On finite‐strain damage of viscoelastic‐fibred materials. Application to soft biological tissues

The aim of this paper is to introduce a fully three‐dimensional finite‐strain damage model for visco‐hyperelastic fibrous soft tissue. The structural model is formulated using the concept of internal variables that provide a very general description of materials involving irreversible effects. Continuum damage mechanics is used to describe the softening behaviour of soft tissues under large deformation. Modelling of the viscoelastic behaviour is based on a local additive decomposition of the stress tensor into initial and non‐equilibrium parts as resulted from the assumed structure of an uncoupled free energy density function. A local multiplicative decomposition of the deformation gradient into volume‐preserving and dilatational parts is used which permits one to model the incompressible properties of soft biological tissues. The presented formulation and the associated algorithmic discretization were efficiently implemented into a finite element code. In order to show the performance of the constitutive model and it's algorithmic counterpart, some simple examples are included. A more complex three‐dimensional numerical application to ligament mechanics is also presented. Results show that the model is able to capture the typical stress–strain behaviour observed in fibrous soft tissues and seems to confirm the soundness of the proposed formulation.