Model and design of dielectric elastomer minimum energy structures

Fixing a prestretched dielectric elastomer actuator (DEA) on a flexible frame allows transformation of the intrinsic in-plane area expansion of DEAs into complex three-dimensional (3D) structures whose shape is determined by a configuration that minimizes the elastic energy of the actuator and the bending energy of the frame. These stuctures can then unfold upon the application of a voltage. This article presents an analytical modelling of the dielectric elastomer minimal energy structure in the case of a simple rectangular geometry and studies the influence of the main design parameters on the actuator's behaviour. The initial shape of DEMES, as well as the actuation range, depends on the elastic strain energy stored in the elastomeric membrane. This energy depends on two independent parameters: the volume of the membrane and its initial deformation. There exist therefore different combinations of membrane volume and prestretch, which lead to the same initial shape, such as a highly prestretched thin membrane, or a slightly prestretched thick membrane. Although they have the same initial shape, these different membrane states lead to different behaviour once the actuation voltage is applied. Our model allows one to predict which choice of parameters leads to the largest actuation range, while specifying the impact of the different membrane conditions on the spring constant of the device. We also explore the effects of non-ideal material behaviour, such as stress relaxation, on device performance. (paper)