You have two options in terms of foam, expanded polystyrene (styrofoam) or expanding polyurethane foam. I have used both over the years with a range of amphibians. the type I used was exterior grade polyurethane foam from one of the big sheds (Homebase or B&Q). I've also seen some very attractive backgrounds made with both of these materials, but I've never personally made a complete background with either myself.
Compared with natural materials they have one potential problem as far as dartfrogs are concerned, they do no retain moisture, so humidity in the vivarium may drop depending on the substrate and how often you spray.
The advantage of polystyrene is that it is easy to cut and shape. With expanding polyurethane foam you have two options - either create a background by spraying the foam onto some sort of support then fit it in the viv, or spray the foam directly onto the viv. You have to be brave to do this as it's not easy to control, and once it's there, it's there for good. The most important thing about expanding polyurethane foam is that it must be allowed to cure completely before you try to do anything to it or put animals anywhere near it. Depending on how thick the foam is, they can take anything from days to weeks, so you need patience. Personally, I think there are easier options.