  In this work, the Cosserat formulation of geometrically exact beam dynamics
is extended by adding the electric potential as an additional degree of freedom
to account for the electromechanical coupling in the Dielectric Elastomer
Actuators (DEAs). To be able to generate complex beam deformations via
dielectric actuator, a linear distribution of electric potential on the beam
cross section is proposed. Based on this electric potential, the electric field
and the strain-like electrical variable are defined for the beam, where the
strain-like electrical variable is work-conjugated to the electric
displacement. The electromechanically coupled strain energy for the beam is
derived consistently from continuum electromechanics, which leads to the direct
application of the material models in the continuum to the beam model. The
electromechanically coupled problem in beam dynamics is first spatially
semidiscretized by 1D finite elements and then solved via variational time
integration. By applying different electrical boundary conditions, different
deformations of the beam are obtained in the numerical examples, including
contraction, shear, bending and torsion. The damping effect induced by the
viscosity as well as the total energy of the beam are evaluated. The
deformations of the electromechanically coupled beam model are compared with
the results of the 3D finite element model, where a good agreement of the
deformations in the beam model and that in the 3D finite element model is
observed. However, less degrees of freedom are required to resolve the complex
deformations in the beam model.
