On the size-dependent electro-mechanical response of the piezoelectric microbeam

Abstract

Classical piezoelectric elasticity theory fails to explain the size-dependent electro-mechanical behaviour. The strain gradient elasticity and flexoelectricity are responsible for the size effects phenomenon. In this paper, the general strain gradient elasticity is incorporated into the flexoelectric elasticity theory to describe the size dependency. The degeneration analysis of the flexoelectric elasticity theory incorporating the general strain gradient elasticity is performed. The flexoelectric elasticity theory incorporating the general strain gradient elasticity includes all strain gradients, and can degenerate to the simplified flexoelectric elasticity theories incorporating the approximated strain gradient elasticity when some strain gradients are ignored. Subsequently, the differences between the general theory and the simplified theories in describing the size effects are revealed by solving the direct/inverse electro-mechanical problems of the laminated microbeam with a partially covered piezoelectric layer under the uniformly distributed load and external voltage. Compared with the general theory, the simplified theories predict larger collected charge, polarization, electric potential and deflection, and thus underestimate the size-dependent electro-mechanical response. Moreover, the contributions from the strain gradient elasticity and flexoelectricity to the electro-mechanical behaviour are further identified, respectively. The strain gradient elasticity consideration significantly weakens the flexoelectricity and piezoelectricity when the beam thickness is comparable to the material length-scale parameters. The flexoelectricity enhances the polarization, weakens the electric potential while hardly affects the deflection when the beam thickness is in micron range.