A non-linear stochastic approach of ligaments and tendons fractional-order hereditariness

In this study the non-linear hereditariness of knee tendons and ligaments is framed in the context of stochastic mechanics. Without losing the possibility of generalization, this work was focused on knee Anterior Cruciate Ligament (ACL) and the tendons used in its surgical reconstruction. The proposed constitutive equations of fibrous tissues involves three material parameters for the creep tests and three material parameters for relaxation tests. One-to-one relations among material parameters estimated in creep and relaxations were established and reported in the paper. Data scattering, observed with a novel experimental protocol used to characterize the mechanics of the tissue, was modelled as the outcome of the random mechanical parameters. The numerical example proposed in the paper shows that for an assigned probability density function of the material random parameters, the parameters of the probability density function (pdf) may be obtained by a statistical analysis of the experimental data.