An analytical and numerical study of failure waves

Based on recent observations in shock experiments on glasses, a new failure process has been suggested for a certain type of brittle solids, in which a failure wave propagates through a solid at some distance behind the compressive stress wave near but below the Hugoniot elastic limit. Since the failure wave phenomenon is different from the usual inelastic shock waves, a combined analytical and numerical effort is made in this paper to explore the impact failure mechanisms associated with the failure wave. Based on the experimental data available, it appears that the physical picture of failure wave is related to local dilatation due to shear-induced microcracking. A mathematical argument then leads to the conclusion that the failure wave should be described by a diffusion equation instead of a wave equation, which is in line with the bifurcation analysis for localization problems. However, the occurrence of different governing equations in a single computational domain imposes both an analytical and a numerical challenge on the design of an efficient solution scheme. With the use of a partitioned-modeling approach, a simple solution procedure is proposed for failure wave problems, which is verified by the comparison with data.