Dynamic Cracking Simulation By The Nonlocal Macro-Meso-Scale Damage Model For Isotropic Materials

The newly proposed nonlocal macro-meso-scale damage (NMMD) model is extended to dynamic cracking simulation. For this purpose, the framework of continuum damage mechanics and damage constitutive model are firstly described. The NMMD, where the meso-scale damage is determined according to the deformation of material bond and then the macroscopic topologic damage is endowed with the weighted averaging over the meso-scale damage in the influence domain of the material point, is then elaborated and incorporated into the framework. Specifically, the criterion of meso-scale damage is renormalized. The numerical algorithms including the spatial discretization by the finite element methods and the time integration methods by an explicit scheme are outlined. Several examples are studied in detail, showing the effectiveness of the proposed method. In particular, due to the nonlocal property, there is no spatial mesh size sensitivity. Owing to the scale renormalization of the meso-scale damage, the results are insensitive to the influence radius in some examples. The dynamic cracking, including the crack propagation velocity, the damage dissipation rate, and the connection to the dynamic crack branching, is discussed in detail based on the computed results.