A lumped parameter model for strip-shaped dielectric elastomer membrane transducers with arbitrary aspect ratio

Dielectric elastomer (DE) membrane transducers allow to achieve large strain, low energy consumption, low-noise, and highly compact mechatronic devices. To optimize the design of membrane DEs via numerically efficient software tools, as well as to develop accurate control and self-sensing algorithms, a lumped parameter model is required. In the case of rectangular DE strips clamped at both ends and subject to a uniaxial in-plane load, the resulting necking and inhomogeneous deformation turn out to be challenging to be described via standard lumped models, thus making it necessary to rely on numerically involved finite element (FE) tools. In this paper, we present a novel modeling framework that permits to accurately describe clamped DE membranes with generic aspect ratio in a control-oriented fashion. The model is grounded on an anisotropic free-energy function, which maps the inhomogeneities due to clamping within the constitutive membrane behavior. In this way, a lumped description of the DE can be obtained in terms of average stress and stretch quantities. After presenting the model, an extensive validation is performed by means of comparative studies with FE simulations as well as experimental results. It is observed how the proposed model permits to accurately describe the electro-mechanical response of clamped DE membranes for a wide range of aspect ratios, including nearly-uniaxial, nearly-pure shear, as well as intermediate configurations.