Dynamic modeling, simulation and design of smart membrane systems driven by soft actuators of multilayer dielectric elas
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ORIGINAL PAPER
Dynamic modeling, simulation and design of smart membrane systems driven by soft actuators of multilayer dielectric elastomers Kai Luo
. Qiang Tian . Haiyan Hu
Received: 18 June 2020 / Accepted: 3 October 2020 Ó Springer Nature B.V. 2020
Abstract A multilayer membrane element of absolute nodal coordinate formulation is proposed for dynamic modeling of multilayer dielectric elastomer actuators (DEAs). The coupled dynamics of rigidbody 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 largedeformation 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-a 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
K. Luo (&) Q. Tian H. Hu Department of Mechanics, School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China e-mail: [email protected] Q. Tian e-mail: [email protected] H. Hu e-mail: [email protected]
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. Keywords Multilayer dielectric elastomers Dynamic modeling ANCF elements Soft robotics Space applications
1 Introduction Dielectric elastomers (DEs) are a sort of electro-active polymers such as silicones, acrylics and PDMS (polydimethylsiloxane). Dielectric elastomer actuators (DEAs) can be made by coating films of DEs on both sides with compliant electrodes (e.g., carbon grease and carbon nanotubes). When an electric voltage is applied, the DE films are compressed in thickness and expanded in area by the electrostatic forces, generating large strains. The DEAs are regarded as one of the most potential artificial muscles due to their superior performances of large actuation strains, fast and high-frequency responses and high energy density. Diverse applications have been proposed such as grippers for soft robotics [1, 2], a soft lifter [3], soft logic switches [4], a micro-adjuster of
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membrane wrinkles for adaptive infrared reflection [5], soft docking for space applications [6, 7] and soft wings for flying microrobots [8]. Conventional DEAs generated active strains below 50%. In 2000, Pelrine et al. demonstrated that prestretches of
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