  We present a theory for the toughness, damage tolerance, and tensile strength
of a class of hierarchical, fractal, metamaterials. We show that the even
though the absolute toughness and damage tolerance decrease with increasing
number of hierarchical scales, the specific toughness (toughness per-unit
density) grows with increasing number of hierarchical scales in the material,
while the specific tensile strength and damage tolerance remain constant.
