Simulating the evolution of localization based on the diffusion of damage

Based on the failure mechanisms of brittle solids under dynamic loading conditions, a strain-based damage di€usion model is proposed to simulate the evolution of localization due to microcracking. A three-dimensional di€usion equation is formulated with local rate-independent and rate-dependent damage evolution laws, respectively. The diffusion equation governing the evolution of damage is incorporated into the hyperbolic equation governing the wave propagation in a parallel setting. A parametric study is performed to investigate the e€ects of model parameters on the di€usion of damage. One- and two-dimensional sample problems are considered to illustrate how the dynamic evolution of localization can be simulated without using nonlocal models in the strain±stress space. The relationship between the proposed approach and the existing ones for localization problems is also discussed based on the preliminary results obtained in this paper. It appears that the proposed approach might be an e€ective numerical procedure to simulate the evolution of localization, with parallel computing, in a single computational domain involving di€erent lower-order governing di€erential equations