Elastic waves in a hyperelastic solid near its plane-strain equibiaxial cohesive limit

Propagation of elastic waves near the cohesive limit of a solid is of interest in understanding the speed at which strain energy is transported in front of a mode-I crack tip. It can be argued that the crack propagation velocity is limited by how fast the 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. In this letter, wave speeds near the plane-strain equibiaxial cohesive stress sigma(max) are studied using the hyperelasticity theory of continuum mechanics, with no specific assumptions on the atomic structure of the solid other than that it remains homogeneous and isotropic in the plane of analysis. It is found that the cohesive-state wave speed is equal to (sigma(max)/rho)(1/2), where rho is the density of the solid. This behaviour resembles that of wave propagation along a string under tension.