A residual stiffness-based model for the fatigue damage of biological soft tissues

Abstract Biologically-derived and chemically-treated collagenous tissues such as glutaraldehyde-treated bovine pericardium (GLBP) are widely used in many medical applications. The long-term cyclic loading-induced tissue fatigue damage has been identified as one of the primary factors limiting the durability of such medical devices and an in-depth understanding of the fatigue behaviors of biological tissues is critical to increase device durability. However, a limited number of fatigue damage experiments were performed on biological tissues due to complexity and time-consuming nature of such fatigue experiments. Consequently, accurate constitutive models for fatigue damage are also lacking. In this study, we performed a rigorous fatigue experiment on GLBP tissues. The stress, strain and permanent set at a maximum of 8 different fatigue cycles, up to 15 million cycles, were obtained, which demonstrated a nonlinear stress softening and a nonlinear permanent set accumulation. Based on the experimental data, we developed a novel residual stiffness-based fatigue model. The fatigue model considers the fatigue-induced reduction of initial stiffness and stiffening effect, in contrast to our previous damage-based model that only considered the fatigue-induced reduction of the initial stiffness. Moreover, a new constitutive relation was proposed to describe how the fatigue life (the cycle number at failure) depends on the equivalent strain, analogous to the stress versus fatigue life (S-N) curve for traditional engineering material. The new fatigue model can characterize the stress softening and nonlinear permanent set effects when referring to the pre-fatigued configuration. It can also describe the nonlinear stress stiffening effect when referring to the post-fatigued configuration. The model predictions are in good agreement with the experiment. The experimental results and the novel model could be applied to fatigue analyses of medical devices to improve the durability.