Analysis of a three-dimensional arbitrarily shaped interface crack in a one-dimensional hexagonal thermo-electro-elastic quasicrystal bi-material. Part 1: Theoretical solution

The extended displacement discontinuity boundary integral-differential equation method is adapted to analyze a three-dimensional interface crack of arbitrary shape in a one-dimensional, hexagonal thermo-electro-elastic quasicrystals bi-material. The extended displacement discontinuities include phonon and phason displacement discontinuities, electric potential discontinuity, as well as temperature discontinuity across the interface crack; while the extended stresses represent phonon and phason stresses, electric displacement and heat flux, respectively. An analysis method is proposed based on the analogy between the governing equations for one-dimensional hexagonal electro-thermo-elastic quasicrystals and three-dimensional transversely isotropic magnetoelectrothermoelastic media. By using the analogy method, the fundamental solutions for unit-point extended displacement discontinuities on the interface are obtained. Using the superposition principal, the extended displacement discontinuity boundary integral-differential equations are established. The singular indices and the singular behaviors of the near crack border fields are studied, and the combined extended stress intensity factors (SIFs) are derived in terms of the EDDs.