Instabilities of an electroelastic plate

In this paper the theory of nonlinear electroelasticity is used to examine diffuse modes of instability for two problems involving a thin dielectric plate subject to large deformations. The analysis is based on the equations governing linearized incremental deformations and electric displacements and accompanying boundary conditions superimposed on a known finitely deformed configuration in the presence of a known electric field (the underlying configuration). For each problem the underlying deformation is taken to correspond to an equibiaxial stretch with the electric field normal to the major faces of the plate. In the first problem the electric field is generated by equal and opposite charges applied to flexible electrodes on the major surfaces, while in the second problem there are no electrodes and the field is applied externally.Numerical results are obtained in respect of a simple model of an electroelastic material by way of illustration. The critical stretch corresponding to loss of stability of the uniform underlying configuration is obtained as a function of a dimensionless measure of the initial thickness of the plate for a series of values of the electric (displacement) field and of the parameters included in the material model. For the first problem, the results obtained for the critical stretch are compared with the results based on the so-called Hessian approach, which provides only a limited analysis of stability. It neither takes account of the plate thickness nor allows for non-homogeneous deformations, and significant differences in the predictions of the two methods are identified.