I suggest you rework the geometry so you can mesh the facesheets with shell elements and eliminate bonded contact between the facesheets and the core solid. You do this by using Shared Topology. The benefit of using shell elements is that the thickness of the facesheet is easily adjusted to help match experimental data on the bending stiffness of the sandwich. The shell elements are given an offset to put the thickness above the nodes on the top surface and below the nodes on the bottom surface.
Prepare the geometry by deleting the facesheet solids. In SpaceClaim, make a New Component, select the face of the core and type Ctrl-C and Ctrl-V to copy the face and paste a surface into Component1. On the Workbench tab, you will click the Share button. That will cause the shell mesh on the surface to share the same nodes as the solid elements on the core solid. It will be best if you mesh the solid core using a Multizone or Sweep method to get Hex-shaped elements. If you use sweep, set the number of sweep elements to 4 through the thickness of the core. Set the Mesh Element Order to Linear which will reduce the number of nodes in the model and reduce the solution time.
Make another New Component and drag the solid for the potting adhesive (blue) and drop it into Component2. Repeat for the metallic insert and the bottom plate.
Create additional surfaces (or planes) so you can use them to cut all bodies along the red lines shown below to make a sweep mesh possible. When you are done, use the Share button on all components to connect all the separate bodies using the mesh.
The lower metal plate could also be converted to a Midsurface and meshed with shell elements. It can make frictional contact with the facesheet shell elements, you just need to put the offset (facesheet thickness + 1/2 plate thickness) into the contact definition.
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