Numerical investigations of shock wave propagation in polymethylmethacrylate

Abstract

Using the Maxwell model of viscoelastic medium, we numerically investigate the influence of the viscoelastic properties of polymethylmethacrylate on the variation of the shock wave amplitude with depth. Parameters of the Maxwell model are chosen by comparison with experimental data on the high-speed impact of plates in order to fit the modeling results with the experimentally measured profiles of the free-surface velocity. A caloric equation of state is used to calculate the pressure from density and internal energy. It is shown that at the limit of weak shock waves, the accounting of the viscoelastic properties allows one to achieve a better agreement between calculated and experimental data for the magnitude of the shock wave velocity in comparison with the case of hydrodynamic calculations. Using the viscoelastic and hydrodynamic approaches, we investigated the dynamics of shock waves in polymethylmethacrylate initiated by micro-, nano- and picosecond pulses of pressure on the sample surface. The calculation results show that the changes in the shock wave amplitude with depth are approximately identical in the hydrodynamic and viscoelastic cases.