I wanted to make some panels in which styrofoam sheets are sandwiched in between 2 steel sheets. What kind of adhesives are best for this job. I also want the fastest curing time for adhesive because I want to make these panels using a fast technique.
The "strongest" thing that I have ever found for attatching styrofoam was silicone. My opinion is that silicone works well because it is soft and seeps into the crevices between the styrofoam pearls. But silicone takes 24 hours to dry; also you may want/need to rough-sand the steel to help the silicone stick to it. Another ok choice for much less money is Elmers (water based glue); but if it is beading up on the foam it's probably too watery. You can add acetone or MEK to help it spread on styrofoam. There are different kinds of foams (or materials that get called styrofoam) and glues, so be sure to test the acetone or ketone solvent on a small piece of foam and test the solvent with a small amount of glue, to make sure it all works well. I suppose it's well known that petrol will dissolve styrofoam.
To get a quick grab, use the pull-apart technique with panel adhesive that's suitable for foam. (Standard construction adhesive has solvents that ruin foam, and therefore don't bond.)
Apply the adhesive in a suitable pattern using about a 1/4" bead. Press the components firmly together, then pull them apart. Let them sit exposed to the air for a few minutes, then press them together again. They'll act as contact adhesive, so position the parts carefully. You may need to experiment a bit with your particular adhesive, climate, and humidity to get the right timing.
If you use foam board adhesives with solvent will dissolve the foam and not grip as well.
I have used PL300 from loctite or you could use an equivalent. It has worked well bonding to concrete and wood.