Continuum and atomistic modeling of dynamic fracture at nanoscale

Abstract

Crack branching and instability phenomena are believed to be closely related to the circumferential or hoop stress in the vicinity of the crack tip. In this paper we show that the hoop stress around a mode I crack in a harmonic solid becomes bimodal at a critical speed of about 73 percent of the Rayleigh speed, in agreement with the continuum mechanics theory. Additionally, we compare the energy flow field predicted by continuum theory with the solution of molecular-dynamics simulations and show that the two approaches yield comparable results for the dynamic Poynting vector field. This study exemplifies joint atomistic and continuum modeling of nanoscale dynamic systems and yields insight into coupling of the atomistic scale with continuum mechanics concepts.