The aim of the work is the mathematical modelling of the plastic flow generated during the process of wedge insertion into a convex workpiece. In the course of solving the problem, the following equations were derived: a system of equations for the construction of the plastic region and the deformed surface of the material at each instant; a relation that allows us to determine the load required for the introduction of the wedge; expressions for calculating the deformations produced by the material particles on the displacement velocity gap line and in the center of the fan of slip lines. A numerical solution of a special case of the problem of wedge insertion in a hyperbolic cylinder has been obtained, for which: plots of the variation of the opening angle of the fan of features and of the load required for wedge insertion, of the plastic region and of the deformed surface have been constructed; deformations produced by material particles in the vicinity of the features of the slip line field have been calculated.

Ilya V. Kanashin, Senior Lecturer; e-mail: kanashin94@mail.ru; AuthorID: 1094116

Anna L. Grigorieva, Candidate of Physical and Mathematical Sciences, Associate Professor, Head of Applied Mathematics Department; e-mail: naj198282@mail.ru; AuthorID: 166322

Yan Yu. Grigoriev, Candidate of Physical and Mathematical Sciences, Associate Professor of Applied Mathematics Department; e-mail: prorector-ur@knastu.ru; AuthorID: 166323