The J-integral for gradient theory of piezoelectricity

The size-dependent features concerning the mechanical behavior of the micro/nano electronic structures are well known from experiments. They are described by the strain-gradient effect in this paper since the classical elasticity theory fails to capture the size effect of the nanostructures. 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 path independent J-integral is derived for fracture mechanics analysis of piezoelectric solids described by the gradient theory