Effect of polymer chains entanglements, crosslinks and finite extensibility on the nonlinear dynamic oscillations of dielectric viscoelastomer actuators

Soft materials exhibiting large deformation under external stimuli have gained an increasing attention in the recent past because of their potential applications in soft transducers aimed at achieving biomimetic actuation. This paper theoretically analyzes the effect of internal properties, including entanglements, crosslinks and finite extensibility of polymer chains along with inherent viscoelastic properties of polymers on the performance of Dielectric Elastomer actuator (DEA) in dynamic modes of actuation. A physics based nonaffine material model proposed by Davidson and Goulbourne is used to model the polymer chains entanglements, crosslinks and finite extensibility. To incorprate the viscoelastic properties, a rheological material model based on the additive decomposition of the isotropic strain energy density into equilibrium and viscous parts is implemented. A computationally efficient method, which relies on the principle of least action is used for extracting the governing equation representing the dynamic motion of the DE actuator. The results demonstrate that DEAs with strong entanglements and crosslinks along with small finite extensibility of polymer chains exhibits lower deformation level in DC dynamic modes of actuation. It is inferred that the strong entanglements and crosslinks in polymer chains enhances the resonant frequency, but debilitate the intensity of vibration of viscoelastic DEAs. Further, the periodicity and stability of the nonlinear oscillations exhibited by the viscoelastic DEAs are assessed by employing the Poincare maps and phase portraits. The results of the present investigation can be applied effectively in bridging the mechanism between the microcosmic polymer chains and macroscopic dynamic behavior of viscoelastic DE actuators.