Electromechanical Coupling and Piezoelectric Behaviour of (PDMS)-Graphene Elastomer Nanocomposites

Elastomer-based nanocomposites combining polymer flexibility with conductive nanofillers provide lightweight, stretchable systems with tunable electromechanical properties for wearable electronics, soft robotics, and self-powered sensors. However, predicting their nonlinear response remains challenging because the observed piezoelectric-like response arises from strain-dependent interfacial polarization and evolving piezoresistive conduction pathways within heterogeneous microstructures. We introduce a continuum electro-hyperelastic framework combining the Mooney-Rivlin model for large-strain elasticity with a Helmholtz free-energy approach for electrostatic coupling. Analytical expressions for stress, electric displacement, and apparent piezoelectric coefficients are derived and implemented in finite element simulations. The model accurately reproduces the experimental mechanical, dielectric, and electromechanical behaviour of polydimethylsiloxane (PDMS) nanocomposites with 0.1-1 wt% graphene. These show increased stiffness, relative permittivity (from 3.4 to 4.0, ≈18%), and quasi-static d₃₃ coefficients (from -5.6 to -10.0 pC N^-1, ≈80% enhancement). Analytical and finite element method (FEM) results show consistent trends across the full deformation range, with Maxwell stress agreement within 10% at lower deformation levels, while deviations of 33-40% for coupled electromechanical quantities at an axial displacement u_z = ~-1 mm (~16.7% compressive strain) are attributable to three-dimensional shear effects absent from the uniaxial analytical assumption. Simulations reveal that graphene boosts Maxwell stress, yielding a four-fold increase at lower stretch ratios. This reframes PDMS-graphene composites as electro-hyperelastic materials, offering a predictive, extensible framework. It highlights apparent piezoelectricity as an emergent, tunable effect from charge redistribution in a compliant hyperelastic matrix-guiding the design of next-generation flexible devices leveraging field-induced coupling over intrinsic polarization.