Numerical simulations of shock attenuation in solids and reevaluation of scaling law

Abstract

In order to reevaluate the scaling law on impact fragmentation, attenuation of shock waves induced by impact events is numerically simulated in two-dimensional axial symmetry using the cubic interpolation propagation method in wide stress regime: not only the regime where targets respond plastically, but also the regimes where shock stresses are comparable to the Hugoniot elastic limit (HEL) of target materials. As a constitutive equation of state for brittle materials that lose the strength, we newly propose a "brittle model" based on experimental data. Comparing our results with previous studies on shock attenuation, an "elastic-plastic regime" in the vicinity of HEL where the attenuation becomes rapid is newly found. We calculate the antipodal stresses normalized by the dynamic compressive strength through simulations for some previous impact experiment data using rocks and ices and reevaluate a scaling law of the impact fragmentation. The results suggest that the description of the fragmentation process that the largest fragment is mainly produced by the tensile waves emanated from the free surface at the antipodal point is plausible.