Extended displacement discontinuity method for analysis of cracks in 2D thermal piezoelectric semiconductors

The extended displacement discontinuities method has previously been used for crack analysis of elastic materials, piezoelectric media, magneto-electro-elastic media and piezoelectric semiconductors. Here, this method is extended to study cracks in two-dimensional n-type thermal piezoelectric semiconductors. The extended displacement discontinuities include the conventional displacement discontinuity, electric potential discontinuity, carrier density discontinuity, as well as temperature discontinuity across crack faces; correspondingly, the extended stresses represent conventional stress, electric displacement, electric current, and heat flux. Employing a Fourier transform, the fundamental solutions for a line crack under uniformly distributed extended displacement discontinuities on the crack faces are derived under mechanical, electrical, and heat loading. Based on the obtained fundamental solutions, an extended displacement discontinuity boundary element method is developed. The stress and heat flux intensity factors at the crack tip are calculated under different combined loadings.