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Abstract: The problem of stress singularities due to multi-material junctions is described in this paper. A semi-analytical approach is proposed based on an asymptotic model in the case of anisotropic linear elasticity in three dimensions. The advantage of the present method is the quasi-explicit knowledge of the stress and displacement fields around the junctions. Thus, after a brief explanation of the approach leading to the mechanical fields around the singular line at the junction between different materials, numerical results are presented concerning various configurations of an assembly with rivets included in a bi-layer composite that illustrate this method. [Copyright &y& Elsevier]