According to the project the scientific activities were concentrated on the following topics:

• Derivation of transmission conditions for different interface models.

• BVPs under nonclassical transmission conditions in domains with irregular boundaries.

• Asymptotic behaviour of elastic field near the interface crack tip under various non-ideal interfaces.

• Fracture mechanics analysis of the interface crack lying at nonideal interface.

• Radial basis functions for solving near singular and singular BVPs.

The joint research concerns problems related to interface phenomenon: evaluation of appropriate mathematical models taking into account various mechanical and geometrical features of the interphase zone between the matched materials, asymptotic behaviour of the elastic field near the interface crack tip, fracture mechanics analysis of the interface crack utilizing the asymptotics obtained. In this way, various nonclassical transmission conditions (the so-called soft, stiff, rigid and perfect interface models) are investigated depending on the interphase feature.

It can be shown that the asymptotics of the solution near the crack tip exhibits different behaviour for the models under consideration. Moreover, the shape of the thin intermediate zone in the vicinity of the interface crack tip can influence in a drastic way the stress singularity and the number of the singular terms. All these facts have to be taken into account in fracture mechanics analysis.

A new research concerning numerical derivation of the nonclassical transmission conditions from FEM analysis and effective numerical evaluation of the stress singularities near complex 3-D geometry defects is just processed.