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Stable algorithm for the stress field around a multiply branched crack. (English) Zbl 1084.74058

Summary: We 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.

MSC:

74S30 Other numerical methods in solid mechanics (MSC2010)
74G70 Stress concentrations, singularities in solid mechanics
74R10 Brittle fracture
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