Hugoniostat, direct shock simulations and viscoelastic modeling in polymer melts

The interest for the behavior of polymers under shock loading is increasing because of applications such as car equipment, sport gear and plastic-bonded explosives. Molecular dynamics (MD) simulations are a powerful tool to explore the molecular and mechanical properties of polymers under shock loading but they require long simulation times to relax the polymer chains and large simulation boxes to study the stationary state of the shock wave propagation. The Hugoniostat method has been widely used on atomic and molecular crystals to reproduce the shocked state of materials far from the shock front using much smaller simulation boxes. In this work, we show that the Hugoniot curve of the cis-1,4-polybutadiene melt is correctly predicted by the Hugoniostat method and compare well with direct shock simulations and previous results. However, the shear stress is very different in direct shock simulations, where it is large and decays slowly away from the shock front, and in the Hugoniostat method where they are nearly zero. In order to account for this difference, we use a Prony series model, usual for viscoelastic liquids, which reproduces the slow decay of the normal stress differences with several relaxation times.