Modeling of shock-wave deformation of polymethyl metacrylate

A model of a Maxwellian elastoplastic body is constructed to describe the behavior of polymethyl metacrylate (C$_5$O$_2$H$_8$)$_n$ under loading. A principal feature of this model is supplementing the governing equations with the relaxation time of shear stresses in the form of a continuous dependence on parameters characterizing the state of the medium. The analytical form of the dependence is chosen with allowance for microstructural and mesostructural mechanisms of irreversible deformation. Another specific feature of the model is the equation of state of the medium, which includes the dependence of the internal energy on the first and second invariants of the strain tensor. Such an approach allows obtaining a unified mathematical description of all physical states of polymers. Particular attention is paid at the stage of model verification to comparisons of model predictions with experimental data for the temperature of the shock-compressed material and decay of the shock wave due to its interaction with overtaking and side rarefaction waves. This comparison shows that the model provides an adequate description of shock-wave processes in polymethyl metacrylate.