GuangTao Xu

Extended displacement discontinuity boundary integral equation and boundary element method for cracks in thermo-magneto-electro-elastic media

The extended displacement discontinuity boundary integral equation (EDDBIE) and boundary element method is developed for the analysis of planar cracks of arbitrary shape in the isotropic plane of three-dimensional (3D) transversely isotropic thermo-magneto-electro-elastic (TMEE) media. The extended displacement discontinuities (EDDs) include conventional displacement discontinuity, electric potential discontinuity, magnetic potential discontinuity, as well as temperature discontinuity across crack faces; correspondingly, the extended stresses represent conventional stress, electric displacement, magnetic induction and heat flux. Employing a Hankel transformation, the fundamental solutions for unit point EDDs in 3D transversely isotropic TMEE media are derived. The EDDBIEs for a planar crack of arbitrary shape in the isotropic plane of a 3D transversely isotropic TMEE medium are then established. Using the boundary integral equation method, the singularities of near-crack border fields are obtained and the extended stress field intensity factors are expressed in terms of the EDDs on crack faces. According to the analogy between the EDDBIEs for an isotropic thermoelastic material and TMEE medium, an analogical solution method for crack problems of a TMEE medium is proposed for coupled multi-field loadings. Employing constant triangular elements, the EDDBIEs are discretized and numerically solved. As an application, the problems of an elliptical crack subjected to combined mechanical-electric-magnetic-thermal loadings are investigated.

Fundamental solutions and analysis of rectangular crack in 3D thermopiezoelectric media

Due to their pronounced piezoelectric, dielectric and pyroelectric properties, thermo piezoelectric materials have being widely used in sensors, actuators, transducers and intelligent structures, etc. Considering thermal effects, this paper derives the fundamental solutions for uniformly distributed extended displacement discontinuities on rectangular elements in the isotropic plane of a 3D thermo piezoelectric medium and investigates a rectangular crack subjected to thermal loadings.

Extended displacement discontinuity method for analysis of cracks in 2D thermopiezoelectric media

Based on the operator theory, the general solutions of the extended displacements and stresses in two-dimensional thermopiezoelectric media are expressed in terms of a potential function. By introducing the Fourier transform, the fundamental solutions for the unit point extended displacement discontinuities are derived. The extended displacement discontinuity boundary integral equation method is developed and used to analyze the singularities of near-crack tip fields, and the extended intensity factors are obtained in terms of the extended displacement discontinuities across the crack faces.

Dielectric Breakdown Model for an Electrically Semi-Permeable Penny-Shaped Crack in Three-Dimensional Piezoelectric Media

The dielectric breakdown (DB) model for a penny-shaped crack under a semipermeable boundary condition in a three-dimensional piezoelectric medium is studied. An approximate analytical solution is derived by using the boundary integral equation with extended displacement discontinuity, and the corresponding boundary element method with double iterative approaches is developed to analyze the semi-permeable crack. The effect of electric boundary conditions on crack faces is discussed on the basis of DB model. By comparing the DB model with the polarization saturation (PS) model for different piezoelectric materials, some interesting phenomena related to the electric yielding zone and local J-integral are observed.

A new discovery of bending behaviors of low-dimensional piezoelectric materials

The measurement of mechanical and electrical properties has become an important topic in studying low-dimensional piezoelectric materials. In this paper, the analytical solution of a piezoelectric beam is derived based on the Bernoulli hypothesis and the three-dimensional constitutive equations. The bending behaviors of the piezoelectric cantilever beam with and without electrodes are studied. It is found that the form of the governing equations and final solutions for the piezoelectric beam is similar to the one for an elastic beam by defining the equivalent bending stiffness.

Extented crouch fundamental solutions of parabolic elements for 2D piezoelectric media

In order to simulate the singularity of the solution near crack tips, the parabolic element at the crack tip is used in displacement discontinuity method. The extended Crouch fundamental solutions of parabolic elements for 2D piezoelectric media are derived based on the extended displacement discontinuity fundamental solution. Extended displacement discontinuity method (EDDM) using parabolic elements at crack tips under impermeable boundary condition is implemented. Numerical results show that the precision and efficiency of the EDDM can be greatly improved by using the parabolic elements.

Analysis method of mixed mode crack in 2D finite piezoelectric media

In this paper, the Hybrid Extended Displacement Discontinuity-Charge Simulation Method (HEDD-CSM) [1] is used to study the mixed mode cracks in two-dimensional finite piezoelectric media under combined mechanical-electrical loadings. The HEDD-CSM combines the extended displacement discontinuity method (EDDM) and the charge simulation method (CSM). The solution for an electrically impermeable crack is approximately expressed by a linear combination of fundamental solutions of the governing equations which includes the extended point force fundamental solutions with the sources placed at chosen points outside the domain of the problem under consideration and the extended Crouch fundamental solutions with the extended displacement discontinuities placed on the crack. The coefficients of the fundamental solutions are determined by letting the approximated solution satisfy the conditions on the boundary of the domain and on the crack face. The center cracks in piezoelectric strips are analyzed by HEDD-CSM. The stress intensity factors and the electric displacement intensity factor are calculated. Meanwhile the effect of finite domain size on these intensity factors is studied. One of the most interesting findings is that the intensity factor KII decouples from K1 and KD even in a finite piezoelectric medium.