Аннотация
The description of the problems, solved within the frame of deformability theory is given. The mathematical statement of the basic problem of deformability theory for obtaining the analytical dependеnces of ultimate strains in closed form is considered. It is shown that this problem, even applying the principle of linear damage accumulation is connected with the solution of a nonlinear integral equation, that can be composed in a number of ways. The general solution of the integral equation for the case, set by deformations path, is obtained. Analytical solutions of the basic problem of deformability theory for separate cases are obtained and analyzed, in particular, for deformations path, that occurs on the free surface at axisymmetric compression of cylindric specimen by flat rough plates.