Abstract. The goal of this work is to apply the matching asymptotic method combined with a variational approach to study the initiation and the propagation of a cohesive crack from the tip of a preexisting notch following the Dugdale cohesive force model when the characteristic length of the material (included in the Dugdale model) is small by comparison with the characteristic length of the body.
We consider a domain made of a linear elastic material which contains an angular point. A small defect, like a cavity or a crack, is located in the neighborhood of the tip of the wedge. In order to study its influence both on the local and global responses of the body, we use a matched asymptotic expansion method. After the general construction of the matched asymptotic expansions for an arbitrary defect, we develop the method in the particular case where the defect is a small crack. The numerical results obtained from the method are finally compared with those given by the classical finite element method. All the analysis is made in an antiplane setting in order to make easier the calculations.
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