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We present a unified framework to tie overlapping meshes in solid mechanicsapplications. This framework is a combination of the X-FEM method and themortar method, which uses Lagrange multipliers to fulfill the tyingconstraints. As known, mixed formulations are prone to mesh locking whichmanifests itself by the emergence of spurious oscillations in the vicinity ofthe tying interface. To overcome this inherent difficulty, we suggest a newcoarse-grained interpolation of Lagrange multipliers. This technique consistsin selective assignment of Lagrange multipliers on nodes of the mortar side andin non-local interpolation of the associated traction field. The optimal choiceof the coarse-graining spacing is guided solely by the mesh-density contrastbetween the mesh of the mortar side and the number of blending elements of thehost mesh. The method is tested on two patch tests (compression and bending)for different interpolations and element types as well as for differentmaterial and mesh contrasts. The optimal mesh convergence and removal ofspurious oscillations is also demonstrated on the Eshelby inclusion problem forhigh contrasts of inclusion/matrix materials. Few additional examples confirmthe performance of the elaborated framework.

Stabilized MorteX method for mesh tying along embedded interfaces