for the numerical implementation of anisotropic hyperelastic material models including non-local damage

The highly nonlinear mechanical behaviour of soft tissues solicited within the physiological range usually involves degradation of the material properties. Mechanically, having these biostructures undergoing such stretch patterns may bring about pathological conditions related to the steady deterioration of both collagen fibres and material’s ground substance. Tissue and subject variability observed in the phenomenological mechanical characterisation of soft tissues often hinder the choice of the computational constitutive model. Therefore, this contribution brings forth a detailed overview of the constitutive implementation in a computational framework of anisotropic hyperelastic materials with damage. Surmounting the challenge posed by the mesh dependency pathology requires the incorporation of an integral-type non-local averaging, which seeks to include the effects of the microstructure in order to limit the localisation phenomena of the damage variables. By adopting this approach, one can make use of multiple developed material models available in the literature, a combination of those, or even propose new models within the same numerical framework. The numerical examples of three-dimensional displacement and force-driven boundary value problems highlight the possibility of using multiple material models within the same numerical framework. Particularities concerning the considered material models and the damage effect implications to represent the Mullins effect, induced anisotropy, hysteresis, and mesh dependency are discussed.