Exact solutions produce a full picture of crack behavior in dynamic fracture

The theory of fracture normally describes cracks as propagating discontinuities in a continuous medium where stresses vanish on free crack faces. We describe cracks instead at the particle level and obtain more general analytical results than were available previously. Using dynamical crack solutions for widely varying dissipation and general isotropic elastic moduli, we construct a catalog of 100,000 crack solutions and from it a general picture of when cracks are stable. For our exactly solvable model of dynamic fracture, the surface wave speed sometimes sets an upper limit on crack velocity, as expected. However tensile cracks traveling faster than the shear wave speed are possible and their stability is enhanced when they travel along weak interfaces, when dissipation increases, and when system sizes are small. Our results reinforce a standard view that supersonic cracks require supersonic energy transport near the tip, but we show it can come from dissipation as well as hyperelasticity.