On the Mullins effect and hysteresis of fibered biological materials: A comparison between continuous and discontinuous damage models

Deformation induced softening is an inelastic phenomenon frequently accompanying mechanical behavior of soft biological tissues. This paper presents and compare continuous and discontinuous damage approaches to model softening effects in fibered materials such as soft biological tissues. The structural model is formulated using the concept of internal variables that provides a very general description of materials involving irreversible effects. We consider the internal variables associated to damage to correspond to separated contributions of the matrix and the fibers. Local damage accumulation is related to two phenomenological variables, the maximum value and the arclength of the effective free energy attained during the loading process, respectively. A local multiplicative decomposition of the deformation gradient into volume-preserving and dilatational parts is used that permits to model the incompressibility property of most types of soft biological tissues. In this context, damage is related only to the isochoric part of the deformation. Finally, simulations of biaxial and uniaxial tests in two directions are used to compare the performance of both models. Numerical simulations indicate that only a mixed model that consider both, continuous and discontinuous, damage models is able to capture the softening phenomenon of soft biological tissues.