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In this work, the Cosserat formulation of geometrically exact beam dynamicsis extended by adding the electric potential as an additional degree of freedomto account for the electromechanical coupling in the Dielectric ElastomerActuators (DEAs). To be able to generate complex beam deformations viadielectric actuator, a linear distribution of electric potential on the beamcross section is proposed. Based on this electric potential, the electric fieldand the strain-like electrical variable are defined for the beam, where thestrain-like electrical variable is work-conjugated to the electricdisplacement. The electromechanically coupled strain energy for the beam isderived consistently from continuum electromechanics, which leads to the directapplication of the material models in the continuum to the beam model. Theelectromechanically coupled problem in beam dynamics is first spatiallysemidiscretized by 1D finite elements and then solved via variational timeintegration. By applying different electrical boundary conditions, differentdeformations of the beam are obtained in the numerical examples, includingcontraction, shear, bending and torsion. The damping effect induced by theviscosity as well as the total energy of the beam are evaluated. Thedeformations of the electromechanically coupled beam model are compared withthe results of the 3D finite element model, where a good agreement of thedeformations in the beam model and that in the 3D finite element model isobserved. However, less degrees of freedom are required to resolve the complexdeformations in the beam model.

An electromechanically coupled beam model for dielectric elastomer actuators