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

• Published in: Journal of the Brazilian Society of Mechanical Sciences and Engineering Vol. 45; no. 1
• Main Authors: Radmehr, Mehdi, Yi, Jianjun
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 2023; Springer Nature B.V
• Subjects: Angular velocity; Constitutive equations; Constitutive relationships; Differential equations; Electric fields; Electrical properties; Engineering; Equilibrium equations; Functionally gradient materials; Gibbs free energy; Homogeneity; Mechanical analysis; Mechanical Engineering; Piezoelectricity; Quadratures; Rotating spheres; Size effects; Strain; Stress analysis; Technical Paper; Functionally graded piezoelectric material; Micro-sphere; Flexoelectricity; Strain gradient theory; Differential quadrature method
• ISSN: 1678-5878; 1806-3691
• DOI: 10.1007/s40430-022-03876-2

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.