Consider cork sheet over and under your preferred composite cloth. Cork is an impact absorbing material.
Information from a manufacturer of helmets:
“Cork is also able to absorb a lot of punishment. Its cells have a unique 14 sided polyhedron structure that can be compressed to 15% of their normal volume and then regain most or all of its size and shape slowly. This compression capacity combined with a very slow rebound allows cork to act as a very effective energy dampener, thus its popular use in flooring and noise proofing.”