Size-dependent model of electroelasticity for a solid coated cylinder

The study of the problem of gradient electroelasticity for a solid radially polarized cylinder with a coating is carried out. A constant normal mechanical load acts on the non-electrodized side surface of the coating. The electroelasticity model includes one gradient mechanical parameter. This takes into account the effect of the strain gradient, but does not take into account the effect of the gradient of the electric field strength. In the framework of the gradient formulation, boundary conditions and conjugation conditions additional to the classical formulation are set. After eliminating the electric potential, the problem is reduced to the problem of the gradient theory of elasticity with stiffened elastic moduli. In the case of a homogeneous coating, analytical expressions are obtained for finding radial displacements and stresses. In the case of an inhomogeneous coating, the numerical solution is based on the targeting method. Calculations of the displacements, Cauchy stresses and moment stresses of both homogeneous and inhomogeneous coatings are carried out. A comparative analysis of the results obtained on the basis of classical and gradient electroelasticity models depending on the values of the scale parameter is carried out. The influence of the laws of heterogeneity of the material characteristics of the coating on the distribution of displacements has been studied. It was found that: 1) the Cauchy stresses experience a jump at the boundary between the cylinder and the coating; 2) couple stresses take a peak value on the mating surface; 3) an increase in the scale parameter reduces the values of radial displacements.