Armaflex
Is a type of foam pipe-insulation available in hollow tubes or as an adhesive tape.
The foam is strong, dense, soft and rubbery. In the tape form it is 1/8" thick. Because of its weight, Armaflex is best used as an outermost layer to make a weapon hit softer, and as an innermost layer to protect against degradation of the innermost foam due to rubbing against the core.
The adhesive of the tape is quite strong, and can be used by itself without Dap or any other additional adhesive.
Armaflex is available at Home Depot, and possibly other hardware stores as well.