In a stressed body, crack propagation is the main vehicle for material failure. Cracks create large stress amplification at their tips, leading to large material deformation. The material response within this highly deformed region will determine its mode of failure. Despite its great importance, we have only a limited knowledge of the structure of this region, because it is generally experimentally intractable. By using a brittle neo-Mookean material, we overcame this barrier and performed direct and precise measurements of the near-tip structure of rapid cracks. These experiments reveal a hierarchy of linear and nonlinear elastic zones through which energy is transported before being dissipated at a crack's tip. This result provides a comprehensive picture of how remotely applied forces drive material failure in the most fundamental of fracture states: straight, rapidly moving cracks.