Boiko A. Displacement plastic spall of rigid inclusions at the conditions of incomplete contact with medium.

The object of the study is the elastic-plastic bodies with rigid inclusions of complex form with the presence of inter-phase cracks. The aim of the study is to develop the analytical method of investigation of plasticexfoliation of fibers with complex cross-section in reinforced and composite materials under high shear stresses with the presence of inter-phase cracks. The used methods are the methods of ideal plasticity, the mathematical methods of solving non-linear boundary problems of theory of analytical functions, in particular, the method of conformal mapping and Keldysh-Sedov problem. The novelty is that the analytical solutions of a number of new problems for inclusions of different forms were obtained; the initial stageof the development of plastic layers is investigated; the formulas for the length of plastic layers depending on stress intensity factors were derived.