Use of SHPB tests for incorporating a compaction constitutive equation within a two-phase model

The well-known Split Hopkinson Pressure Bar (SHPB) set-up is used for analysis of compaction of calcite sand samples within a gauge instrumented confinement. A two-phase material model, used previously for simulation of sand behaviour under extreme shock loading, requires a constitutive equation for a parameter responsible for the compaction response within a non-equilibrium loading path tending to the solid Hugoniot. A mathematical formulation approximating the present experimental set-up is suggested and used for inverse adjustment of parameters in the constitutive equation. This equation determined from the SHPB tests and incorporated in the two-phase model is used for description of the behaviour of explosively driven sand with the help of the CTH shock physics code. Comparison with available independent experiments shows a good agreement.