On the constitutive modelling of biological soft connective tissues. A general theoretical framework for strongly anisotropic fiber-reinforced composites at finite strain

This research describes a general theoretical framework for the constitutive modeling of biological soft connective tissues. The approach is based on the theory of continuum fiber-reinforced composites at finite strain. Explicit expressions of the stress tensors in the material and spatial configurations are first established in the general case, without precluding any assumption regarding possible kinematic constraints or any particular mechanical symmetry of the material. Original expressions of the elasticity tensors in the material and spatial configurations are derived and new coupling terms, characterizing the interactions between the constituents of the continuum composite material, are isolated and their biological significance highlighted. Further to this, expressions of the elasticity tensors are degenerated in order to take into account special type of material symmetries. Kinematic constraints and constitutive requirements are also briefly discussed.