The effects of flexoelectricity and strain gradient on the stress analysis of piezoelectric micro-spheres subjected to physical loadings

摘要

Flexoelectricity is associated with a particular electro-mechanical coupling phenomenon between polarization and strain gradients displaying a promising size effect as the dimensions of nanostructures decline. This paper aims to present a size-dependent analysis of micro-rotating spheres made of functionally graded piezoelectric (FGP) materials according to the strain gradient elasticity considering flexoelectric effects. According to a power-law distribution, mechanical and electrical properties are assumed to vary in the thickness direction. Herein, Gibbs free energy density, which is a function of strain, strain gradient, and electric field, is employed to derive the constitutive equations. Two coupled electro-mechanical differential equations in terms of radial displacement and electric potential are extracted using electric and mechanical equilibrium equations. The coupled differential equations are solved utilizing the differential quadrature method, which is a powerful numerical discretization tool. Numerical results show the effects of flexoelectric, strain gradient parameter, non-homogeneity constant, and angular velocity on the size-dependent electro-mechanical response of the FGP micro-sphere. Also, a comparison study between classic piezoelectricity and flexoelectricity-strain gradient theory is performed.