Three-dimensional deformation and stress distribution in an analytical/computational model of the anterior cruciate ligament

In this study, a constitutive equation for the ACL composite was formulated, and 3-D finite deformations and stress distributions of the ACL were calculated using a finite element method to simulate knee flexion. The mathematical model of the ACL was created by a structurally motivated phenomenological approach. It was assumed that the ACL can be ideally represented as a homogeneous hyperelastic matrix (Mooney–Rivin material) in which two families of densely distributed extensible fibers are embedded; the fibers in one family have a parallel orientation, the other fibers extend radially in eight equally spaced directions. The non-linear stress–strain characteristic exhibited by collagen fibers was represented by a tri-linear curve. Simulation was performed and the results provided some original data; the stress distribution within the ACL body as well as that over the surface, the 3-D defeormations and stress distributions of the ACL viewed from other sides in addition to those from the medial side, and the variations of the stress distribution pattern in the ACL which occured when the tibia was displaced anteriorly or posteriorly.