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- 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

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!

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

__assumption!__*plane strain*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!

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