Diffraction of elastic waves by three coplanar Griffith cracks in an orthotropic medium

BIEM for 2D steady-state problems in cracked anisotropic materials

“…For solving it we transform it into the canonical form. We can consider n, jnjZ1 since only such n is used in the inverse Radon transform (13). The 2!2 matrix CZ{C ij (n)} is positive and symmetric due to the condition (4).…”

“…Karin and Kundu [10,11] considered the dynamic response of a layered anisotropic half-space with anti-plane interfacecracks and an orthotropic half-space with a subsurface inplane crack. Kundu and Bostrom [12] studied wave scattering by a circular crack in a transversely-isotropic solid and the dynamic response of three co-planar cracks in an infinite orthotropic medium in [13]. Although BIEM is a very well suited approach for the type of problems considered here, only a few works can be found for dynamic anisotropic crack problems.…”

“…Lekhnitski's [3,4] and Savin's [5] systematic formulations of anisotropy are regarded as a foundation for the anisotropic elasticity. The methods used for the solution of anisotropic crack problems are semi-analytical in Ohyoshi [6,7], Dhawan [8,9], Karim and Kundu [10,11], Kundu and Bostrom [12], Sarkar et al [13]; numerical as finite-difference schemes in Hua et al [14]; finite-element method in Brebbia and Venturini [15], Pageau and Biggers [16], Pageau et al [17], BIEM in Snyder and Cruse [18], Chan and Cruse [19], Zhao et al [20], Tan and Gao [21], Aliabadi and Brebbia [22], Chandra et al [23], Pan and Amadei [24], Saez et al [25], Ang et al [26], Zhang [27], Saez and Dominguez [28][29][30], Abuquerque et al [31], Wang and Achenbach [32][33][34] and hybrid methods in Song and Wolf [35].…”

Interaction between line cracks in an orthotropic layer

“…Now using Hilbert transform technique (see Sarkar et al [17]), the solution to (3.27) is found to be…”

Transient stress intensity factors of an anti‐plane crack propagating in anisotropic layered media

“…However, there have not been many studies for dynamic fracture analysis of anisotropic solids in the literature. Most investigations on elastodynamic crack analysis of anisotropic solids have been limited to transversely isotropic (Kundu and Boström, 1992;Rizza and Nair, 1999;Zhao, 2001;Brock and Hason, 2002) or orthotropic (Kassir and Bandyopadhyay, 1983;Shindo and Nozaki, 1991;Sarkar et al, 1995;Patra, 1996, 1998;Itou and Haliding, 1997;Rubio-Gonzalez and Mason, 1999, 2001Brock and Hason, 2002) materials. A very good review on early work on these topics can be found in Zhang and Gross (1998).…”