Dynamic Modeling and Response Analysis of Dielectric Elastomer Incorporating Fractional Viscoelasticity and Gent Function

Dielectric Elastomer (DE) has been recognized for its remarkable potential in actuation and sensing applications. However, the functionality of most DE materials is restricted by their high viscoelastic effects. Currently, there is a lack of dynamic models that consider both viscoelasticity and stiffening effects. To address this research gap, we propose a fractional-order model in this study. Specifically, the model comprehensively integrates both viscoelastic and stiffening effects under electromechanical coupling, utilizing the principle of virtual work. Further, the effects of the system parameters are analyzed. The results indicate that the fractional-order derivative influences the hysteresis behaviors during the transient state and affects the duration of the transient process. Furthermore, when the system’s energy surpasses a certain threshold, the steady-state response can transition between two distinct potential wells. Through the manipulation of electromechanical coupling parameters, bifurcation can be induced, and the occurrence of snap-through and snap-back behaviors can be controlled. These findings have significant implications for the design and optimization of DE materials in various applications.