When an electric voltage is applied across the thickness of a thin layer of an dielectric elastomer, the layer reduces its thickness and expands its area. This electrically induced deformation can be rapid and large, and is potentially useful as soft actuators in diverse technologies. Recent experimental and theoretical studies have shown that, when the voltage exceeds some critical value, the homogenous deformation of the layer becomes unstable, and the layer deforms into a mixture of thin and thick regions. Subsequently, as more electric charge is applied, the thin regions enlarge at the expense of the thick regions. On the basis of a recently formulated nonlinear field theory, this paper develops a meshfree method to simulate numerically this instability.

A subdomain collocation method based on Voronoi diagrams and reproducing kernel approximation is presented. The unkonwn field variables are approximated via reproducing kernel approximation. The body integration arising from the numerical evaluation of Galerkin weak form is converted into much cheaper contour integration along the boundary of each Voronoi cell. The Voronoi cells also provide an natural structure to perform h-adaptivity.