Fracture mechanics analysis of size-dependent piezoelectric solids

The finite element method (FEM) is developed to analyse general 2D boundary value problems in size-dependent piezoelectric, elastic solids with cracks. The size-effect phenomenon in micro/nano electronic structures is described by the strain-gradient effect. 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-gradient piezoelectricity. The path-independent J-integral is also derived for fracture mechanics analysis of such solids. Numerical examples are presented to demonstrate the veracity of the formulations.