The MLPG for crack analyses in composites with flexoelectricity effects

The meshless Petrov-Galerkin (MLPG) method is developed to analyse 2-D crack problems where the electric field and displacement gradients exhibit a size effect. The size-effect phenomenon in micro/nano electronic structures is described by the strain- and electric field-gradients. Both the electric intensity vector and strain gradients are considered in the constitutive equations of the material and the governing equations are derived with the corresponding boundary conditions using the variational principle. The coupled governing partial differential equations (PDE) for stresses and electric displacement field are satisfied in a local weak-form on small fictitious subdomains. All field quantities are approximated by the moving least-squares (MLS) scheme. After performing the spatial integrations, we obtain a system of algebraic equations for the nodal unknowns.