Effects of electric field and strain gradients on cracks in piezoelectric solids

The paper presents a general approach to analyze 2-D crack problems where the electric field and displacement gradients exhibit a size effect. The finite element method (FEM) is developed to analyze the general 2D boundary value problems in size-dependent piezoelectric solids with cracks if the electric field gradients are considered in the constitutive equations for the electric displacements. The size-effect phenomenon in micro/nano electronic structures is described by the strain- and electric field-gradient effects. The electric field-strain gradient coupling is considered in the constitutive equations of the material and the governing equations are derived with the corresponding boundary conditions using the variational principle. The FEM formulation is subsequently developed and implemented for strain- and electric field-gradient piezoelectricity. In the framework of this theory the path-independent J-integral is derived.