Numerical method for elastic-plastic waves in cracked solids, Part 2: plane strain problem

1993 ◽  
Vol 63 (4-5) ◽  
pp. 283-295 ◽  
Author(s):  
X. Lin ◽  
J. Ballmann
Keyword(s):  
Numerical Method ◽  
Plane Strain ◽  
Plane Strain Problem ◽  
Elastic Plastic ◽  
Cracked Solids

scholarly journals Finite Pure Plane Strain Bending of Inhomogeneous Anisotropic Sheets

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 145
Author(s):  
Sergei Alexandrov ◽  
Elena Lyamina ◽  
Yeong-Maw Hwang
Keyword(s):  
Plane Strain ◽  
Yield Criterion ◽  
Large Strains ◽  
Rigid Plastic ◽  
Plastic Properties ◽  
Elastic Plastic ◽  
Starting Point ◽  
The Difference ◽  
Inside Radius ◽  
Elastic Unloading

The present paper concerns the general solution for finite plane strain pure bending of incompressible, orthotropic sheets. In contrast to available solutions, the new solution is valid for inhomogeneous distributions of plastic properties. The solution is semi-analytic. A numerical treatment is only necessary for solving transcendent equations and evaluating ordinary integrals. The solution’s starting point is a transformation between Eulerian and Lagrangian coordinates that is valid for a wide class of constitutive equations. The symmetric distribution relative to the center line of the sheet is separately treated where it is advantageous. It is shown that this type of symmetry simplifies the solution. Hill’s quadratic yield criterion is adopted. Both elastic/plastic and rigid/plastic solutions are derived. Elastic unloading is also considered, and it is shown that reverse plastic yielding occurs at a relatively large inside radius. An illustrative example uses real experimental data. The distribution of plastic properties is symmetric in this example. It is shown that the difference between the elastic/plastic and rigid/plastic solutions is negligible, except at the very beginning of the process. However, the rigid/plastic solution is much simpler and, therefore, can be recommended for practical use at large strains, including calculating the residual stresses.

Equilibrium equations and boundary conditions of strain gradient theory in arbitrary curvilinear coordinates

2014 ◽  
Vol 23 (5-6) ◽  
pp. 169-176
Author(s):  
Mikhail Guzev ◽  
Chengzhi Qi ◽  
Jiping Bai ◽  
Kairui Li
Keyword(s):  
Boundary Conditions ◽  
Plane Strain ◽  
Strain Gradient ◽  
Special Form ◽  
Curvilinear Coordinates ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Equilibrium Equations ◽  
Plane Strain Problem

AbstractEquilibrium equations and boundary conditions of the strain gradient theory in arbitrary curvilinear coordinates have been obtained. Their special form for an axisymmetric plane strain problem is also given.

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.

The Comparison of the Loess Mechanical Properties under Plane Strain and Conventional Triaxial Experiments

2014 ◽  
Vol 919-921 ◽  
pp. 791-794
Author(s):  
Lin Ma
Keyword(s):  
Mechanical Properties ◽  
Moisture Content ◽  
Plane Strain ◽  
Confining Pressure ◽  
Test Method ◽  
The Other ◽  
Strain Condition ◽  
Plane Strain Problem ◽  
Plain Strain ◽  
The Impact

Plane strain problem is currently prevalent in the loess engineering. However, this problem still using conventional triaxial test method for processing. So the paper conducted the plain strain test, analyze differences in plane strain experiments with conventional triaxial experiments under different moisture content and confining pressure. Research shows two points, the first one is the impact on the strength of the soil is more under moisture content than confining pressure, the other is that the soil strength under the plane strain condition is significantly greater than conventional triaxial conditions. It shows that the results were conservative under the plane strain problem at past. It played a certain role in guiding the engineering.

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