Link to publicationCitation for published version (APA): Englund, J. (2007). A higher order scheme for two-dimensional quasi-static crack growth simulations.
SUMMARYWe present an algorithm for the computation of the stress field around a branched crack. The algorithm is based on an integral equation with good numerical properties. Our equation is obtained through a left regularization of an integral equation of Fredholm's first kind. Complex valued functions involving repeated products of square roots appear in the regularization. A new and effective scheme for correct evaluation of these functions is described. For validation, mode I and II stress intensity factors are computed for simple branched geometries. The relative errors in the stress intensity factors are typically as low as 10 −12 . A large scale example is also presented, where a crack with 176 branching points is studied.
SUMMARYThe stress field in a finite, edge cracked specimen under load is computed using algorithms based on two slightly different integral equations of the second kind. These integral equations are obtained through left regularizations of a first kind integral equation. In numerical experiments it is demonstrated that the stress field can be accurately computed. Highly accurate stress intensity factors and T -stresses are presented for several setups and extensive comparisons with results from the literature are made. For simple geometries the algorithms presented here achieve relative errors of less than 10 −10 . It is also shown that the present algorithms can accurately handle both geometries with arbitrarily shaped edge cracks and geometries containing several hundred edge cracks. All computations were performed on an ordinary workstation.
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