Hyperelastic model for nonlinear elastic deformations of graphene-based polymer nanocomposites

Graphene-based polymer nanocomposites (PNCs) are increasingly important in engineering applications involving large deformations. However, the nonlinear behavior of these materials has not been thoroughly studied. Current models do not address the specific nonlinear effects of graphene nanofillers under large strains, lack sufficient comparison with experimental data, and primarily focus on uniaxial behavior without exploring biaxial responses, which are relevant in technological applications. This study investigates PNCs composed of silicone elastomer and graphene nanoplatelets (GNPs). We present experimental tests conducted in both simple tension and biaxial inflation on circular membranes. A homogenized hyperelastic model is developed, incorporating distinct contributions from the matrix and the nanofiller. Specifically, we introduce a novel strain energy function for the nanofiller contribution, tailored to reproduce the observed experimental behavior. The model accurately predicts the nonlinear elastic response of the studied PNCs across varying contents of GNPs. The proposed strain energy function is implemented in MATLAB to obtain an exact numerical solution for the inflation of circular PNC membranes. Finally, to demonstrate its broader applicability, the hyperelastic model is applied to additional experimental data from other PNCs found in the literature. This model contributes to establishing a robust framework for the effective use of PNCs.