An analytical and numerical study of failure wave

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 di}erent from the usual inelastic shock waves\ a combined analytical and numerical e}ort 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 di}usion equation instead of a wave equation\ which is in line with the bifurcation analysis for localization problems[ However\ the occurrence of di}erent governing equations in a single computational domain imposes both an analytical and a numerical challenge on the design of an e.cient solution scheme[ With the use of a partitioned!modeling approach\ a simple solution procedure is proposed for failure wave problems\ which is veri_ed by the comparison with data