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Br--1995
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- TL;DR Summary
- Find a corresponding analytical solution for the strain in the x-direction caused by the poisson ratio.
Hi, I ran into problems using the poisson ratio.
For a FE simulation I created a simple 2D 1mm x 1mm block, and prescribed a 0.1 mm displacement at the top edge.
Furthermore, the bottom edge is constraint in the y-dir, and the left edge in the x-dir.
The material parameters are E = 100, and v (poisson ratio) = 0.3.
Note the simulation is executed for a plane strain assumption!
To verify the results I would like to solve the analytical solution for this problem.
This is quite simple tbh, I use the 2D strain-stress relations for the plane strain problem.
However, the simulation shows that the strain_yy = -0.1 (as expected) but the strain_xx = 0.04285714.
I really cannot figure out the analytical solution for the strain_xx, I would expect this to be 0.03 (strain_xx = -v * strain_yy).
I know that the 0.0428.. value should be the correct one, because I tried the simulation in different simulation software.
Hopefully someone can explain me how to get this value analytically?
Thanks in advance!
![Strain_xx.PNG Strain_xx.PNG](https://www.physicsforums.com/data/attachments/255/255407-2519a76ecf94785f7cd35f94b63584ac.jpg)
For a FE simulation I created a simple 2D 1mm x 1mm block, and prescribed a 0.1 mm displacement at the top edge.
Furthermore, the bottom edge is constraint in the y-dir, and the left edge in the x-dir.
The material parameters are E = 100, and v (poisson ratio) = 0.3.
Note the simulation is executed for a plane strain assumption!
To verify the results I would like to solve the analytical solution for this problem.
This is quite simple tbh, I use the 2D strain-stress relations for the plane strain problem.
However, the simulation shows that the strain_yy = -0.1 (as expected) but the strain_xx = 0.04285714.
I really cannot figure out the analytical solution for the strain_xx, I would expect this to be 0.03 (strain_xx = -v * strain_yy).
I know that the 0.0428.. value should be the correct one, because I tried the simulation in different simulation software.
Hopefully someone can explain me how to get this value analytically?
Thanks in advance!
![Situation_sketch.PNG Situation_sketch.PNG](https://www.physicsforums.com/data/attachments/255/255406-03e2f45fca47246b0e7d2c608869ef2f.jpg)
![Displacement_x.PNG Displacement_x.PNG](https://www.physicsforums.com/data/attachments/255/255405-8f210a6038d8cde5933c8116cf6b8755.jpg)
![Strain_xx.PNG Strain_xx.PNG](https://www.physicsforums.com/data/attachments/255/255407-2519a76ecf94785f7cd35f94b63584ac.jpg)
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