Hyperelasticiy in dynamic fracture: The characteristic energy length scale

Abstract

A fact that has been neglected in most theories of brittle fracture is that the elasticity of a solid should depend on its state of deformation: metals tend to soften and polymers tend to 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. We show by large-scale atomistic simulations that hyperelasticity, the elasticity of large strains, can play a governing role in the dynamics of fracture and that linear theory is incapable of capturing all phenomena. We introduce a new 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. The new length scale, heretofore missing in the existing theories of dynamic fracture, helps to explain recent observations of super-Rayleigh and supersonic fracture in computer simulations and experiments.