Biomechanical stresses in a residually stressed idealized intervertebral disc

Intervertebral discs are soft biological tissues that have an important function in accommodating the movement of the spine during which the discs deform and act as shock absorbers to protect the spine from damage. Therefore, it is important to understand and model their mechanical properties to predict their response under various loading conditions. Towards this end, a simplified geometry of a single intervertebral disc, consisting of the nucleus pulposus within the anulus fibrosus, is modelled as a nonlinearly elastic solid. Pre-existing residual stresses in the unloaded state are taken into account in the radial and circumferential directions. In particular, the nucleus pulposus is considered to be isotropic, which becomes anisotropic with residual stress, while the anulus fibrosus consists of fibre families described by two standard reinforcing anisotropic models. The stress components associated with compressive and torsional deformations are determined analytically and illustrated for a simple constitutive model.