Modeling Fatigue Failure of Cartilage and Fibrous Biological Tissues Using Constrained Reactive Mixture Theory

Abstract

Fatigue failure in biological soft tissues plays a critical role in the etiology of chronic soft tissue injuries and diseases such as osteoarthritis (OA). Understanding failure mechanisms is hindered by the decades-long timescales over which damage takes place. Analyzing the factors contributing to fatigue failure requires the help of validated computational models developed for soft tissues. This study presents a framework for fatigue failure of fibrous biological tissues based on reaction kinetics, where the composition of intact and fatigued material regions can evolve via degradation and breakage over time, in response to energy-based fatigue and damage criteria. Using reactive constrained mixture theory, material region mass fractions are governed by the axiom of mass balance. Progression of fatigue is controlled by an energy-based reaction rate, with user-selected probability functions defining the damage propensity of intact and fatigued material regions. Verification of this reactive theory, which is implemented in the open-source FEBio finite element software, is provided in this study. Validation is also demonstrated against experimental data, showing that predicted damage can be linked to results from biochemical assays. The framework is also applied to study fatigue failure during frictional contact of cartilage. Simulating previous experiments suggests that frictional effects slightly increase fatigue progression, but the main driver is cyclic compressive contact loading. This study demonstrated the ability of theoretical models to complement and extend experimental findings, advancing our understanding of the time progression of fatigue in biological tissues.