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We have made a aluminum box to fit inside a Van and want to cover it
in that white sheet plastic foam. I think the two materials are some
what smooth or greasy to the touch. Is there a good recommendation on
attaching the two materials together.

Need to know what type of plastic. Polyethylene does not stick to anything.
Polystyrene will dissolve with some solvent based adhesives. Consider
mechanical fasteners like a big washer and a bolt through the aluminum.