Solution Behavior Near Very Rough Walls under Axial Symmetry: An Exact Solution for Anisotropic Rigid/Plastic Material

Abstract

Rigid plastic material models are suitable for modeling metal forming processes at large strains where elastic effects are negligible. A distinguished feature of many models of this class is that the velocity field is describable by non-differentiable functions in the vicinity of certain friction surfaces. Such solution behavior causes difficulty with numerical solutions. On the other hand, it is useful for describing some material behavior near the friction surfaces. The exact asymptotic representation of singular solution behavior near the friction surface depends on constitutive equations and certain conditions at the friction surface. The present paper focuses on a particular boundary value problem for anisotropic material obeying Hill’s quadratic yield criterion under axial symmetry. This boundary value problem represents the deformation mode that appears in the vicinity of frictional interfaces in a class of problems. In this respect, the applied aspect of the boundary value problem is not essential, but the exact mathematical analysis can occur without relaxing the original system of equations and boundary conditions. We show that some strain rate and spin components follow an inverse square rule near the friction surface. An essential difference from the available analysis under plane strain conditions is that the system of equations is not hyperbolic.