Dynamic fracture in irregularly structured systems

Although commonly used materials are composed of irregular microstructures, most existing numerical methods for fracture dynamics are developed via regular discretizations. In the present Rapid Communication we investigate the dynamic fracture numerically by irregular domain discretizations. To explore the relationship between microscopic crack branching and the macroscopic instability of fracture dynamics, we simulate detailed diagrams for the crack branching and also calculate the crack speeds by varying the parameters of crack-tip cohesion. In particular, an equation to describe the relation between the crack speed and the fracture energy is proposed based on the simulation results. The present results indicate that the irregularities of mesoscopic structure contribute to the intrinsic instabilities of dynamic fracture and eventually to the crack speed. And the single-crack continuum theory should be at least carefully modified to describe the dynamic fracture governed by the complex branching and fluctuations.