Hyperelastic Modeling of Dynamic Crack Tip Instabilities

摘要

Most of the existing theories of dynamic fracture are based on small deformation constitutive models such as elasticity, plasticity, viscoelasticity, viscoplasticity, etc.. However, an important fact is that extraordinarily large (hyperelastic) deformation occurs in brittle fracture. To demonstrate the significance of the hyperelastic nature of crack-tip deformation, we present a study of elastic wave propagation in a hyperelastic solid subjected to equibiaxial cohesive stress under plane strain conditions. This stress state resembles that a material particle experiences in front of a mode I crack tip. The crack propagation velocity is limited by how fast strain energy can be transported ahead of the crack tip to sustain the bond breaking processes in the fracture process zone. From this point of view, the cohesive-state wave speed leads to the concept of local limiting fracture speed which provides a possible explanation for the "mirror-mist-hackle" instabilities widely observed in experimental and numerical investigations of dynamic fracture. It is shown that the cohesive-state wave speed is equal to sq root #sigma#_(max)/#rho# where #sigma#_(max) is cohesive stress and #rho# is the density of the solid. This behavior resembles that of wave propagation along a string under tension.