Polyconvex hyperelastic modeling of rubberlike materials

In this work a number of selected, isotropic, invariant-based hyperelastic models are analyzed. The considered constitutive relations of hyperelasticity include the model by Gent (G) and its extension, the so-called generalized Gent model (GG), the exponential-power law model (Exp-PL) and the power law model (PL). The material parameters of the models under study have been identified for eight different experimental data sets. As it has been demonstrated, the much celebrated Gent's model does not always allow to obtain an acceptable quality of the experimental data approximation. Furthermore, it is observed that the best curve fitting quality is usually achieved when the experimentally derived conditions that were proposed by Rivlin and Saunders are fulfilled. However, it is shown that the conditions by Rivlin and Saunders are in a contradiction with the mathematical requirements of stored energy polyconvexity. A polyconvex stored energy function is assumed in order to ensure the existence of solutions to a properly defined boundary value problem and to avoid non-physical material response. It is found that in the case of the analyzed hyperelastic models the application of polyconvexity conditions leads to only a slight decrease in the curve fitting quality. When the energy polyconvexity is assumed, the best experimental data approximation is usually obtained for the PL model. Among the non-polyconvex hyperelastic models, the best curve fitting results are most frequently achieved for the GG model. However, it is shown that both the G and the GG models are problematic due to the presence of the locking effect.

Automated summary

This work analyzes selected isotropic invariant-based hyperelastic models, identifying material parameters through curve fitting for eight experimental datasets. The Gent model may not always provide acceptable data approximation quality, and conditions proposed by Rivlin and Saunders often lead to best curve fitting results but are contradictory with polyconvexity requirements. The assumption of polyconvexity results in a slight decrease in curve fitting quality, with the power law model usually achieving the best approximation when energy polyconvexity is assumed. Among non-polyconvex models, the generalized Gent model frequently achieves the best curve fitting results, although both Gent and the generalized Gent models are problematic due to the locking effect.