It's a worthy thought, but I can't think of a material that behaves appropriately outside of a university lab...essentially you are looking for something that deforms, but returns to original shape quickly, and has high fracture toughness...I had a prof working on a self-healing composite structure aimed at aircraft wings: http://m.iopscience.iop.org/0964-1726/22/2/025031

All yours for $1 million. In the mean time, I'll continue putting thin webbing in the back of the trunk, has considerably reduced the number of these repairs, as has avoiding the bottom.