Continuum Modelling of the Anisotropic Elastic-Plastic In-Plane Behavior of Paper in Small and Large Strains Regimes

2019 ◽  
pp. 1-18
Author(s):  
Ahmad Alajami ◽  
Yujun Li ◽  
Jaan-Willem Simon
Keyword(s):  
Large Strains ◽  
Elastic Plastic ◽  
Continuum Modelling ◽  
Anisotropic Elastic

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.

Anisotropic elastic and elastic–plastic bending solutions for edge constrained beams

2005 ◽  
Vol 42 (18-19) ◽  
pp. 4927-4946 ◽  
Author(s):  
J.G. Williams ◽  
H. Hadavinia ◽  
B. Cotterell
Keyword(s):  
Plastic Bending ◽  
Elastic Plastic ◽  
Anisotropic Elastic

scholarly journals Anisotropic elastic-plastic deformation of paper: In-plane model

2016 ◽  
Vol 100-101 ◽  
pp. 286-296 ◽  
Author(s):  
Yujun Li ◽  
Scott Edward Stapleton ◽  
Stefanie Reese ◽  
Jaan-Willem Simon
Keyword(s):  
Plastic Deformation ◽  
Plane Model ◽  
Elastic Plastic ◽  
Anisotropic Elastic
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