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

Abstract

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.

Theoretical Nanoarchitectonics of GaN Nanowires for Ultraviolet Irradiation-Dependent Electromechanical Properties

“…Taking a 1-D GaN nanorod with a length of 2 L as an example (see Figure 2 ), the c-axis is along the z-direction, with a uniform beam of ultraviolet light vertically irradiated on the upper surface. Its physical and mechanical behaviors are governed by the motion equation, electrostatics Gauss’s law, and the current continuity equation [ 27 , 28 , 29 , 30 ], that is where σ zz , D z , , and denote the stress tensor, electric displacement, electron concentration density, and hole current density. and represent the ionization degrees of donor and acceptor impurities, respectively.…”

Nonlinear analysis of a crack in 2D piezoelectric semiconductors with exact electric boundary conditions

“…Based on an iterative boundary element method, an elliptical hole problem and a central crack problem in PSCs with linear constitutive equations were directly solved (Zhang et al 2017b), and an elliptical hole problem in PSCs with nonlinear constitutive equations was solved by adopting the Gaussian integral transformation (Zhao et al, 2019). In consideration of thermal-mechanical coupling effect, a central crack problem in thermal PSCs was studied by using the extended displacement discontinuity method (Zhao et al, 2017). A few of crack problems in three-dimensional (3D) PSCs were also investigated by using the extended displacement discontinuity method, such as, singularity indexes of near-border fields of a planar crack in 3D transversely isotropic PSCs (Zhao et al, 2016a), a penny shaped crack problem in 3D PSCs (Zhao et al, 2016c), and a penny shaped crack problem in 3D thermal PSCs (Zhao et al, 2018a).…”

A shooting method for nonlinear boundary value problems in a thermal piezoelectric semiconductor plate

“…Zhao et al. [14, 15] studied a central crack and a penny‐shaped crack in PSCs. They observed that a thermal load induced displacement discontinuity, temperature discontinuity, and a mode II stress intensity factor.…”

“…Sladek et al [13] numerically analyzed the effect of the initial electron density on the fracture behavior of a PSC under a purely thermal load. Zhao et al [14,15] studied a central crack and a penny-shaped crack in PSCs. They observed that a thermal load induced displacement discontinuity, temperature discontinuity, and a mode II stress intensity factor.…”

“…To study the interactions of the pyroelectric effect, piezoelectric effect, and thermoelastic property, Jin and Yang [18,19] analyzed the effect of the pyroelectric coefficient on the mechanical and electric fields and energy conversion efficiency of one-dimensional (1D) thermal PSCs. However, studies of the thermal effect on PSCs are rare, and simplifications, such as ignoring the coupling effect between the temperature and the mechanical or electric field [13][14][15][16][17], and linear constitutive equations [18,19] are often used.…”