Influence of electric conductivity on intensity factors for cracks in functionally graded piezoelectric semiconductors

Influence of electric conductivity on intensity factors for cracks in conducting piezoelectric materials is investigated. Mechanical and electric loads are considered for 2D crack problems. The electric displacement in conducting piezoelectric materials is influenced by the electron density and it is coupled with the electric current. The coupled governing partial differential equations (PDE) for stresses, electric displacement field and current are satisfied in a local weak-form on small fictitious subdomains. Nodal points are spread on the analyzed domain and each node is surrounded by a small circle for simplicity. Local integral equations are derived for a unit function as the test function on circular subdomains. All field quantities are approximated by the moving least-squares (MLS) scheme. Interaction integral method is developed for evaluating the intensity factors in functionally graded conducting piezoelectric materials.