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Mode III near and far fields for a crack lying in or along a joint. (English) Zbl 0994.74057

Summary: Matched asymptotic expansions allow one to give, at two scales, a description of solution to the antiplane problem on two different elastic substrates bonded together by a thin elastic adhesive layer with a crack lying inside or even outside at a short distance of it. The leading term is the classical solution obtained, by finite elements for instance, when perfect transmission conditions are assumed through the line modelling the interface. The corrections depend on the relative stiffnesses of components and on the thickness of the joint. It also depends on crack location, within the joint or outside. Here we define two kinds of mode III stress intensity factors, fictitious and an actual one, they are called far and near (or remote and local) by the authors. The fictitious one is meaningless and must be rescaled by an appropriate coefficient to give the actual one.

MSC:

74R05 Brittle damage
74G70 Stress concentrations, singularities in solid mechanics
74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics
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