The Deformational Energy in Hyperelastic Bodies and in Biological Tissues

Hyperelastic materials belong to the most important objects of study in the nonlinear theory of elasticity. This theory predicts the behavior of materials exposed to small and large deformations. Owing to the rubber-like properties (e.g., the ability to withstand gigantic deformations returning to the original state or close to it when the load is lifted), hyperelastic materials are widely applied in modern science and technology. Study of the properties of hyperelastic materials is exceptionally important for medical materials science since all soft tissues of human and animal bodies are considered hyperelastic. The energy approach is very important and informative to explore deformation properties in these materials. We calculate the energy W of deformable hyperelastic incompressible bodies under tension using an example of aortic valve biomaterial. We make use of the most common hyperelastic models: the neo-Hookean model, the Mooney-Rivlin (two-parameter) model, the Ogden (first order) model, the polynomial (second order) model, the Yeoh (third order) model, and the Veronda–Westmann model. The statistical indicators of the value of W obtained are analyzed for all models. The mean value of W is 0.377 ± 0.03 J/cm³ (M ± SD), the coefficient of variation being CV = 7.45%. It is established that the average relative deviation of W from the average value for other (linear, bilinear, and exponential) deformation models is 10.08%, which is almost two times higher than that of hyperelastic models (p < 0.05).