Dynamic modeling, simulation and design of smart membrane systems driven by soft actuators of multilayer dielectric elastomers

A multilayer membrane element of absolute nodal coordinate formulation is proposed for dynamic modeling of multilayer dielectric elastomer actuators (DEAs). The coupled dynamics of rigid-body motion and large deformation interacting with electric fields is considered. For the kinematic description, a modified version of the Kirchhoff–Love assumptions is proposed taking the thickness shrinking of the membrane into account. Two material models are introduced based on the Helmholtz free energy in thermodynamics. One is the material model of ideal deformable dielectrics. The other is the large-deformation St. Venant–Kirchhoff model which is a geometrically nonlinear but material linear model. Afterward, the generalized internal forces and their Jacobians are given. The dynamic equations of the systems are solved by the generalized-α algorithm. Finally, three case studies are presented. First, the proposed modeling method is validated by comparing the analytical and simulated solutions. Second, the statics and dynamics of a bending DEA are investigated and the results are compared with the experimental results. Third, an autonomous membrane machine driven by soft DE joints is proposed for space applications and this case is to demonstrate that dynamic modeling and simulation can aid the design of soft machines.