Three-dimensional Deformation and Stress Distribution of the Anterior Cruciate Ligament in the Knee (Constitutive Formulation and Finite Element Model of a Fiber-Reinforced Hyperelastic Material)

Highly variable deformations of a human anterior cruciate ligament (ACL) cannot be adequately quantified by one-dimensional, localized measurements and/or analyses. This paper describes a new structurally-motivated phenomenological approach. Such assumption was made that the ACL ligament can be idealized as being composed of a homogeneous matrix in which two non-interacting families of densely distributed extensible fibers are embedded. A non-linear stress-strain characteristic exhibited by multiple collagen fibers was represented by the multi-linear curve. Then a constitutive equation for the ACL composite was formulated. Using the finite element method, finite deformation and stress distribution of the ACL as a function of knee flexion were introduced through simulation.