Hyperelastic and viscoelastic modeling of the ovine intervertebral disc tissue

Intervertebral disc (IVD) carries compressive loads and resists the tensile and shear stress, produced during bending and rotational movements. Hence, identifying its mechanical behavior has always encouraged researchers to propose various models for this tissue. Both viscoelastic and hyperelastic behavior have been observed regarding the IVD. Therefore, this study aims at mechanically characterizing the tissue using the existing hyper- and viscoelastic constitutive models and further discuss the best ones. Three stress relaxation tests were performed on ten ovine cervical IVD samples to evaluate their viscoelastic behavior. Models with linear, quasi-linear, and nonlinear behavior were implemented. For the hyperelastic response, another test was carried out using a load with a constant strain rate to fit seven previously suggested hyperelastic constitutive models to our recorded data. All tests were performed as uniaxial compression. Calculations were made using isotropy and incompressibility assumptions. Results approved the nonlinearity of the tissue’s viscoelastic behavior since the linear models predicted divergent responses for different strain inputs. However, modified superposition theory, featuring a time- and strain-dependent relaxation function, was the most accurate model to predict the IVD response at different strain levels. As for hyperelasticity, Mooney-Rivlin, Yeoh, and Veronda-Westmann models fitted the experimental data with higher R2 values.