Finite element implementation of a stochastic three dimensional finite-strain damage model for fibrous soft tissue

A fully three dimensional finite-strain damage model for fibrous soft tissue is here presented. The model assumes uncoupled contributions for the matrix and collagen fibers, and uncoupled bulk and deviatoric response over any range of deformations. A simple isotropic damage mechanism within the framework of continuum damage mechanics has been used to describe the softening behavior under deformation for the matrix. On the other hand, statistical aspects related to the length distribution of the reinforcing fibers lead to a damage model for the reinforcing material. As a result, a general theoretical framework for constitutive modeling of biological soft tissue with continuum damage is obtained. The formulation has been implemented in a finite element framework and the capabilities of the model tested in three computer simulations of inhomogeneous boundary value problems. The results show the quadratic rate of convergence of the implementation and the ability to describe typical stress–strain behavior of fiber reinforced soft tissues.