A comparative study of three BEM for transient dynamic crack analysis of 2-D anisotropic solids

Abstract

International audienceThree different boundary element methods (BEM) for transient dynamic crack analysis in two-dimensional (2-D), homogeneous, anisotropic and linear elastic solids are presented. Hypersingular traction boundary integral equations (BIEs) in frequency-domain, Laplace-domain and time-domain with the corresponding elastodynamic fundamental solutions are applied for this purpose. In the frequency-domain and the Laplace-domain BEM, numerical solutions are first obtained in the transformed domain for discrete frequency or Laplace-transform parameters. Time-dependent results are subsequently obtained by means of the inverse Fourier-transform and the inverse Laplace-transform algorithm of Stehfest. In the time-domain BEM, the quadrature formula of Lubich is adopted to approximate the arising convolution integrals in the time-domain BIEs. Hypersingular integrals involved in the traction BIEs are computed through a regulariza-tion process that converts the hypersingular integrals to regular integrals, which can be computed numerically, and singular integrals which can be integrated analytically. Numerical results for the dynamic stress intensity factors are presented and discussed for a finite crack in an infinite domain subjected to an impact crack-face loading

On two hypersingular time-domain BEM for dynamic crack analysis in 2D anisotropic elastic solids

“…In Eq. (17), v G ij ðx; y; tÞ and w G ij ðx; y; tÞ are the traction and the higher-order traction fundamental solutions, which are defined as follows v G ij ðx; y; tÞ ¼ ÀC icpd e c ðxÞu G pj;d ðx; y; tÞ; ð18Þ w G ij ðx; y; tÞ ¼ ÀC icpd e c ðxÞC jakb e a ðyÞu G jk;db ðx; y; tÞ: ð19Þ…”

“…Similarly, Laplace-domain BEM can also be applied to transient dynamic analysis of anisotropic elastic solids by a subsequent inverse Laplace-transform. A comparative study of the timedomain BEM using the convolution quadrature formula of Lubich [25,26], the frequency-domain BEM and the Laplace-domain BEM for transient elastodynamic crack analysis in infinite, homogeneous, anisotropic and linear elastic solids has been presented by García-Sánchez and Zhang [17].…”

2D Elastodynamics of Interface Microcracks: The Effect of Cracks Interaction

“…However, taking into account the fact that the components of structures are frequently subjected to dynamic loading, the understanding of the mechanism of composite materials dynamic fracture has a great importance [2,8,9]. Since the analytical solutions are limited to a very small number of idealized model problems, the problems for cracked solids under dynamic loading can be solved using advanced numerical methods [3,[10][11][12][13]. Today, due to the great improvement in computer technology and computational methods, it is possible to solve many complex interlaminar crack problems accurately and efficiently.…”

A hypersingular time‐domain BEM for 2D dynamic crack analysis in anisotropic solids

“…Another variant of the TDBEM for transient dynamic crack analysis in anisotropic solids has been presented recently by García-Sánchez and Zhang [23] and García-Sánchez et al [24]. In the TDBEM presented in [23,24], the convolution quadrature formula of Lubich [21,22] has been adopted for the temporal discretization, while a collocation method has been implemented for the spatial discretization. Yet another variant of the TDBEM has been developed recently by Beyer et al [25], who applied the collocation method for both temporal and spatial discretizations.…”

“…Likewise, Laplace-domain BEM can be implemented and applied to transient dynamic analysis of cracked/uncracked anisotropic solids by utilizing an inverse Laplace-transform. A comparative study of the time-domain, frequencydomain, and Laplace-domain BEM for transient dynamic crack analysis in anisotropic solids can be found in [23]. A review of different BEM formulations for crack analysis in anisotropic solids is given by Zhang [30].…”