A rectangular plate of dielectric elastomer exhibiting gradients of material properties through its thickness will deform inhomogeneously when a potential difference is applied to compliant electrodes on its major surfaces, because each plane parallel to the major surfaces will expand or contract to a different extent. Here we study the voltage-induced bending response of a functionally graded dielectric plate on the basis of the nonlinear theory of electroelasticity, when both the elastic shear modulus and the electric permittivity change with the thickness coordinate. The theory is illustrated for a neo-Hookean electroelastic energy function with the shear modulus and permittivity varying linearly across the thickness. In general the bending angle increases with the potential difference, and this enables the material inhomogeneity to be tuned to control the bending shape. We derive the Hessian criterion that ensures stability of the bent configurations in respect of a general form of electroelastic constitutive law specialized for the considered geometry. This requires that the Hessian remains positive. For the considered model we show that the bent configuration is stable until the voltage reaches the value for which the cross section of the bent configuration forms a complete circle.

在其厚度范围内显示出材料特性梯度的介电弹性体的矩形板将不均匀变形当在主表面上的柔顺电极上施加电势差时，因为平行于主表面的每个平面都会以不同程度扩展或收缩。在此，当弹性剪切模量和介电常数均随厚度坐标变化时，我们将基于电弹性非线性理论，研究功能梯度电介质板的电压诱导弯曲响应。说明了新霍克电弹性能函数的理论，其剪切模量和介电常数沿厚度线性变化。通常，弯曲角度随着电势差而增加，并且这使得材料不均匀性能够被调整以控制弯曲形状。我们推导出了一种Hessian准则，该准则确保了针对所考虑的几何形状的一般形式的电弹性本构法的弯曲构造的稳定性。这就要求黑森州保持积极。对于所考虑的模型，我们表明弯曲构造在电压达到弯曲构造的横截面形成完整圆的值之前是稳定的。