Gradient models of deformation of composite electroelastic bodies

The stress-strain state of layered electroelastic bodies is studied taking into account large-scale effects. To account for the scale effects, a gradient model of electroelasticity with one mechanical and one electrostatic parameters is used. As examples, the problem of deformation of a composite electroelastic rod, the antiplane problem of deformation of an electroelastic strip with a coating, the problem of deformation of a solid piezocylinder with a coating are considered. On the basis of the variational principle of gradient electroelasticity, refined equations of equilibrium and electrostatics are obtained, as well as an expanded list of boundary conditions and interface conditions for the tasks set. Several simplified formulations of gradient electroelasticity problems for composite bodies are considered, when only one of the gradient effects, mechanical or electrostatic, is taken into account. The dimensionalization was carried out and analytical solutions of simplified problems were obtained. Calculations of displacements and stresses of composite electroelastic bodies are carried out on specific examples. Solutions of problems in classical and gradient formulations are graphically presented; a comparative analysis of the solutions obtained is carried out. It is found out that if the scale parameters are taken into account in the vicinity of the conjugation of layers, the following is observed: 1) a smoother distribution of displacements and electric potential compared to classical theory; 2) a jump of components of the Cauchy stress tensor and components of the electric induction vector; 3) a continuity of some components of the moment stress tensor and quadrupole moment; 4) a continuity of total stresses. The jump of the components of the Cauchy stress tensor and the components of the electric induction vector is explained by the continuity of the displacements, the electric potential and their first derivatives. The dependence of displacements and electric potential on the magnitude of mechanical and electrostatic scale parameters is investigated. It was found out that with an increase in the scale parameters both the displacement and electric potential decrease.