The Time-Domain Dbem for Rapidly Growing Cracks

Abstract

SUMMARYThe time-domain Dual Boundary Element Method (DBEM) is developed to analyse rapidly growing cracks in structures subjected to dynamic loads. Two-dimensional problems, where the velocity of the crack growth is constant and the path is not predefined are studied. The present method uses the dual boundary formulation, i.e. the displacement and the traction boundary integral equations to obtain the solution by discretizing the boundary of the body and the crack surfaces only. The crack growth is modelled by adding new elements ahead of the crack tip. It is assumed that the direction of the increment is perpendicular to the direction of maximum circumferential stress. The method is used to analyse growing cracks in infinite sheet and finite plates, and the results are compared with other reported solutions, showing good agreement.1997 by John Wiley & Sons, Ltd.

Modern topics and challenges in dynamic fracture

“…These results agree well with theoretical and experimental findings of other authors (Hawong and Kobayashi, 1987;Ramulu and Kobayashi, 1985;Shukla et al, 1990). Since boundary element methods facilitate the analysis of arbitrary crack paths and the formation of microcracks, crack branching, crack closure and friction, they are being adopted and further developed as an appropriate tool for other macroscopic problems, including problems at the geophysical scale (Fedelinsky and Aliabadi, 1997;Tada and Yamashita, 1997).…”

New Applications of the Boundary Element Method in Dynamics of Solids

“…The computer code calculates boundary displacements and tractions, the crack path, the crack velocity and DSIFs in time. The formulation and application of the method were presented by Fedelinski, Aliabadi and Rooke [2]. Practical applications of the method were presented by Fedelinski [3].…”

Dynamic Propagation Problems of Mode Iii Semi-Infinite Crack

“…A lot of researches on mode III crack dynamic propagation problems were performed cautiously (Freund, 1998;Sih and MacDonald, 1974;Srolovitz and Source, 1997;Gao, 1996;Andrew, 1976;Rosakis et al, 1999;Tang and Sih, 2004). In view of the complexity, cockamamie and difficulty in mathematical operations, fracture dynamics problems are not investigated enough thoroughly (Sih, 1968;Kostrov, 1964;Freund, 1998;Sih and MacDonald, 1974;Srolovitz and Source, 1997;Broberg, 1960;RubinGonzalea and Mason, 2000) and numerical solutions acquired (Sih and MacDonald, 1974;Sih, 1973;1991;Fedelinski et al, 1997;Wang et al, 1992;Knauss, 1987;Wang, 1992;Ranjith and Narasimhan, 1996) were much more than analytical solutions (Nian-Chun et al, 2004;2005;2006). On account of those situations mentioned above, therefore it is necessary to study dynamic propagation problem concerning mode III semi-infinite crack.…”