Flexoelectric Effect for Cracks in Piezoelectric Solids

The finite element method (FEM) is developed to analyse 2-D crack problems where the electric field and displacement gradients exhibit a size effect penomenon. This phenomenon in micro/nanoelectronic structures is described by the strain-and electric field-gradients in constitutive equations. The governing equations are derived using variational principles with the corresponding boundary conditions. The FEM formulation with C1-continuous elements is subsequently developed and implemented. An example is presented and discussed to demonstrate the effects of the strain-and electric intensity-gradients on the electro-mechanical behavior of cracked solids.