Simulation of the dynamic compression of polycrystalline Al$_2$O$_3$

A model for the behavior of Al$_2$O$_3$ ceramics under dynamic and shock-wave loading is developed on the basis of the model of a Maxwell-type viscoelastic body, which is used here for ceramics for the first time. An equation for the variation in the internal energy for a nonspherical strain tensor and the relation between the time of relaxation of tangential stresses and the state parameters of the medium are derived. The time of relaxation serves to describe the microstructural mechanisms of irreversible deformation. The applicability of the model is validated by comparing the results of solving a number of problems of dynamic and shock-wave deformation with experimental data.