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

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 184
Author(s):  
Sergei Alexandrov ◽  
Elena Lyamina ◽  
Pierre-Yves Manach
Keyword(s):  
Boundary Value Problem ◽  
Axial Symmetry ◽  
Friction Surface ◽  
Plastic Material ◽  
Boundary Value ◽  
System Of Equations ◽  
Rigid Plastic ◽  
Solution Behavior ◽  
Rigid Plastic Material ◽  
Friction Surfaces

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.

Stamping Rectangular Plates into Doubly-Curved Dies

1984 ◽  
Vol 198 (2) ◽  
pp. 109-125 ◽  
Author(s):  
T X Yu ◽  
W Johnson ◽  
W J Stronge
Keyword(s):  
Plastic Material ◽  
Rectangular Plates ◽  
Rigid Plastic ◽  
Punch Force ◽  
Plate Buckling ◽  
Rigid Plastic Material ◽  
Force Contact ◽  
Curvature Distribution ◽  
Doubly Curved ◽  
Deformation Modes

Shallow spheroidal shell segments have been press formed from rectangular plates by stamping between a die and matching punch that have two degrees of curvature. Experiments on mild steel, copper and aluminium plates that were not clamped in the die have measured the punch force, contact regions and final curvature distribution; and have observed plate buckling for a range of die curvature ratios and plate sizes. An analysis based on a rigid/plastic material idealization and decoupled in-plane forces and bending moments has been correlated with these experiments. The sequence of deformation modes has been identified; initially these are bending but in later stages, in-plane forces predominate.

Theory of compression of a compressible rigid-plastic material

1974 ◽  
Vol 10 (3) ◽  
pp. 323-326
Author(s):  
I. S. Degtyarev ◽  
V. L. Kolgomorov
Keyword(s):  
Plastic Material ◽  
Rigid Plastic ◽  
Rigid Plastic Material

Response of a Rigid-Plastic Ring to Impulse Loading

1967 ◽  
Vol 34 (2) ◽  
pp. 329-336 ◽  
Author(s):  
G. B. Cline ◽  
W. E. Jahsman
Keyword(s):  
Incident Energy ◽  
Plastic Material ◽  
Maximum Magnitude ◽  
Impulse Loading ◽  
Rigid Plastic ◽  
Plastic Ring ◽  
Stress Mode ◽  
Rigid Plastic Material ◽  
Impulse Load ◽  
Final Deformation

Formulas are derived which describe the dynamic response of a ring of rigid-plastic material which is subjected to an arbitrarily distributed impulse load. When the impulse is distributed over half the ring in a cosine fashion, the final deformation is proportional to the square of the maximum magnitude of the applied impulse. Although the predominant deformation is in a bending or “ovaling” mode, one half of the incident energy is dissipated in the “membrane” or direct stress mode. The remainder is divided equally between bending (plastic work at the hinges) and kinetic energy.

Rigid-Plastic Meshfree Method for Metal Forming Simulation

2003 ◽  
Author(s):  
Young H. Park
Keyword(s):  
Metal Forming ◽  
Plastic Material ◽  
Meshfree Method ◽  
Large Plastic Deformation ◽  
Rigid Plastic ◽  
Mesh Distortion ◽  
Forming Simulation ◽  
Rigid Plastic Material ◽  
Plastic Analysis ◽  
Main Variable

In this paper, material processing simulation is carried out using a meshfree method. With the use of a meshfree method, the domain of the workpiece is discretized by a set of particles without using a structured mesh to avoid mesh distortion difficulties which occurred during the course of large plastic deformation. The proposed meshfree method is formulated for rigid-plastic material. This approach uses the flow formulation based on the assumption that elastic effects are insignificant in the metal forming operation. In the rigid-plastic analysis, the main variable of the problem becomes flow velocity rather than displacement. A numerical example is solved to validate the proposed method.

Pressbrake Bending in the Punch-Sheet Contact Region—Part 1: Modeling Nonuniformities

1988 ◽  
Vol 110 (2) ◽  
pp. 124-130 ◽  
Author(s):  
F. Pourboghrat ◽  
K. A. Stelson
Keyword(s):  
Shear Stress ◽  
Simple Model ◽  
Stress Distribution ◽  
Plastic Material ◽  
Contact Region ◽  
Rigid Plastic ◽  
Material Models ◽  
Rigid Plastic Material

A simple model of pressbrake bending in the punch-sheet contact region is presented. The pressure and shear stress at the punch-sheet interface cause the stress distribution in the sheet to change as a function of angle. In Part 1 of this paper, a model to predict nonuniformities as a function of the geometry and the frictional conditions is presented. In Part 2, the model will be used to predict the formation of a gap between the sheet and the punch. Elastic and rigid-plastic material models of the sheet are considered, and are shown to produce remarkably similar results.

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