Extended displacement discontinuity method for an interface crack in a three-dimensional transversely isotropic piezothermoelastic bi-material. Part 1: Theoretical solution1

The extended displacement discontinuity boundary integral-differential equation method is developed to analyze interface cracks of arbitrary shape in three-dimensional transversely isotropic piezothermoelastic bi-materials. The fundamental solutions for unit-point extended displacement discontinuities on the interface are derived, and the induced extended displacements and stresses are all expressed in terms of extended displacement discontinuities. An analysis method is proposed based on the analogy between the obtained boundary integral-differential equations and those for interface cracks in isotropic thermoelastic bi-materials. The singular indices and the singular behaviors of the near crack-tip fields are studied and two new extended stress intensity factors are obtained. Meanwhile, the extended stress intensity factors (SIFs) including two new fracture modes are derived in terms of the extended displacement discontinuities.