Analytical Modeling of Clamped Dielectric Elastomer Strip Membranes Exhibiting Necking Effect

Abstract

Dielectric elastomer (DE) strip membranes permit to design mechatronic transducers enabling large-strain, low-energy consumption, and compactness. To optimize the design of strip DE actuators by means of software tools, as well as to synthesize accurate control algorithms, analytical models have to be developed. Modeling of strip DE membranes clamped at both ends, having a nearly unitary aspect ratio (i.e., the ratio between the membrane length and width), turns out to be a particularly challenging task. In fact, such membranes are affected by necking and inhomogeneous deformations. Those phenomena are difficult to be described via analytical models, making it necessary to rely on computationally involved finite element tools. In this paper, we develop a modeling framework which permits to describe behavior of clamped DE strips in an analytical fashion. The model is based on an anisotropic free-energy function, which allows to map the effects of the clamping into the material behavior. A comparison between analytical and finite element models is presented for membranes having different aspect ratios, both in simulation and experimental case of studies, showing a remarkable agreement.