Modeling of Passive Behavior of Soft Tissues Including Viscosity and Damage

The mechanical properties of soft tissues depend strongly on the orientation of their fibers, and usually they have a highly nonlinear behavior: their stiffness increases as they are stretched. We are interested here in the passive behavior of soft tissues, when subjected to significant stretches, possibly leading to damage. In this paper we develop a model for a transversely isotropic material that has a damageable viscoelastic behavior. This model is then used to simulate the damage evolution of the tissue. The model is developed with the underlying framework of hyperelasticity, and the corresponding strain energy has different parts associated to different contributions to the material behavior: volumetric, isotropic, anisotropic and dissipative contributions. Since soft tissues are almost incompressible we use a multiplicative split of the deformation gradient into a volume preserving part and a part with (small) volume changes. The anisotropic behavior is characterized by the existence of a family of fiber directions within the tissue. The viscoelastic behavior associated with the non-equilibrium stress is treated as a standard solid material with M Maxwell elements simulating the fact that the response of soft tissues is almost independent of the loading frequency. The total damage is modeled by splitting the energy degradation into one isotropic part and one anisotropic part. That is, we can have fiber degradation independently of the damage of the surrounding matrix.

The model is implemented in the commercial Finite element software ABAQUS and the tissue behavior is described by an user subroutine (UMAT).

Qualitative features of the model are illustrated and discussed.