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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.

Study of the influence of small defects near a singular point in antiplane elasticity by an asymptotic method