A damage model based on micro-structural approach in soft fibered tissue

An anisotropic damage model for vascular tissue is presented here. The widely used strain energy function in the quasi incompressible framework is exploited on its decoupled form to, additively, take into account the volumetric and the deviatoric contributions. Since a wellestablished neo-Hooke law is used to model the deviatoric part of the isotropic ground substance, this work focus on the contribution of the fibers (collagen from now on) over the overall behavior of the material, which is assumed as the anisotropic contribution to the deviatoric part of the splitting. For this purpose, a micro-structurally or more precisely a micro-sphere-based approach was employed to model the contribution of the fibers. In order to deal with the distribution of the fibers, a von Mises orientation distribution function is incorporated. The mechanical (phenomenological) behavior of the micro-fibers is formulated with an exponential model. Moreover, a directional damage model is incorporated over the fiber contribution through a yet developed thermodynamic formulation, which is directly applied in the hyperelastic formulation of the micro-fibers to gather the softening of the tissue. The way or bridge from micro-structural contribution to the macroscopic response is carried out through a computational homogenization scheme involving a numerical integration over the surface of each micro-sphere. A fitting of material parameters (including damage parameters) are performed from uniaxial tension tests with a least-squarebased iterative scheme which is able to reproduce the experimental curves. Moreover, the model is formulated in a finite element code where a homogeneous deformation in just an element was simulated to test the micro-response. Keywords—Hyperelastic, micro-sphere-based, approach, damage, soft tissue.