Gluing Wood To Formica. You want something that sticks well to the formica. Wood glue will not work. I don't think polyurethane glue will do much better than.

Covering A Formica Table With Wood Ehow Wood Countertops Kitchen Rustic Kitchen Rustic Countertops
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Formica contains various forms of paper, saturated with plastic resins and headed under substantal pressure. The top layer of formica is a melamine skin. Making sure you choose the best wood glue is essential.

I would also like to avoid using any nails.

Epoxy will glue almost any materials together and is the adhesive of choice when gluing fiberglass to wood. However, metal washer on wood slides nice. * i have recently changed (glued new formica over the old) my formica tops on two vanities, then decided to add a solid cherry trim to the front edge. Gluing wood together to make larger and thicker pieces can be a problem. I would also like to avoid using any nails. Epoxy will glue almost any materials together and is the adhesive of choice when gluing fiberglass to wood. I realize i can't clamp the wall so i just want to know the best way to secure it while it dries. Contact cement is used to glue formica to plywood;