Abstract
Three 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 regularization 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.
Highlights
Dynamic crack analysis has many important applications in engineering sciences such as in fracture and damage mechanics, quantitative non-destructive material testing, geophysics and geomechanics
From the mathematical points of view, a crack in twodimensional (2-D) elastic solids is a line with two coincident faces, which leads to a degeneration of the classical displacement boundary element method (BEM) formulation over both crack-faces
This problem can be avoided by using the dual BEM, where the displacement boundary integral equations (DBIEs) are used over one of the crack-faces while the traction boundary integral equations (TBIEs) are applied to other crack-face
Summary
Dynamic crack analysis has many important applications in engineering sciences such as in fracture and damage mechanics, quantitative non-destructive material testing, geophysics and geomechanics. TBIEs can be obtained by the partial differentiation of the DBIEs and the subsequent application of the Hooke’s law Another remedy to overcome the degeneration of the DBIEs for crack analysis is the use of the hypersingular TBIEs only on one of the crack-faces, where the crack-openingdisplacements (CODs) are the fundamental unknown quantities. Three different BEM formulations, namely, the frequency-domain [5, 9], the Laplacedomain [3] and the time-domain [2, 24, 25, 29, 33] BEM, are often applied to transient elastodynamic crack analysis To analyze their accuracy and efficiency, a comparative study is performed in this paper. Numerical examples for computing transient elastodynamic SIFs in homogeneous and linear elastic solids of general anisotropy are presented to compare the accuracy and the efficiency of the three different BEM formulations
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