Analytical and numerical study of shape memory polymers as intervertebral discs under pure bending

Rupture of the elastic nucleus is one of the most critical challenges in total disc replacement (TDR). Smart polymers (SMPs) could be good candidates for TDR due to their unique properties such as self-healing, shape memory, adhesion control, adhesive capability and self-assembly. Herein, we investigate the behavior of SMPs as intervertebral discs (IVDs) under pure bending loading using analytical and numerical methods. For this purpose, the lumbar disc was considered as a cantilever beam and constitutive equation for pure bending mode using Euler-Bernoulli beam theory were developed in a full cycle of stress-free strain recovery. Numerical evaluation was performed to understand the effect of frozen volume fraction to determine the appropriate SMP for clinical evaluations. We conduct all analyses for the L4-L5 vertebral section because it is the most susceptible lumbar disc to damage. The numerical results show that SMPs with rescued frozen volume fraction are better representative for natural lumbar disc. Our results also indicate that SMPs that replace IVDs should be able to withstand at least 7.8° and 8.93° angle changes for pure bending and flexion-extension loads without any damage.