Modeling dielectric-elastomer minimum-energy structures using dynamic relaxation with appropriate material behavior
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Modeling dielectric-elastomer minimum-energy structures using dynamic relaxation with appropriate material behavior L. Rhode-Barbarigos1, S. Wagner2, S. Adriaenssens1 1 Form Finding Lab, Department of Civil and Environmental Engineering, Princeton University, Princeton, New Jersey 08544, USA 2 Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA ABSTRACT Form-finding describes the process of finding a stable equilibrium shape for a structure under a specific set of loading for a set of boundary conditions. Both physical (experimental) and numerical (computational) form-finding methods have been employed by structural engineers and architects for the design of shape-resistant structures: structures whose behavior depends mostly on their global spatial configuration and less on the properties of their individual components. The shape of dielectric elastomer minimum energy structures (DEMES) depends on the equilibrium between the pre-stressed elastomeric membrane and its inextensible frame. Therefore, DEMES can be modeled and analyzed using structural form-finding techniques. We applied dynamic relaxation (DR), a well-established explicit and efficient numerical formfinding and analysis method, to simulate DEMES equilibrium shapes and predict the elastic energy of DEMES. The DR-DEMES model shows generally good agreement with its physical implementation counterpart, as it captures the equilibrium shape and also the elastic energy in function of shape. However, we found that the numerical and the physical models differ in the pre-stress that is required to obtain a specific equilibrium shape. Therefore, in this study we introduce hyper-elasticity in the DR-DEMES model. With this refinement in physical parameters the DR-DEMES model approaches the pre-stress state of the physical DEMES implementation more closely, while it maintains the computational efficiency of the form-finding approach. We conclude that dynamic relaxation, with its low computational cost, is a powerful tool for the design of novel DEMES applications. INTRODUCTION Dielectric-elastomer minimum-energy structures are composed of a pre-stretched dielectric elastomer membrane adhered to a thin flexible frame [1]. The strain energy of the prestretched membrane is transferred to the frame and deforms it until a strain-energy balance is obtained. Thus DEMES shapes reflect a local or global minimum energy state of the membraneframe structure [2]. This state can be varied electrically by charging the DEMES capacitance. Therefore, DEMES have been proposed for shape-shifting applications in disciplines such as robotics [1], bioengineering [2] and architecture [3]. However, because of their complex behavior the modeling of DEMES remains a challenging task. Due to their non-linear hysteretic behavior, DEMES models usually include complex analytical formulations or finite element implementations [4]. Early analytical formulations assumed linear elastic behavior to describe the structure [5]. Later on more complex nonlinear analy
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