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.

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 limit load solution for a thick-walled cylinder with a fully circumferential crack under axial tension

2009 ◽  
Vol 44 (6) ◽  
pp. 407-416 ◽  
Author(s):  
P J Budden ◽  
Y Lei
Keyword(s):  
Finite Element ◽  
Plastic Material ◽  
Yield Criterion ◽  
Limit Load ◽  
Cylinder Wall ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Von Mises ◽  
Inside Radius ◽  
Walled Cylinder

Limit loads for a thick-walled cylinder with an internal or external fully circumferential surface crack under pure axial load are derived on the basis of the von Mises yield criterion. The solutions reproduce the existing thin-walled solution when the ratio between the cylinder wall thickness and the inside radius tends to zero. The solutions are compared with published finite element limit load results for an elastic–perfectly plastic material. The comparison shows that the theoretical solutions are conservative and very close to the finite element data.

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.

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.

On the stability of supported excavations

1984 ◽  
Vol 21 (2) ◽  
pp. 338-348 ◽  
Author(s):  
A. M. Britto ◽  
O. Kusakabe
Keyword(s):  
Plane Strain ◽  
Upper Bound ◽  
Plastic Material ◽  
Cohesive Soil ◽  
Perfectly Plastic ◽  
Centrifuge Tests ◽  
Bentonite Slurry ◽  
Undrained Conditions ◽  
Elastic Perfectly Plastic ◽  
The Stability

Unsupported plane strain trenches and axisymmetric shafts cannot be excavated to great depths in a purely cohesive soil. Therefore, it is standard practice to provide some form of support. Timber supports with struts are conventional and quite common. Bentonite slurry support has become more popular in recent years especially in the construction of diaphragm walls. In this paper the effect of rigid lateral support and slurry support on the stability (mode of failure) for both plane strain and axisymmetric excavations are investigated under undrained conditions. When immediate failure is of interest in saturated clays the changes in the water content can be neglected and the soil can be treated as a [Formula: see text] material. For the purposes of the analyses presented here the lateral support is assumed to be rigid and the soil is idealized as an elastic perfectly plastic material with cohesion Cu. The results from upper bound calculations, finite element collapse analyses, and centrifuge tests are presented. The analogy between deep footing failure and base failure of excavation allows the solutions for the footing problem to be interpreted for trench excavations. It is found that slurry support is more effective than rigid lateral support for axisymmetric excavations. The slurry support reduces the amount of surface settlement and also stabilises the trench against base failure. For excavations with rigid lateral support the possibility of base failure is greatly increased. The results are presented in the form of stability charts. Keywords: limit analysis, slurry support, stability number, supported excavation, upper bound solution.

scholarly journals Analysis of stress and strain in a rotating disk mounted on a rigid shaft

2006 ◽  
Vol 33 (1) ◽  
pp. 65-90 ◽  
Author(s):  
Nelli Alexandrova ◽  
Sergei Alexandrov ◽  
Real Vila
Keyword(s):  
Yield Criterion ◽  
Strain Analysis ◽  
Rotating Disk ◽  
Outer Radius ◽  
Constant Thickness ◽  
Flow Rule ◽  
Plane State ◽  
Annular Disk ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

The plane state of stress in an elastic-perfectly plastic isotropic rotating annular disk mounted on a rigid shaft is studied. The analysis of stresses, strains and displacements within the disk of constant thickness and density is based on the Mises yield criterion and its associated flow rule. It is observed that the plastic deformation is localized in the vicinity of the inner radius of the disk, and the disk of a sufficiently large outer radius never becomes fully plastic. The semi-analytical method of stress-strain analysis developed is illustrated by some numerical examples. .

Sign in / Sign up

Export Citation Format

Share Document