3 Constrained cracks in homogeneous materials: How fast can cracks propagate?

In this section we focus on the limiting speed of cracks, discussing recent results on cracks faster than both shear and longitudinal wave speeds in an elastically stiffening material [10, 12, 30, 31].

The elasticity of a solid clearly depends on its state of deformation. Metals will weaken, or soften, and polymers may stiffen as the strain approaches the state of materials failure. It is only for infinitesimal deformation that the elastic moduli can be considered constant and the elasticity of the solid linear. However, many existing theories model fracture using linear elasticity. Certainly, this can be considered questionable since material is failing at the tip of a dynamic crack due to the extreme deformation there. Here we show by large-scale atomistic simulations that hyperelasticity, the elasticity of large strains, can play a governing role in the dynamics of fracture. We introduce the concept of a characteristic length scale for the energy flux near the crack tip and demonstrate that the local hyperelastic wave speed governs the crack speed when the hyperelastic zone approaches this energy length scale [30].