Development of a continuum damage model to predict accumulation of sub-failure damage in tendons

Abstract

Many painful and physically debilitating conditions involve sub-failure mechanical damage to seemingly intact connective tissues such as tendons and ligaments. We found that the amount of denatured collagen in rat tail tendon (RTT) fascicles increased over experiments of cyclic loading to a constant load level (creep cyclic fatigue) with fluorescently tagged collagen hybridizing peptides (CHPs) that bind to denatured collagen. To better understand tendon sub-failure damage progression, computational modeling of tendon materials via finite element analysis in FEBio has been conducted. The objective of this project was to develop, implement, and test the ability of a new continuum damage mechanics (CDM) model in FEBio to represent the sub-failure damage behavior seen in our RTT fascicle creep cyclic fatigue experimental data.There appeared to be two distinct mechanisms responsible for the creep cyclic fatigue softening behavior of RTT fascicles over the number of cycles to failure: the preconditioning effect and overall collagen damage. In our finite element (FE) models, the RTT fascicle undamaged elastic constitutive material was composed of a matrix and fibers described by the Coupled Veronda-Westmann and exponential-linear materials. This undamaged elastic material was convolved with a modified CDM model adapted from Balzani et al., in 2012.The novelty of the Balzani damage model is the inclusion of two interrelated mechanisms described as continuous and discontinuous damage. The continuous damage formulation calculates damage accumulation during the loading and reloading of each new cycle, while the discontinuous damage approach accumulates damage from the maximum strain over the loading history to the current time. We modified the Balzani damage model formulations to represent exponential and sigmoidal increases in damage marked by the preconditioning effect and collagen damage in RTT fascicles as functions of continuous and discontinuous damage. The original Balzani damage model was first verified, then the modified CDM model was implemented into FEBio and used to reproduce the sample specific experimental creep cyclic fatigue stress-strain data as well as predict incremental cyclic fatigue. The resulting model will be useful for future experimental and computational studies of damage mechanics to understand tendon pathologies.