Bifurcation of a finitely deformed functionally graded dielectric elastomeric tube

Soft functionally graded materials have attracted intensive attention owing to their special material inhomogeneity and are realized as various applications. In this paper, we theoretically investigate the finite deformation and superimposed bifurcation behaviors of an incompressible functionally graded dielectric tube subject to a combination of axial stretch and radial voltage. The theoretical framework of nonlinear electroelasticity and the related linearized incremental version is employed. We assume that the modulus and permittivity of the elastomer vary linearly along the thickness of the tube. The surface impedance matrix method is adopted to obtain the bifurcation equation for buckling of the tube. We present numerical calculation for the ideal neo-Hookean dielectric elastomer to study the effects of the applied voltage, geometrical size and material grading parameters on the nonlinear response and the incremental buckling behavior of the tube. We validate our results through comparison with those of the elastic problem. The results can provide solid guidance for the design and realization of dielectric actuators.