Extended displacement discontinuity method for an interface crack in a three-dimensional transversely isotropic piezothermoelastic bi-material. Part 2: Numerical method

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• 作者：HuaYang Dang^a ; ^c ; MingHao Zhao^a ; ^b ; CuiYing Fan^b ; ZengTao Chen^c ; ^{zengtao.chen@ualberta.ca}
• 关键词：Three-dimensional transversely isotropic piezothermoelastic bi-material ; Interface crack ; Extended displacement discontinuity method ; Triangular element ; Fundamental solutions ; Gaussian distribution function ; Electric and thermal boundary conditions ; Extended stress intensity factors ; Energy release rate (ERR) ; Local J-integral
• 刊名：International Journal of Solids and Structures
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：109
• 期：Complete
• 页码：199-209
• 全文大小：2508 K
• 卷排序：109

文摘

The extended displacement discontinuity method is proposed to analyze the nonlinear electric and thermal effects on an interface crack in a three dimensional (3D), transversely isotropic, piezothermoelastic bi-material under combined mechanical-thermo-electrical loadings. The fundamental solutions for uniformly distributed, extended displacement discontinuities applied over a triangular element are obtained by integrating the fundamental solutions for the unit-point, extended displacement discontinuities given by Part 1 over the triangular area. In order to eliminate the oscillatory singularity of the stresses near the crack front, the Delta function in the fundamental solutions is approximated by the Gaussian distribution function, and accordingly, the Heaviside step function is replaced by the Error function. The extended, displacement discontinuity boundary element method with an iterative approach is proposed to determine the value of the fields in the crack interior for opening-crack model. As an example, an elliptical interface crack is studied under different electrical and thermal boundary conditions. The extended stress intensity factors (SIFs) without oscillatory singularities, the forms of the energy release rate (ERR) and local J-integral which can be both expressed in terms of intensity factors are obtained. The numerical method is validated and the influence of combined loadings and material-mismatch on the results is studied. The effects of different boundary conditions and ellipticity ratio on the results are also investigated.