Dovzhyk M. Fracture of materials with close interacting parallel cracks under compression along cracks.

The thesis concerns three-dimensional problems of solids fracture under compression along parallel cracks for small distances between cracks. In the framework of three-dimensional linear theory of elasticity a new analytical-numerical method of solution of Fredholm integral equations with use of a modern mathematical package of symbolical mathematics is proposed. Results for a wide interval of dimensionless distances between cracks are calculated. The mathematical statements of some classes of three-dimensional axisymmetrical problem for solids with interacting circular cracks are given. The critical parameters of fracture for very small distances between cracks are calculated in problems for a half-space with a near-surface crack, for an infinity solid with two parallel coaxial cracks and for a space with periodical system of coaxial cracks. For these problems the criteria of applicability of the approximate design model both concerning parameter thin-walled and concerning boundary conditions used in approximate design model are founded.