A thermomechanical breakage model for shock-loaded granular media

A constitutive model is developed for dry granular materials that smoothly transitions across a wide range of pressures and temperatures. This model handles large deformations and is thermomechanically consistent. Ideas from critical-state soil mechanics, which model granular media at relatively low pressure via a breakage model, are combined with an equation of state for shock-loaded solids to investigate the compaction of initially unconsolidated brittle granular materials. The resulting constitutive equations provide a fully-coupled model containing a natural transition between granular and solid states through the Helmholtz free energy. The model is calibrated to data with a wide range of pressures and strain rates for Ottawa sand and silica and predictions of the model are compared with static compaction, penetration, and shock-loading results. The difference in Hugoniot temperatures between this calibrated model and a “snow-plow” model are negligible for pressures greater than 8 GPa; well below incipient melting.