Finite Deformation of a Dielectric Cylindrical Actuator: A Continuum Mechanics Approach

Abstract

In current scenario, research in smart material deformations introduces a new classical continuum mechanics-based deformation approach that have enough potential to make a bold move from the conventional deformation approaches to a newer one. In line with that, the present work is concerned with the finite deformation modeling of a dielectric cylindrical actuator (DCA) with compliant electrodes. Herein, a common usage of DCA is to realize simultaneous axial and radial displacement with an electric field application across the thickness of the cylinder. Accordingly, we first presented an unified classical continuum mechanics-based approach to model the finite deformation of an incompressible isotropic electro-elastic cylindrical actuator under an applied electric field. Next, we formulate the constitutive relationships following the second law of thermodynamics with an amended form of energy function. This amended energy function successfully resolved the difficulty in the physical interpretation of Maxwell stress tensor exists in the literature under large deformations. In addition, we also propose a new energy density function for a class of an incompressible isotropic electro-elastic material. Further, we obtain a finite electro-elastic deformation model for a dielectric cylindrical actuator (DCA). Finally, we validated the obtained electro-elastic deformation model with their corresponding experimental data existing in the literature.