Plane-Strain Bending With Isotropic Strain Hardening at Large Strains

2010 ◽  
Vol 77 (6) ◽  
Author(s):  
Sergei Alexandrov ◽  
Yeong-Maw Hwang
Keyword(s):  
Strain Hardening ◽  
Plane Strain ◽  
Closed Form Solution ◽  
Bending Moment ◽  
Form Solution ◽  
Isotropic Hardening ◽  
Large Strains ◽  
Rigid Plastic ◽  
Elastic Plastic ◽  
Hardening Law

Finite deformation elastic-plastic analysis of plane-strain pure bending of a strain hardening sheet is presented. The general closed-form solution is proposed for an arbitrary isotropic hardening law assuming that the material is incompressible. Explicit relations are given for most popular conventional laws. The stage of unloading is included in the analysis to investigate the distribution of residual stresses and springback. The paper emphasizes the method of solution and the general qualitative features of elastic-plastic solutions rather than the study of the bending process for a specific material. In particular, it is shown that rigid-plastic solutions can be used to predict the bending moment at sufficiently large strains.

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.

Negative skin friction and the neutral plane

1994 ◽  
Vol 31 (4) ◽  
pp. 591-597 ◽  
Author(s):  
Elmer L. Matyas ◽  
J. Carlos Santamarina
Keyword(s):  
Closed Form ◽  
Key Words ◽  
Skin Friction ◽  
Closed Form Solution ◽  
Form Solution ◽  
Neutral Plane ◽  
Rigid Plastic ◽  
Negative Skin Friction ◽  
Elastic Plastic ◽  
Drag Forces

Current views indicate that negative skin friction on piles can be mobilized at small relative deformations and should be considered in all designs, primarily for serviceability conditions. An elastic-plastic closed-form solution is presented that permits an estimate of down-drag forces and the location of the neutral plane. It is shown that the conventional rigid-plastic solution may overestimate down-drag forces by as much as 50% and may also overestimate the depth of the neutral plane. Key words : piles, negative skin friction, neutral plane, capacity.

Bending and Twisting of Pipes With Strain Hardening

1984 ◽  
Vol 106 (2) ◽  
pp. 188-195 ◽  
Author(s):  
J. H. Lau ◽  
T. T. Lau
Keyword(s):  
Effective Strain ◽  
Closed Form Solution ◽  
Bending Moment ◽  
Small Deformation ◽  
Form Solution ◽  
Simultaneous Action ◽  
Deformation Analysis ◽  
Engineering Practice ◽  
Strain Diagram ◽  
Interaction Curves

A closed-form solution is presented for the small deformation analysis of a straight thin-walled circular cylinder subjected to the simultaneous action of bending and twisting moments. Dimensionless interaction curves and charts which relate the variables, bending moment, curvature, maximum effective strain, twisting moment, and shear strain are also provided for engineering practice convenience. The average stress-strain diagram of the cylinder is described by two straight lines. The result presented herein is not only a good approximation of a wide class of piping materials, but also provides a standard tool for estimating the accuracy of different direct schemes such as numerical integration, finite-difference, and finite-element methods.

scholarly journals Green's functions for unsymmetric composite laminates with inclusions

2020 ◽  
Vol 476 (2233) ◽  
pp. 20190437
Author(s):  
Chia-Wen Hsu ◽  
Chyanbin Hwu
Keyword(s):  
Composite Laminates ◽  
Green's Functions ◽  
Green’S Functions ◽  
Closed Form Solution ◽  
Bending Moment ◽  
Form Solution ◽  
Displacement Discontinuity ◽  
Computational Time ◽  
Out Of Plane ◽  
Logarithmic Functions

It is known that the stretching and bending deformations will be coupled together for the unsymmetric composite laminates under in-plane force and/or out-of-plane bending moment. Although Green's functions for unsymmetric composite laminates with elliptical elastic inclusions have been obtained by using Stroh-like formalism around 10 years ago, due to the ignoring of inconsistent rigid body movements of matrix and inclusion, the existing solution may lead to displacement discontinuity across the interface between matrix and inclusion. Due to the multi-valued characteristics of complex logarithmic functions appeared in Green's functions, special attention should be made on the proper selection of branch cuts of mapped variables. To solve these problems, in this study, the existing Green's functions are corrected and a simple way to correctly evaluate the mapped complex variable logarithmic functions is suggested. Moreover, to apply the obtained solutions to boundary element method, we also derive the explicit closed-form solution for Green's function of deflection. Since the continuity conditions along the interface have been satisfied in Green's functions, no meshes are required along the interface, which will save a lot of computational time and the results are much more accurate than any other numerical methods.

The Elastic-Plastic Analysis of Tubes—II: Variable Loading

1992 ◽  
Vol 114 (2) ◽  
pp. 222-228 ◽  
Author(s):  
W. Jiang
Keyword(s):  
Closed Form Solution ◽  
Yield Condition ◽  
Complex Loading ◽  
Form Solution ◽  
Stress And Strain ◽  
Variable Loading ◽  
Elastic Plastic ◽  
Incremental Method ◽  
Plastic Analysis ◽  
General Program

This paper is concerned with the elastic-plastic analysis of tubes subjected to variable loads. The yield condition for a material having residual stress and strain is first derived. Then by incremental method, the stresses and strains of the tube at any loading stage can be found. A closed-form solution is achieved as an example of tubes incurring ratchetting, and a general program is developed to make the theory applicable to complex loading situations.

Finite Deformations of a Rigid Perfectly Plastic Arch

1962 ◽  
Vol 29 (3) ◽  
pp. 549-553 ◽  
Author(s):  
E. T. Onat ◽  
L. S. Shu
Keyword(s):  
Closed Form ◽  
Yield Point ◽  
Finite Deformation ◽  
Closed Form Solution ◽  
Form Solution ◽  
Finite Deformations ◽  
Deformation History ◽  
Rigid Plastic ◽  
Perfectly Plastic ◽  
History Of

The quasi-static postyield deformation of a rigid-plastic arch in the presence of geometry changes is considered. The problem is formulated in terms of a series of boundary-value problems concerned with rates of stress and velocities. In the present simple case, the consideration of the rate problem associated with the yield-point state of the structure enables one to construct a closed-form solution which describes the entire deformation history of the arch. However, the principal aim of the present study is to stress the central role played by the rate problem in the investigation of the finite deformation of structures.

scholarly journals Effect of Strain Hardening on Elastic-Plastic Contact of a Deformable Sphere against a Rigid Flat under Full Stick Contact Condition

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Biplab Chatterjee ◽  
Prasanta Sahoo
Keyword(s):  
Strain Hardening ◽  
Kinematic Hardening ◽  
Contact Condition ◽  
Isotropic Hardening ◽  
Contact Conditions ◽  
Elastic Plastic ◽  
Finite Element Software ◽  
Hardening Models ◽  
Load Carrying ◽  
Contact Parameters

The present study considers the effect of strain hardening on elastic-plastic contact of a deformable sphere with a rigid flat under full stick contact condition using commercial finite element software ANSYS. Different values of tangent modulus are considered to study the effect of strain hardening. It is found that under a full stick contact condition, strain hardening greatly influences the contact parameters. Comparison has also been made between perfect slip and full stick contact conditions. It is observed that the contact conditions have negligible effect on contact parameters. Studies on isotropic and kinematic hardening models reveal that the material with isotropic hardening has the higher load carrying capacity than that of kinematic hardening particularly for higher strain hardening.

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