Computerized Relaxation Applied to the Plane-Strain Indenter

1969 ◽  
Vol 91 (4) ◽  
pp. 816-821
Author(s):  
J. W. Wesner ◽  
A. S. Weinstein
Keyword(s):  
Stress Distribution ◽  
Plane Strain ◽  
Slip Line ◽  
Relaxation Method ◽  
Strip Thickness ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Distribution Problems ◽  
Plastic Stress

A computer adaptation of Southwell’s Relaxation Method was developed for the solution of elastic-perfectly plastic stress distribution problems. This method was employed to study some aspects of the problem of the plane-strain indenter. For two ratios of strip thickness to indenter width, the load for, and location of, initial yielding and the load for the onset of indentation were found. The results are compared with slip-line solutions.

Plane strain distribution in perfectly plastic regions around circular holes due to unequal biaxial loads

1966 ◽  
Vol 1 (5) ◽  
pp. 394-397 ◽  
Author(s):  
I S Tuba
Keyword(s):  
Stress Distribution ◽  
Plane Strain ◽  
Strain Distribution ◽  
Plastic Region ◽  
Secant Modulus ◽  
Compatibility Equation ◽  
Perfectly Plastic ◽  
Biaxial Loads ◽  
Circular Holes ◽  
Elastic Perfectly Plastic

The elastic-perfectly plastic solution of Galin provides only the stress distribution for the plastic region. The theory is extended and the compatibility equation is solved for the secant modulus. The unfinished problem of Galin is thus completed and the strain distribution is obtained for the perfectly plastic region around a circular hole due to unequal biaxial loads.

Analytical Solutions of Crack Tip Plasticity Zone Shape for a Semi-Infinite Crack

2003 ◽  
Author(s):  
Peihua Jing ◽  
Tariq Khraishi ◽  
Larissa Gorbatikh
Keyword(s):  
Plane Strain ◽  
Plane Stress ◽  
Analytical Solutions ◽  
Yield Criterion ◽  
Plasticity Zone ◽  
Linear Elastic ◽  
Perfectly Plastic ◽  
Classical Plasticity ◽  
Elastic Perfectly Plastic ◽  
Von Mises

In this work, closed-form analytical solutions for the plasticity zone shape at the lip of a semi-infinite crack are developed. The material is assumed isotropic with a linear elastic-perfectly plastic constitution. The solutions have been developed for the cases of plane stress and plane strain. The three crack modes, mode I, II and III have been considered. Finally, prediction of the plasticity zone extent has been performed for both the Von Mises and Tresca yield criterion. Significant differences have been found between the plane stress and plane strain conditions, as well as between the three crack modes’ solutions. Also, significant differences have been found when compared to classical plasticity zone calculations using the Irwin approach.

A Compressible Elastic, Perfectly Plastic Wedge

1958 ◽  
Vol 25 (2) ◽  
pp. 239-242
Author(s):  
D. R. Bland ◽  
P. M. Naghdi
Keyword(s):  
Plane Strain ◽  
Yield Criterion ◽  
The State ◽  
Hardening Material ◽  
Included Angle ◽  
Elastic Plastic ◽  
Numerical Example ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

Abstract This paper is concerned with a compressible elastic-plastic wedge of an included angle β < π/2 in the state of plane strain. The solution, deduced for an isotropic nonwork-hardening material, employs Tresca’s yield criterion and the associated flow rules. By means of a numerical example the solution is compared with that of an incompressible elastic-plastic wedge in one case (β = π/4) for various positions of the elastic-plastic boundary.

Stresses and Displacements in an Elastic-Plastic Wedge

1957 ◽  
Vol 24 (1) ◽  
pp. 98-104
Author(s):  
P. M. Naghdi
Keyword(s):  
Plane Strain ◽  
Isotropic Material ◽  
Complete Solution ◽  
Normal Pressure ◽  
Stress Strain ◽  
Included Angle ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Plastic Domain ◽  
Elastic Perfectly Plastic

Abstract An elastic, perfectly plastic wedge of an incompressible isotropic material in the state of plane strain is considered, where the stress-strain relations of Prandtl-Reuss are employed in the plastic domain. For a wedge (with an included angle β) subjected to a uniform normal pressure on one boundary, the complete solution is obtained which is valid in the range 0 < β < π/2; this latter limitation is due to the character of the initial yield which depends on the magnitude of β. Numerical results for stresses and displacements are given in one case (β = π/4) for various positions of the elastic-plastic boundary.

Plastic Twisting of Thick-Walled Circular Ring Sectors

1956 ◽  
Vol 23 (3) ◽  
pp. 461-463
Author(s):  
W. Freiberger ◽  
W. Prager
Keyword(s):  
Stress Distribution ◽  
Plastic Flow ◽  
Cross Section ◽  
Cross Sections ◽  
Graphical Method ◽  
Plastic Material ◽  
Circular Ring ◽  
Perfectly Plastic ◽  
The Cross ◽  
Plastic Stress

Abstract The paper presents a graphical method of determining the fully plastic stress distribution in a twisted circular ring sector with hollow cross section and the warping of the cross sections of this ring in the ensuing plastic flow. The ring is assumed to consist of a rigid, perfectly plastic material.

Elastic-Plastic Plane Strain Analysis of Compressible Materials

1987 ◽  
Vol 109 (3) ◽  
pp. 357-358
Author(s):  
Hui Fan ◽  
G. E. O. Widera
Keyword(s):  
Plane Strain ◽  
Order Approximation ◽  
Strain Analysis ◽  
Perturbation Parameter ◽  
Incompressible Material ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
First Order Approximation ◽  
Compressible Materials ◽  
Walled Cylinder

The analysis of elastic, perfectly plastic compressible materials under the assumption of plane strain is a statically indeterminate problem. In the present paper, by introducing a perturbation parameter ε = 1/2−ν, the problem can be changed into a series of statically determinate ones. The first-order approximation yields the solution for the incompressible material. In order to show the details of this method, the second-order approximation for the problem of the thick-walled cylinder under internal pressure is obtained.

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