Yukhym R. Method of calculation of the limiting-equilibrium state of deformed bodies with the filled crack-like defects

Object of researches: elasto-plastic bodies with thin elastic inclusions and filled cracks. The aim of the work: development of the mathematical model of the deformation of bodies with the thin elastic inclusions and establishment of the boundary (fracture) loading for such bodies. Methods of investigation: mathematical methods for solving boundary problems of deforming solid mechanics (Kolosov-Mushelishvili potentials theory, harmonic functions), Hankel integral transformations and singular integral equations; method of mechanical quadratures for the numerical solution of singular integral-differential equations. The mathematical model of the deformation of a solid with a thin elastic inclusion is formulated. The deformation criterion of local fracture of bodies with thin heterogeneities of material structure and formulas for determining the maximum (failure) loading of such bodies are developed. The basic regularities of the influence of geometrical and elastic parameters of inclusions (filler) on the stress-strain and boundary states of a piece-wise homogeneous body are established. New problems on interaction of the systems of collinear defects, in particular, the influence of approaching cracks on the intensification of stresses at their tips as well as the approaching of the parallel inclusions are investigated. The limit sizes of the filled cracks for which the Griffith-Irvin criterion is used, are established. The curvature radii at the stress concentrator tip at which defects can be considered as cracks are found. Dissertation results have been used at the State Engineer Center “Techno-Resource" for establishment of the remaining strength and serviceability of the damaged elements of the constructions of Tashlytska HPP and of other building objects, restored by the injections technologies.