Periodic Green Functions for Two-Component Medium with Interface Stresses at the Planar Interface

摘要

The 2-D problem of elasticity for bimaterial with planar interface under the periodic set of point forces is considered at the nanoscale. Complex variable based technique and Gurtin-Murdoch model of surface elasticity, which leads to the hypersingular integral equation, are used. The solution of this equation and explicit formulas for stress field (Green functions) are derived in terms of Fourier series. The fundamental solutions obtained in the work can be used for applying the boundary integral equation method to an analysis of defects such as cracks and inhomogeneities, periodically distributed at the nanometer distances from the interface.