Fracture analysis of flexoelectric double cantilever beams based on the strain gradient theory

Abstract

In this article, the fracture behavior of a flexoelectric double cantilever beam (DCB) under large deformation is investigated using strain gradient theory. Incorporation of electric field-strain gradient coupling, known as flexoelectricity, in the constitutive equations of a 1D cantilever beam is studied. Moreover, due to the enormous surface area to volume ratio at micro/nanoscale, surface effects are also included in the theoretical formulations. The solutions of the cantilever beam deflections and strain energy release rates of the DCB with different configurations are numerically evaluated and compared. Numerical results anticipate significant size effect (higher structural stiffness) as the values of the material length scale parameter (l) and the material flexoelectric coefficient (f31) are increased. DCB with the open circuit boundary condition demonstrates higher stiffness than the short circuit boundary condition. At micro/nanoscale, the effect of uncracked part of the DCB is found to be substantial in determining the strain energy release rate and it must not be ignored even for the slender beams.