Analysis of parameters of deformation models of hyperelastic biotissues

This article is intended for specialists involved in calculating the deformation behavior of hyperelastic materials. For the overwhelming majority of materials, with increasing deformation, the proportional relationship between stress and strain ceases to hold after a certain value of external stress applied to the sample. Elastic reversible deformation is replaced by reversible inelastic, and with a further increase in stress by inelastic with residual deformation when unloading the sample. However, there are materials that can experience huge (hundreds of percent) deformations and then return to their original state or close to it. The Poisson ratio of such materials is close to the theoretical limit of 0.5, and the change in their volume during deformation is small. Such materials are called elastomers, rubber-like or hyperelastic. The authors of the report share their experience of calculating the deformation behavior of hyperelastic materials in the Mathcad 15.0 computer algebra system and compare them with the results of calculating these properties using other models. The list of models corresponds to their “rating” in the world literature on finite deformation mechanics. A total of 7 models were analyzed: neo-Hooke, Mooney-Rivlin (2-parameters), Mooney-Rivlin (3-parameters), Ogden, polynomial, Veronda-Westmann and Yeo. The predictive proximity of the results of model calculations to experimental data was estimated using mathematical statistics indicators. An example of calculating the parameters of a hyperelastic deformation model of a biomaterial (human skin of the back) is given.