  We investigate how material rigidity acts as a key control parameter for the
failure of solids under stress. In both experiments and simulations, we
demonstrate that material failure can be continuously tuned by varying the
underlying rigidity of the material while holding the amount of disorder
constant. As the rigidity transition is approached, failure due to the
application of uniaxial stress evolves from brittle cracking to system-spanning
diffuse breaking. This evolution in failure behavior can be parameterized by
the width of the crack. As a system becomes more and more floppy, this crack
width increases until it saturates at the system size. Thus, the spatial extent
of the failure zone can be used as a direct probe for material rigidity.
