Modelling of shock wave experiments on two-fold compression of polymethyl methacrylate

This paper presents a mathematical model of one- and two-dimensional elastoplastic flows of a medium. The Prandtl – Reuss model is used to describe the plastic properties of a material. The presented model is implemented as a one-dimensional code in a plane geometry and a two-dimensional code in a cylindrical axisymmetric geometry. Also, these program codes allow to calculate the absorption of synchrotron radiation in the volume of the medium at different points in time, which makes it possible to interpret the results of shock-wave experiments using synchrotron diagnostics. In order to verify the numerical code that implements this model, we carried out mathematical modelling of the experiment on the impact of two plates of polymethyl methacrylate and the Taylor problem for a copper cylinder. The application of the Prandtl – Reuss plasticity model to the description of dynamic processes in polymethyl methacrylate showed that this model works quite well in a viscoplastic medium without using any fitting parameters. Also, in 1D and 2D formulations, we carried out mathematical modelling of an experiment with synchrotron diagnostics on shock-wave loading of a cylindrical sample of polymethyl methacrylate in counter-propagating shock waves. The calculated profiles of the relative absorption of synchrotron radiation are consistent with the experimental ones, which makes it possible to give an unambiguous interpretation of the results of experiments using synchrotron radiation. The study of the role of radial unloading showed that the stress profiles for 1D and 2D calculations at the stage of shock wave convergence to the center are in good agreement, however, as shown by two-dimensional calculations, a significant density inhomogeneity along the radius arises during unloading due to re-reflection of shock waves, which complicates interpretation of experimental results using synchrotron diagnostics.