In this paper, we solve fundamental boundary value problems in a theory of antiplane elasticity which includes the effects of material microstructure. Using the real boundary integral equation method, we reduce the fundamental problems to systems of singular integral equations and construct exact solutions in the form of integral potentials. Mathematics Subject Classification (2000). 45E05, 74K20.

Artículo de publicación ISIIn this paper, we use the weight function for an elliptical crack embedded in an infinite elastic media in conjunction with the alternating method to derive the exact analytical solution for the stress intensity factor for a semi-elliptical surface crack subjected to an arbitrary mode I loading

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Abstract. In this paper we tackle the simulation of microstructured materials modelled as heterogeneous Cosserat media with both perfect and imperfect interfaces. We formulate a boundary value problem for an inclusion of one plane strain micropolar phase into another micropolar phase and reduce the problem to a system of boundary integral equations, which is subsequently solved by the boundary element method. The inclusion interface condition is assumed to be imperfect, which permits jumps in both displacements/microrotations and tractions/couple tractions, as well as a linear dependence of jumps in displacements/microrotations on continuous across the interface tractions/couple traction (model known in elasticity as homogeneously imperfect interface). These features can be directly incorporated into the boundary element formulation.The BEM-results for a circular inclusion in an infinite plate are shown to be in an excellent agreement with the analytical solutions. The BEM-results for inclusions in finite plates are compared with the FEM-results obtained with FEniCS.

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