Electro-active polymers (EAPs) have emerged as a new class of active materials, which produce large deformations in response to an electric stimulus. EAPs have attractive characteristics of being lightweight, inexpensive, stretchable, and flexible. Additionally, EAPs are conformable, and their properties can be tailored to satisfy a broad range of requirements. These advantages have enabled many target applications in actuation and sensing. A general constitutive formulation for isotropic and anisotropic electro-active materials is developed using continuum mechanics framework and invariant theory. Based on the constitutive law, electromechanical stability of the electro-elastic materials is investigated using convexity and polyconvexity conditions. Implementation of the electro-active material model into a commercial finite element software (ABAQUS 6.9.1, PAWTUCKET, RI, USA) is presented. Several boundary and initial value problems are solved to investigate the actuation and sensing response of isotropic and anisotropic dielectric elastomers (DEs) subject to combined mechanical and electrical loads. The numerical response is compared with experimental results to validate the theoretical model. For the constitutive formulation of the electro-elastic materials, invariants for the coupling between two families of electro-active fibers (or particles) and the applied electric field are introduced. The effect of the orientation of the electro-active fibers and the electric field on the electromechanical coupling is investigated under equibiaxial extension. Advantage of the constitutive formulation derived in this research is that the electromechanical coupling can be illustrated easily by choosing invariants for the deformation gradient tensor, the electro-active fibers, and the electric field. For the electromechanical stability, it is shown that the stability can be controlled by tuning the material properties and the orientation of the electro-active fibers. The electromechanical stability condition is useful to build a stable free energy function and prevent the instabilities (wrinkling and electric breakdown) for the electro-elastic materials. The invariant-based constitutive formulation for the electro-elastic materials including the isotropic and anisotropic DEs is implemented into a user subroutine (UMAT in ABAQUS: user defined material) by using multiplicative decomposition of the deformation gradient and the applicability of the UMAT is shown by simulating a complicated electromechanical coupling problem in ABAQUS/CAE. Additionally, the static and dynamic sensing and actuation response of tubular DE transducers (silicone and polyacrylate materials) with respect to combined electrical and mechanical stimuli is obtained experimentally. It is shown that the silicone samples have better dynamic and static sensing characteristics than the polyacrylate. The theoretical modeling accords well with the experimental results. / Ph. D.

The thesis is devoted to study of continuum mechanics and thermodynamics and the related mathematical analysis. It consists of four self-contained chapters dealing with different aspects. The first chapter focuses on peridynamics, a non-local theory of continuum mechanics, and its relation to conventional local theory of Cauchy-Green elasticity. Similar compar- isons has been used for proving consistency and for determining some of the material coefficients in peridynamics, provided the material parameters in the local theory are known. In this chapter the formula for the non-local force-flux is computed in terms of the peridynamic interaction, relating the fundamental concepts of these two theories and establishing hence a new connection, not present in the previous works. The second and third chapters are both devoted to Rate-Independent Systems (RIS) and their applications to continuum mechanics. RIS represents a suitable approximation when the internal, viscous, and thermal effects can be neglected. RIS has been proven to be useful in modeling hysteresis, phase transitions in solids, elastoplasticity, damage, or fracture in both small and large strain regimes. In the second chapter the existence of solutions to an evolutionary rate-independ- ent model of Shape Memory Alloys (SMAs) is proven. The model...