Electroelastic singularities and intensity factors for an interface crack in piezoelectric–elastic bimaterials

Abstract

A symplectic approach based on the Hamiltonian system is proposed to analyze the electroelastic singularities and intensity factors of an interface crack in piezoelectric–elastic bimaterials. By introducing a total unknown vector consisting of generalized displacements and stresses, the Lagrangian equations are transformed to the Hamiltonian equations which can be solved by using the method of separation of variables. The total unknown vector can be expanded analytically in symplectic eigensolutions series (zero- and non-zero-eigensolutions). The unknown coefficients of the eigensolutions series are determined from the continuity conditions at the interface (electric conductor/insulation conditions) and outer boundary conditions. The study concludes that electroelastic singularities and intensity factors directly depend on the first few terms of non-zero-eigensolutions. Numerical examples for various conditions are given to show variations of singularity orders and intensity factors. These analyses may provide some guidance for the design of piezoelectric–elastic bimaterial system.