A micro-electromechanical analysis at finite strain, based on the homogenization technique for composites with periodic microstructure, is presented for the modeling and prediction of the effective behavior of dielectric elastomers with embedded dielectric particles. The elastomer matrix is soft and possesses a relatively low dielectric permittivity, and is modeled as a hyperelastic dielectric material. Two-way electromechanical coupling exists according to which the mechanical deformation and the electric field affect each other. Two types of constitutive equations which govern the behavior of the dielectric elastomers are employed, the second of which exhibits anisotropic response. The inclusions are selected as a ceramic material with a very high dielectric permittivity. Based on the properties of the constituents and their volume fractions, the derived finite strain micro-electromechanics analysis establishes the instantaneous electromechanical concentration tensors which relate the currently applied electromechanical far-field to the local one within the composite. The established concentration tensors readily provide the instantaneous effective electromechanical tangent tensors from which the current response of the composite can be predicted. Applications of the offered analysis are given for the prediction of the induced deformations (usually referred to as actuating strains) of the composite that is subjected to applied electric field. This response is predicted for both traction-free and pre-stretched composites. The effects of various interfacial conditions at the boundaries between the fillers and matrix on the predicted response are shown. These include air-filled holes, rigid inclusions and electrically impermeable holes.
Aboudi, J. (2015). Micro-electromechanics of soft dielectric matrix composites. International Journal of Solids and Structures, 64, 30–41. https://doi.org/10.1016/j.ijsolstr.2015.03.011