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I used Google Translate on your first paragraph to read the following:

Unfortunately, I will not be able to reach the model until the 30th of the month due to a problem with the network remotely, but I would like to share the details. When I used bonded contact, the middle parts of the core edge and plate were holding each other when everything was in program controlled. That's why I decided to use a fixed joint. There is no facesheet in my model and when I thought about the logic of the test, I thought the joints should be rigid.

I agree that the load travels diagonally through the core, so it is good to have a Csys that creates the diagonal plane. The force on the top test plate should be applied in a coordinate direction of that Csys. What face of the top test plate did you select to apply the force to? In the figure above, the end face near the pivot pin would be a good selection if the centroid of that face lies on the diagonal plane. If the centroid of that face is not on the diagonal plane, then you should use a Remote Force and set the coordiantes of the remote point to be on the diagonal plane by using the diagonal Csys and typing in a zero on the axis normal to the plane.

If the bottom side of the core has a Fixed Support, there is no need for any displacement boundary condition on the top test plate, there should only be a force. Please clarify what displacement you are applying to the top plate.

I also agree that the test plates are much stiffer than the core so treating them as perfectly rigid will not alter the results too much.

I agree that you want the initial slope of the shear deformation, so a linear solution is all you need. Don't bother to turn on large deflection, you are not interested in the nonlinear response. In a linear solution (large deflection off), the load can be an arbitrary number like 500 N or 1 N since you are simply creating a ratio. In a linear solution, time is irrelevant, the End Time is usually 1 second. In a Static Structural, the strain rate is irrelevant. In a linear solution, you only need 1 step to solve. Again, what displacement are you applying?

To get a Modulus, you either apply a force and measure the displacement, or you apply a displacement and measure the reaction force. If you are applying a force, there should be no applied displacement, only a directional deformation value of the remote point where the force was applied.