Hyperelastic materials behavior modeling using consistent strain energy density functions

Abstract

Hyperelastic materials have high deformability and nonlinearity in load–deformation behavior. Based on a phenomenological approach, these materials are treated as a continuum, and a strain energy density is considered to describe their hyperelastic behavior. In this paper, the mechanical behavior characterization of these materials is studied from the continuum viewpoint. For this purpose, the strain energy density is expressed as sum of independent functions of the mutual multiple of principal stretches. These functions are determined by applying the governing postulates on the form of the strain energy density. It is observed that a consistent strain energy density is expressible in terms of the mathematical functions of polynomial, power law, logarithmic and particularly exponential. The proposed strain energy density functions cover modeling both of compressible and incompressible materials. Moreover, the material parameters of these models are calculated based on the correlation between the values of the strain energy density (rather than the stresses) cast from the test data and the theory. In order to investigate the appropriateness of the proposed models, several experimental data for incompressible and compressible isotropic materials under homogeneous deformations are examined in which the predictions of the proposed models show a good agreement with experimental data.