Modeling mechanical and electromechanical behavior of polymers

This study proposes a compact, hybrid hyperelastic strain-energy formulation for soft elastomers that blends invariants of both the right Cauchy–Green tensor (C) and the right stretch tensor (U), aiming to capture deformation-mode dependence with minimal parameters. The model uses a three-parameter energy function combining an exponential-polynomial term in the first invariant (I1) with a linear term in the second principal invariant of U (i2), and enforces physical admissibility via the Baker–Ericksen inequality. Validation is carried out in two stages: (i) simultaneous fitting against diverse published datasets (including classic vulcanized rubber, natural rubber, silicone rubber, and a very soft polymer hydrogel) under multiple deformation modes (uniaxial, equibiaxial, pure shear), and (ii) new in-house multiaxial experiments on Latex, Oppo, and Ecoflex elastomers. Comparative benchmarking against established hyperelastic models (including Gent–Gent, a stretch-based formulation, and a micromechanical model) shows the proposed formulation achieves consistently low fitting errors across deformation modes while using only three parameters. The framework is then extended to electroactive polymers by coupling the hyperelastic energy to an electro-mechanical free-energy potential using electro-mechanical invariants (e.g., I4–I6), and is verified against published voltage–deformation data for dielectric elastomer VHB 4905 across different pre-stretch conditions, reproducing voltage-induced actuation behavior with high fidelity. Overall, the work provides a computationally efficient constitutive modeling approach for large-deformation elastomers and electroactive polymer systems relevant to soft robotics and smart structures.