The Problem of Stretching a Hollow Cylinder

The problem of uniaxial tension of a hollow cylinder made of a rigid-plastic material is considered. Within the framework of the theory of an ideal rigid-plastic body, this problem has many solutions. Based on the Strain-Energy Criteria of choosing the preferred solution, this problem can be solved unambiguously.

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

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.

Torsion of rods made of anisotropically hardening material under a linearized plasticity condition

В работе исследовано кручение стержней из анизотропно упрочняющегося жесткопластического материала. Получены интегралы, определяющие напряженное и деформированное состояния стержня при линеаризованном условии пластичности. Построены линии разрыва напряжений. The torsion of rods made of anisotropically hardening rigid-plastic material is studied. Integrals are obtained that determine the stress and strain States of the rod under the linearized plasticity condition. Stress discontinuity lines are constructed.

Torsion of inhomogeneous rods made of an ideal rigid plastic material under a linearized plasticity condition

В работе исследовано кручение неоднородных стержней из идеального жесткопластического материала. Получены интегралы, определяющие напряженное и деформированное состояния стержня при линеаризованном условии пластичности. Определено предельное состояние призматического стержня при кручении, найдены линии разрыва напряжений. The torsion of inhomogeneous rods made of an ideal rigid-plastic material is studied. Integrals are obtained that determine the stress and strain States of the rod under the linearized plasticity condition. The limit state of the prismatic rod during torsion is determined, and the stress break lines are found

Torsion of anisotropic and non-uniform cylindrical rods with elliptical section

In work the limit state of cylindrical and prismatic rods from anisotropic ideal rigid-plastic material is investigated under torsion for arbitrary condition of plasticity, and the torsion of anisotropic and non-uniform rods with elliptic section under the condition of Mises-Hill plasticity is considered. The integrals determining the stressed state of an anisotropic rod under arbitrary condition of plasticity are obtained, the field of characteristics of the basic ratios for anisotropic and composite rods under the condition of Mises-Hill plasticity is constructed, the ratios along characteristics are obtained, the envelopes of the family of characteristics and lines of tension rupture are found.