A 10 mm thick displacement of the bottom facesheet relative to the top facesheet with a 10 mm thick core is an absurdly large amount. What is core material and wall thickness? What is the facesheet material and thickness?
Is the core manufactured by corrigating and bonding two thin sheets together? That creates a double thick wall in one direction. Did you do that in your model?
Here is the test apparatus from ASTM C273 -11 Standard Test Method for Shear Properties of Sandwich Core Material.
If you don't want to switch to Force, I recommend that you select the row of nodes on the bottom facesheet at the opposite end of the sandwich from the row that has the x,y constraints on the top face sheet. Use a Displacement of Y=0 to prevent rotation about the first edge. Is the sample 50 mm long? In that case, 1% strain would be 0.5 mm. Use a Displacement of X= -0.5 mm to those bottom edge nodes to put the facesheets into tension at each end. Use 100 initial and minimum substeps, 1000 substeps maximum, in the solution.
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