Analytical study of the singularities arising at multi-material interfaces in 2D linear elastic problems

The problem of stress singularities due to multi-material junctions in the material microstructure is addressed in the framework of the eigenfunction expansion method, provided that the eigenvalues are explicitly assumed complex. A novel efficient numerical procedure for computing the order of the stress singularity is presented. The numerical method can also be used to solve analogous singularity problems in anisotropic elasticity. According to this procedure, new problems of bi- and tri-material junctions occurring in the material microstructure are examined, paying special attention to the role played by Mode-I and Mode-II deformation. The effects of both the properties of the matrix and of the presence of transgranular cracks on the order of stress singularities are carefully investigated.