Complex bifurcation maps in electroelastic elastomeric plates

Stress-strain relationships for rubbery materials are highly non-linear. In this work, a particular configuration of electroactive material is considered: an isotropic, incompressible electroelastic squared plate is subjected to equal biaxial homogeneous deformation and a scalar electrical potential is applied on the sides of compliant electrodes. This case is analysed according to two methodologies: the Hessian approach and the use of incremental deformation together with increment in the electric displacement. First, an extended Mooney-Rivlin model is considered for the material and then an Ogden model is also analysed. Results, show, that despite of available experimental results, some predictions can be made and the pertinent analysis show complex bifurcation maps. This can help in the future progress in the knowledge of the instabilities and bifurcation phenomena which should appear in these materials. The present paper has been mainly motivated by the work of Ogden and Dorfmann.