Ideal plastic half-space indentation by the elliptical cylinder

R. I. Nepershin

Moscow State Technological University "Stankin"

Abstract: Numerical simulation of the plane strain ideal plastic half-space indentation by the rigid elliptical cylinder with Prandtl's contact fiction consideration is presented. The slip lines and velocities on the hodograph plane with positive plastic dissipative function are defined by numerical calculation of differential equations of the plane strain plastic flow theory. Curved form of the stress free boundary of the plastic region, which is function of the cylinder indentation depth, is defined by the plastic incompressibility condition. The numerical simulation satisfies the full equations system of the plane strain ideal plastic theory with Mises yield criterion and positive dissipative function in the plastic region. The simulation is constrained by the limit indentation depth, when in the case of the contact boundary curvature decreasing the centered fun slip lines region is degenerated, or in the case of the contact boundary curvature increasing by nucleation of small regions with negative plastic dissipative function, with indentation depth increase.

Keywords: ideal plastic half-space, indentation, rigid elliptical cylinder, plane strain theory, contact friction, slip lines, velocities hodograph, plastic dissipative function.

Received: 01.02.2023
Revised: 06.06.2023
Accepted: 05.05.2023

DOI: 10.37972/chgpu.2023.55.1.009