Dissipation and recovery in collagen fibrils under cyclic loading: a molecular dynamics study

Collagen protein is the building block of load-bearing tissues like bone, tendons, ligaments, etc. Collagen-based tissues exhibit diverse mechanical properties resulting from the differences in their hierarchical structure from nano to macroscale. The hysteretic behavior exhibited by collagen fibrils, when subjected to cyclic loading, is known to result in both dissipation and the accumulation of residual strain. On subsequent relaxation, partial recovery has also been reported. Cross-links have been considered to play a key role in overall mechanical properties. Here, we modify an existing coarse-grained molecular dynamics model for collagen fibril with initially cross-linked collagen molecules, which is known to reproduce the response to uniaxial strain, by incorporating reformation of cross-links to allow for possible recovery of the fibril. Using molecular dynamics simulations, we show that our model successfully replicates the key features observed in experimental data, including the movement of hysteresis loops, the time evolution of residual strains and energy dissipation, as well as the recovery observed during relaxation. We also show that the approach to steady state is exponential and controlled by a characteristic cycle number that has a value similar to that in experiments. We also emphasize the vital role of the degree of cross-linking on the key features of the macroscopic response to cyclic loading.