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A steel parallelepiped with a square cross-section fits exactly into the cavity. it's loaded from the top surface(see picture). how can I calculate the stress in X- and Y-direction if the strain in X- and Y-direction is zero.

enter image description here enter image description here

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Depending on the structural properties of the surrounding material, you will have transfer of stress and strain between the two.

But let's assume there is no side strain for now.

Then you have to superpose two cases.

1- the vertical loading

2- assuming 1/3 strain along X and Z axis, calculate the pressure that would deflect them back to zero and apply that as lateral loading.

You can do this by a couple of iterations, and I guess some FEM programs allow for setting this up as a support constrain.

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  • $\begingroup$ Thank you very much for your answer, I calculate with ANSYS APDL. I have an additional comment. -if the side of parallelepiped should freely move (see picture) the strain in X- and Z-direction should be calculated like this (see linked picture). -This strain in the 1st case (with the walls, see 1. comment) are blocked. has the strain in the 2nd case (the side of parallelepiped freely move) what to do with stress in the 2nd case. $\endgroup$ – Zouhir Bensebban Jan 17 '19 at 8:08

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