Abstract
The simplest phenomenological models of materials having different resistances to tension and compression are constructed using a rheological method supplemented by a new element — a rigid contact. The problems of the solvability of static boundary-value problems for small deformations of the medium are considered within the framework of the regularized model. A generalization of the static and kinematic theorems of the theory of limiting equilibrium is given. The upper bound of the limiting load and the angle of emergence of the linear zone of deformation localization in the problem of the rupture of a cylindrical specimen with a radial notch when there is pressure on the sides of the notch is obtained as an example of the application of these theorems
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