The annulus fibrosus plays a central role in biomechanical properties of the intervertebral disc;​ its collagen fibers span the vertebral bodies above and below it, serving to contain nuclear pressure, guide spinal motion, and allow flexibility. The nonlinear, anisotropic material properties of the annulus are largely defined by its highly organized collagenous architecture that can be compared to an angle-ply composite. A particularly useful annular constitutive model would reflect the structure of the annulus in the mathematical formulation. To this end, a strain energy function with separate terms to represent the matrix, the fibers, and the interactions between the constituents has been developed in the research described in this dissertation. Additionally, the tensile and compressive stress-strain response of the annulus in the circumferential direction and the tensile stress-strain response of the annulus in the axial direction both before and after the test specimens have been incubated in a glycadon solution are reported. Using nonlinear regression, the strain energy function is simultaneously applied to these new data and to data from a wide range of experimental protocols reported in the literature to determine values for the material coefficients appearing in the constitutive equation.

It is determined that the elastic modulus of the annulus is essentially continuous through the point of zero strain in the circumferential direction. By choosing experimental protocols that all use a nearly stress-free reference configuration, a comprehensive formulation for the multiaxial annular elastic behavior is developed. Non-enzymatic collagen crosslinking is shown to induce a statistically significant change in the material properties of the annulus in the axial direction. Furthermore, the collagen crosslink density is shown to correlate positively only with the material coefficients of the interactions terms in the strain energy function. As a validation, the strain energy function is extrapolated to predict the results from an experimental protocol that had not been included in the nonlinear regression. In the future, this mechanistic constitutive relationship may be used to correlate specific features of tissue architecture to material properties, providing further insight into the structure-function relationships of the annulus fibrosus.