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 引用本文: 朱伯靖 石耀霖 秦太验. 同震断层三维裂纹扩展波动时域超奇异积分法[J]. 力学学报, 2010, 42(3): 456-474.
Bojing Zhu, Yaolin Shi, Taiyan Qin. 3D crack propagation mechanism on co-seismic slip under P- and S- waves by wave time-domain hypersingular integral method[J]. Chinese Journal of Theoretical and Applied Mechanics, 2010, 42(3): 456-474.
 Citation: Bojing Zhu, Yaolin Shi, Taiyan Qin. 3D crack propagation mechanism on co-seismic slip under P- and S- waves by wave time-domain hypersingular integral method[J]. Chinese Journal of Theoretical and Applied Mechanics, 2010, 42(3): 456-474.

## 3D crack propagation mechanism on co-seismic slip under P- and S- waves by wave time-domain hypersingular integral method

• 摘要: 应用波动时域超奇异积分法将P波、S波和磁电热弹多场耦合作用下同震断层任意形状三维裂纹扩展问题转化为求解以广义位移间断率为未知函数的超奇异积分方程组问题；定义了广义应力强度因子，得到裂纹前沿广义奇异应力增量解析表达式；应用波动时域有限部积分概念及体积力法，为超奇异积分方程组建立了数值求解方法，编制了FORTRAN程序，以三维矩形裂纹扩展问题为例，通过典型算例，研究了广义应力强度因子随裂纹位置变化规律；分析了同震断层裂纹扩展中力、磁、电场辐射规律.

Abstract: This work presents a wave time-domain hypersingularintegral equation (WTD-HIE) method proposed by the authors for modeling 3Dcrack propagation problem on co-seismic slip under fully coupledelectromagnetothermoelastic P- and S- wave fields through theoretical analysisand numerical simulations. First, the general extended incrementaldisplacement wave solutions are obtained by wave time-domain Green'sfunction method. Then, based on the nonlinear boundary element method, theproblem is reduced to solving a set of WTD-HIEs coupled with nonlinearboundary integral equations, in which the unknown functions are the generalextended displacement discontinuity waves. The behavior of the generalextended singular stress indices around the crack front terminating at theslip surface is analyzed by the time-domain main-part analysis method. Thegeneral extended incremental singular stress waves and the extended stressintensity factors are obtained by closed-form solutions. In addition, anumerical method for the problem is put forward with the extendedincremental displacement discontinuity waves approximated by the product oftime-domain basic density functions and polynomials. Finally, extendedstress intensity factors radiation distribution for P- and S- waves at the cracksurface are calculated, and the results are presented to demonstrate theapplicability of the proposed method.

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