Effect of viscoelasticity on the nonlinear dynamic behavior of dielectric elastomer minimum energy structures

Abstract

Dielectric elastomer minimum energy structure (DEMES) formed by clinging a pre-stretched dielectric elastomer (DE) membrane to the compliant frame possess both material and geometrical nonlinearity. The viscous and hyperelastic nature of the DE membrane and coupling between the compliant frame and membrane forms the basis of these nonlinearities. Practically, DE membrane based DEMES actuator executes the transient motion which is significantly affected by the viscoelastic behavior of the DE membrane. Hence, for an efficient design of such devices, it is very important to analyse the effect of membrane viscoelasticity on the dynamic response of DEMES. In the present work, we have developed an analytical model to analyse the viscoelastic effect of DE membrane on the nonlinear dynamic behavior of the DEMES. In order to incorporate the viscous effect, the Zener rheological model consisting of a spring element connected in parallel to a Maxwell element is employed. The neo-Hookean material model based on the additive decomposition of the isotropic strain energy density into equilibrium and viscous parts is considered. The governing differential equation representing the dynamic behavior of DEMES actuator is derived using Euler–Lagrange equation of motion for non-conservative system. The isotropic viscous stretch is obtained by using the thermodynamically consistent evolution equation. The developed dynamic model predicts the initial shape, DC and AC response, periodicity of the DEMES for different values of viscosity parameter. The result reveals that the onset of equilibrium state delays as viscosity parameter increases. Further, the bending angle of DEMES actuator is significantly affected by the applied electric field and viscoelastic behavior of the DE membrane. Poincaré maps along with phase diagrams are presented to analyse the periodicity of nonlinear oscillation of the system. Further, the structure executes a stability transition (stable-unstable-stable) as the value of viscosity parameter increases. The obtained results can help in robust and efficient designing of DEMES based actuators subjected to dynamic loading.