Hyperelastic materials modelling using a strain measure consistent with the strain energy postulates

In this article, a strain energy density function of the Saint Venant-Kirchhoff type is expressed in terms of a Lagrangian deformation measure. Applying the governing postulates to the form of the strain energy density, the mathematical expression of this measure is determined. It is observed that this measure, which is consistent with the strain energy postulates, is a strain type with the characteristic function more rational than that of the Seth-Hill strain measures for hyperelastic materials modelling. In addition, the material parameters are calculated using a novel procedure that is 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 evaluate the performance of the proposed model of the strain energy density, some test data of pure homogeneous deformations are used. It is shown that there is a good agreement between the test data and predictions of the model for incompressible and compressible isotropic materials.