Failure criterion of collagen fiber: Viscoelastic behavior simulated by using load control data

A nonlinear Zener model is developed to model the viscoelastic behavior of collagen fibers, a building block of the biological soft tissues in the skeletal system. The effects of the strain rate dependency, the loading history, rest, and recovery on the stress-strain relationship of collagen fibers were investigated using the Zener model. The following loading conditions were simulated: (1) the stress relaxation after cyclic loading, (2) the constant strain rate loading before and after cyclic loading (stabilization) and post recovery, and (3) the constant strain rate loading over a wide range of loading rates. In addition, we explored the critical values of stress and strain using different failure criteria at different strain rates. Four major findings were derived from these simulations. First of all, the stress relaxation is larger with a smaller number cycles of preloading. Second, the strain rate sensitivity diminishes after the stabilization and recovery from resting. Third, the stress-strain curve is dependent on the strain rate except for extreme loading conditions (very fast or slow rates of loading). Finally, the strain energy density (SED) criteria may be a more practical failure criterion than the ultimate stress or strain criterion for collagen fiber. These results provide the basis for interpretation of the viscoelastic and failure behaviors of complex structures such as spinal functional units with more economical CPU than full finite element modeling of the whole structure would have required.