Novel fractional viscoelastic model of ligaments for high strain rates
Injuries to cervical spine ligaments are a common occurrence in high-rate events. To build an accurate computational model that describes the mechanical behaviour of these ligaments at a fast strain rate, their viscoelastic behaviour needs to be accounted for. [1] provided a linear viscoelastic model of the anterior longitudinal ligament (ALL) in the cervical spine, describing the instantaneous elastic response and the relaxation behaviour using exponential reduced relaxation functions. A novel fractional order viscoelastic model is proposed, offering the potential to consistently describe viscoelastic behaviour over longer time scales while using fewer parameters. Stress and strain measurements from high-rate uniaxial bone-ligament-bone segment tensile tests were obtained from the original study, and integer and fractional order viscoelastic model results were compared with each other and the experimental stress data. The linear instantaneous elastic properties of the ligaments were confirmed, and a linear instantaneous elastic function was used in both the integer and fractional models. The fractional order model proved competitive with the traditional integer order model at short time scales. Further studies including stress relaxation at both very short and very long time scales are needed to distinguish between models.
