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.

软功能梯度材料由于其特殊的材料不均匀性而引起了广泛的关注，并已实现了多种应用。在本文中，我们从理论上研究了在轴向拉伸和径向电压的共同作用下不可压缩的功能梯度电介质管的有限变形和叠加分叉行为。采用非线性电弹性的理论框架和相关的线性化增量版本。我们假设弹性体的模量和介电常数沿管的厚度线性变化。采用表面阻抗矩阵法得到管屈曲的分叉方程。我们提供理想的新霍克电介质弹性体的数值计算，以研究施加电压的影响，几何尺寸和材料分级参数对管的非线性响应和增量屈曲行为的影响。我们通过与弹性问题的比较来验证我们的结果。研究结果可为介电执行器的设计和实现提供可靠的指导。