Nonlinear dynamic analysis of anisotropic fiber-reinforced dielectric elastomers: A mathematical approach

Abstract

In this paper, the primary purpose is to have a complete understanding of the importance of fibers in dielectric elastomers due to the influence of fiber orientation in decreasing the applied voltage to simulate the structure and improving mechanical performance. Fibers will also reduce the chance of failure like Wrinkling instabilities and increase the response rate under electric displacement. Implementing the dielectric elastomers with anisotropic structure, despite their great potential, has not adequately analyzed in previous researches. Therefore, based on nonlinear continuum mechanics and large inelastic deformations, the constitutive relationships and equations governing the behavior of viscoelastic dielectric elastomers under harmonic electrical loading are extracted and analyzed in different states. The numerical results, such as phase and frequency-amplitude diagrams and the oscillation, illustrate the dynamic behavior of an anisotropic dielectric elastomer with different fiber orientations. To describe the viscoelasticity behavior of the material, hyperelastic models and the rheological model, are used in conjunction with electrical coupling. Using the theory of anisotropic dielectric elastomers, a geometrically nonlinear formulation under finite deformations is developed by the Euler-Lagrange equations and solved mathematically.