Analysis of microstructure-based network models for the nonlinear electrostriction modeling of electro-active polymers

Relaxor ferroelectric polymers are a unique branch of electroactive polymers (EAPs) that generate high electromechanical strain with relatively low hysteresis and high nonlinearity. Polyvinylidene fluoride-based EAPs possess these qualities due to the semicrystalline nature of their microstructure. The interactions of electric dipoles within the microstructure of the material generate large strains under an external electric field, and the reduced crystalline domain sizes yield a relaxor effect by exhibiting low hysteresis and hyperelastic properties. This phenomenon has been partially modeled by previous works, but micro-electro-mechanisms for electrostriction in the microstructure have been largely ignored. This study focuses on the effects of various microstructural frameworks on the nonlinear dielectric behavior of dipole-based, semicrystalline EAPs. The Helmholtz free energy function of a microscopic representative volume element (RVE) is composed of an electrostatic energy and an elastic energy. The dipole-dipole interaction energy is prescribed for the electrostatic forces observed among the crystalline regions, and the elastic component attributed to the relaxation of the amorphous phase is modeled by the hyperelastic eight-chain model, which is microstructure-based. The RVE of the system is modeled by a central dipole surrounded by dipoles whose relative spatial locations are determined by a probability distribution function (PDF). The hyperelastic amorphous phase constitutes the volume separating the central and surrounding dipoles. The free energy of the RVE is implemented into a continuum description of the equilibrium of the system to obtain electromechanical relations. Additionally, this electromechanical response data is applied to a 1D structural mechanics model for simulating the large deformation of a multi-layered beam. The effects of microstructure on electrostrictive coupling are explored by varying the centers and deviations of dipole locations within the PDF. Discrete microstructural arrangements representing 3-chain network averaging schemes may be studied alongside more continuous ellipsoidal or random models of dipole spatial arrangements. The simulation results of the PDF-based networks are in good agreement with experimental data. The results indicate that the electrostrictive behavior of EAPs is strongly dependent on (1) the relative dipole spatial locations and (2) the extent of the regions containing dipoles, which represent crystalline domains. The model finds that adding extra crystalline domains in the network averaging schemes generates a better characteristic behavior due to a broader averaging of spatial orientations. These results offer a gateway to predicting microstructurally-dependent dipole-based behavior that can lead to the predictive theoretical tailoring of microstructures for desired electromechanical properties.