Probabilistic constitutive law for damage in ligaments

A new constitutive equation is presented to describe the damage evolution process in parallel-fibered collagenous tissues such as ligaments. The model is formulated by accounting for the fibrous structure of the tissues. The tissue’s stress is defined as the average of the collagen fiber’s stresses. The fibers are assumed to be undulated and straightened out at different stretches that are randomly defined according to a Weibull distribution. After becoming straight, each collagen fiber is assumed to be linear elastic. Damage is defined as a reduction in collagen fiber’s stiffness and occurs at different stretches that are also randomly defined by a Weibull distribution. Due to the lack of experimental data, the predictions of the constitutive equation are analyzed by varying the values of its structural parameters. Moreover, the results are compared with the available stress–strain data in the biomechanics literature that evaluate damage produced by subfailure stretches in rat medial collateral ligaments.