Model analysis to investigate the contribution of ground substance to ligament stiffening

In our previous study, tensile tests on ligament and fascicle from swine hind limbs revealed that the tangent modulus in the stress–strain curve of the ligaments, i.e. stiffness, was higher than that of the fascicles. Since the ligament is a composite of fascicles and ground substance whose stiffness is almost negligible, our finding was contrary to a current notion about the strength of materials that a composite can never be stronger than its constituent elements. To answer this puzzling question, we hypothesized that the fascicles’ stiffness is not uniform along the longitudinal axis, and that because the weaker portions are mainly elongated during tensile tests, their stiffness is underestimated. During tensile testing on ligament, the weaker portions of fascicles are reinforced by the stronger portions of the adjoining fascicles. In this study, to confirm that our hypothesis hold, we performed tensile tests on fascicles, thereby finding that fascicles do not elongate uniformly. Next, we developed a continuous elastic model, by taking into account a fascicle's kinematic non-uniformity along its longitudinal direction and mechanical interaction between fascicles and the ground substance. Simulation results demonstrated the inverse characteristics between ligaments and fascicles. Furthermore, the results helped us to understand ligament's failure mechanism.