Dynamic modeling of dielectric elastomer-based minimum energy structures with membrane entanglements and finite extensibility

The shape morphing behavior of dielectric elastomer-based minimum energy structures (DEMES) generated by combining an inextensible frame and a pre-stretched dielectric elastomer membrane is unique. The geometrical and material properties of the DE membrane and compliant frame are responsible for the DEMES actuator's shape morphing capabilities. The internal polymer networks of the dielectric elastomer have strong perplexed entanglements and finite extensibility that alter significantly the dynamic behavior of the DE membrane. In this paper, we present a theoretical framework for investigating the impact of intrinsic entanglements and finite extensibility of the dielectric elastomer polymer networks on the DEMES actuator's nonlinear dynamic performance. The nonlinear equation that governs the dynamic motion of the DEMES actuator is obtained by employing the least action principle-based Euler-Lagrange's equation. The main results of the present work prove that the attained initial (equilibrium) and final configurations of the DEMES actuator are altered appreciably by the entanglements and finite extensibility of the polymer chains of the DE membrane. A parametric investigation reveals that the initial pre-stretch associated with the DE membrane and bending stiffness of the compliant frame governs the acquired equilibrium configuration of the DEMES actuator. The framework established provides a constructive platform for integrating the microcosmic features of the DE membrane polymer chains with the macroscopic dynamic behavior of the DEMES actuator.