The fast and soft elastic response of thin dielectric elastomers to electric stimulus has established these materials as a paradigm for the development of a technology of low cost, lightweight, high energy density storage, large deformation elastomer actuators (DEAs) and smart materials. These features result in a very significant technology that permits the manufacture of actuators, and smart materials in a wide variety of configurations for applications spanning a wide range of scales. Furthermore, this technology could potentially revolutionize many aspects of consumer devices, energy conservation, and environmental impacts. The present dissertation is concerned with the modeling and simulation of dielectric elastomer materials, two important issues concerning the understanding, and further development of DEAs, and smart materials. First, a thermodynamic analysis is presented to construct the continuum theory of deformable dielectrics.

This theory is general in the sense that it is valid for conservative/ non-conservative materials, and encompasses different material types, i.e. piezoelectric, dielectric, or electrostrictive. Moreover, the constitutive response of the materials to combined electromechanical loading is left to be determined by experiments. Next, the methods of statistical mechanics are utilized to model the hierarchical, and statistical, features of the different material scales present in the structure of dielectric elastomers. In this manner, models for the deformation dependent permittivity and elastic stiffening of dielectric elastomers are constructed. It is found that both of these material features, prominent and concurrent in some dielectric elastomers subject to large levels of deformation, have very important implications in the electromechanical stability, dielectric breakdown and fracture of DEAs.

Finally, the continuum theory of solid dielectrics is used to construct a rigorous finite element method for the simulation of quasi-incompressible dielectric elastomers subject to combined non-uniform electromechanical loading, and high levels of electric field and deformation. This method is intended to assist in the assessment of performance and electromechanical integrity of DEAs and smart materials. The constitutive laws described above, including the deformation dependent permittivity and elastic stiffening of dielectric elastomers, form part of the material library. Some model problems for DEAs are solved to demonstrate the ability of the finite element method code to correctly evaluate the effects of material and geometric non-linearities for a given material constitutive law.