Anisotropic and piezoelectric materials fracture analysis by BEM

A mixed boundary element approach for two-dimensional anisotropic and piezoelectric fracture mechanics problems is presented in this paper. The numerical approach is based on displacement and traction integral equations for external and crack boundaries, respectively. Integrals with strongly singular and hypersingular kernels are analytically transformed into weakly singular and regular integrals prior to any numerical evaluation. This is achieved by the simple election of an integration variable consistent with the material characteristic parameters. The generality of the method allows for the use of curved and quarter-point elements and the evaluation of stress and electric displacement intensity factors from nodal values next to the crack tip. Several crack problems in anisotropic and piezoelectric materials are solved. The obtained results are in good agreement with previous solutions for cases where these solutions exist. The present BE approach is more general and simple than previous procedures and has allowed for solution of a variety of crack problems including curved cracks in piezoelectric materials which had never been studied before.