A thermomechanical breakage model for shock-loaded granular media

• Published in: Journal of the mechanics and physics of solids 2020-04, Vol.137 (C), p.103813, Article 103813
• Main Authors: Herbold, E.B., Homel, M.A., Rubin, M.B.
• Format: Article
• Language: English
• Subjects: CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Constitutive equations; Constitutive model; Constitutive models; Constitutive relationships; Critical state; ENGINEERING; Equations of state; Free energy; GEOSCIENCES; Granular material; Granular materials; Granular media; Low pressure; Mathematical models; MATHEMATICS AND COMPUTING; Shock loading; Silicon dioxide; Soil compaction; Soil mechanics; Thermomechanical; Thermomechanical analysis
• ISSN: 0022-5096; 1873-4782
• DOI: 10.1016/j.jmps.2019.103813

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.