Deformation and fracture of a material in one-dimensional elastoplastic problems

The ideal plasticity model based on the Tresca-Saint-Venant criterion is used to solve one-dimensional problems of deformation and fracture of solids with circular boundaries. A thickwalled cylinder and a hollow sphere under pressure, cylindrical and hollow cavities in an unbounded body, and uniform extension at infinity of a plate with a free circular hole are considered. In simple elastoplastic problems, the proposed approach allows one to determine the value of the maximum external load at the fracture initiation and the motion of the fracture front for a given displacement of points of the contour on which this load acts.