  The recent discovery of electro-active polymers has shown great promises in
the field of soft robotics, and was logically followed by experimental,
numerical and theoretical developments. Most of these studies were concerned
with systems entirely covered by electrodes. However, there is a growing
interest for partially active polymers, in which the electrode covers only one
part of the membrane. Indeed, such actuation can trigger buckling instabilities
and so represents a route toward the control of 3D shapes. Here, we study
theoretically the behaviour of such partially active electro-active polymer. We
address two problems: (i) the electrostatic elastica including geometric
non-linearities and partially electro-active strip using a variational
approach. We propose a new interpretation of the equations of deformation, by
drawing analogies with biological growth, in which the effect of the electric
voltage is seen as a change in the reference stress-free state. (ii) we explain
the nature of the distribution of electrostatic forces on this simple system,
which is not trivial. In particular we find that edge effects are playing a
major role in this problem.
