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A numerical and analytical study is made of the macroscopic or homogenized mechanical response of a random isotropic suspension of liquid n -spherical inclusions ( n = 2, 3), each having identical initial radius A , in an elastomer subjected to small quasistatic deformations. Attention is restricted to the basic case when the elastomer is an isotropic incompressible linear elastic solid, the liquid making up the inclusions is an incompressible linear elastic fluid, and the interfaces separating the solid elastomer from the liquid inclusions feature a constant initial surface tension γ . For such a class of suspensions, it has been recently established that the homogenized mechanical response is that of a standard linear elastic solid and hence, for the specific type of isotropic incompressible suspension of interest here, one that can be characterized solely by an effective shear modulus  n in terms of the shear modulus μ of the elastomer, the initial elasto-capillary number eCa = γ /2 μA , the volume fraction c of inclusions, and the space dimension n . This paper presents numerical solutions—generated by means of a recently introduced finite-element scheme—for  n over a wide range of elasto-capillary numbers eCa and volume fractions of inclusions c . Complementary to these, a formula is also introduced for  n that is in quantitative agreement with all the numerical solutions, as well as with the asymptotic results for  n in the limit of dilute volume fraction of inclusions and at percolation . The proposed formula has the added theoretical merit of being an iterated-homogenization solution. 

This work lays out the two-potential framework for the constitutive modeling of dielectric elastomers. After its general presentation, where the constraints imposed by even electromechanical coupling, material frame indifference, material symmetry, and entropy imbalance are all spelled out, the framework is utilized to put forth a specific constitutive model for the prominent class of isotropic incompressible dielectric elastomers. The model accounts for the non-Gaussian elasticity and electrostriction typical of such materials, as well as for their deformation-enhanced shear thinning due to viscous dissipation and their time-dependent polarization due to electric dissipation. The key theoretical and practical features of the model are discussed, with special emphasis on its specialization in the limit of small deformations and moderate electric fields. The last part of this paper is devoted to the deployment of the model to fully describe the electromechanical behavior of a commercially significant dielectric elastomer, namely, the acrylate elastomer VHB 4910 from 3M.