A rigorous solution for the piezoelectric materials containing elliptic cavity or crack with surface effect

Abstract

A theoretical study on the problem of piezoelectric materials with a nano elliptic cavity considering surface effect subjected to far‐field antiplane mechanical load and inplane electric load is reported. Surface effect is introduced based on the theory of Gurtin‐Murdoch surface/interface model. A rigorous whole‐field solution is presented by using the complex variable elasticity theory and the conformal mapping method, in terms of which closed‐form solution of the stress/electric displacement fields and the stress/electric displacement intensity factors is obtained. The results reveal that the stress/electric displacement fields and the stress/electric displacement intensity factors are size dependent when the size of the cavity/crack is on the order of nanometer. The present solution approaches to the classical electroelastic results with the increase of the size of the nano elliptic cavity and crack. The influences of the elliptic cavity shape ratio on the stress and electric displacement concentration factors are discussed.