Keywords: contact interaction, finite element analysis, coupled problem, heterogeneity, defect, tribomechanical system, wheel-rail.

Under contact interactions in such tribomechanical systems as frictionless bearings, gear transmissions, "wheel-rail-brake block" systems, etc., different defects can appear and mechanical properties of materials in the near-surface layers can vary as a result of high pressures, temperatures, plastic strains and contact fatigue. The indicated factors define the interest in the investigation of mechanical and thermo-mechanical problems of the contact interactions for media with heterogeneities, defects and dislocations. For the analysis of real tribomechanical systems, especially taking into account heterogeneity, plasticity, temperature fields and defects, it is necessary to use direct numerical approaches such as finite element method which appeared to be the most effective one.

In the present work the set of contact problems for elastic, elastoplastic and thermoelastic bodies with piecewise homogeneous and continuously homogeneous material properties, cracks and dislocations is considered. For solving these problems the finite element techniques and specialized software for package ANSYS are used.

The stages of solving the contact problems with inhomogeneous properties the following stages involve such processes as the creation of the finite element model for homogeneous bodies with concentration near to a supposed contact zone, finite element modifications by redefinition of their material properties according to the law of heterogeneity, creation of the finite element contact pairs, numerical solution of the nonlinear contact finite element problem, and postprocessing of contact interaction results.

For elastic bodies with dislocations the technique considered is complemented by the modeling of multiplex edge dislocations with Burgers vectors, construction of the finite element mesh with dislocations and evaluation of additional vectors for the finite element system because of the nodal forces caused by dislocations.

For contact problems with cracks both usual structural finite elements and special quadratic finite elements with middle nodes shifted to the apex of the crack have been used. The contact problems with thin multi-layer surfaces are considered separately. Some models for shells, layers and functionally gradient materials are analysed.

The problems arising from the investigation of the contact interaction for an inhomogeneous railway wheel with a rail are noted. As it has been revealed earlier, after a long-term use of a railway wheel the mechanical properties in the near-surface layers, close to the rolling surface, vary considerably. These modifications have quasiperiodic character on the depth and are stabilized at a distance of about 25-35 mm from a surface.

Solid and finite-element models of the railway wheel (GOST 9036-88) and rail (R65) have been constructed accounting for inclination and conicity. The finite-element calculations of contact interaction between wheel and rail are carried out for homogeneous and inhomogeneous material properties of the wheel. As the calculations have shown, the types of heterogeneity considered have negligible impact on the deflected mode of the tribomechanical "wheel-rail" system in comparison with the case when the Young's modulus is constant and equal to the average value. For example, the difference in the magnitudes of contact and effective stresses in the vicinity of the contact zone does not exceed 5%. The difference of the effective stresses in a far zone is more essential, but the absolute values of stresses there are much less, than in the near zone.

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