The role of instabilities of plastic flow at plastic deformation of various materials is one of the important cross-disciplinary problems which is equally important in physics, mechanics and material science. The strain rate sensitivities under slow and high strain rate conditions of loading have different physical nature. In the case of low strain rate, the sensitivity arising from the inertness of the defect structures evolution can be expressed by a single parameter characterizing the plasticity mechanism. In our approach, this is the value of the characteristic relaxation time. In the dynamic case, there are additional effects of "highspeed sensitivity" associated with the micro-localization of the plastic flow near the stress concentrators. In the frames of mechanical description, this requires to introduce additional strain rate sensitivity parameters, which is realized in numerous modifications of Johnson-Cook and Zerilli-Armstrong models. The consideration of both these factors is fundamental for an adequate description of the problems of dynamic deformation of highly inhomogeneous metallic materials such as steels and alloys. The measurement of the dispersion of particle velocities on the free surface of a shock-loaded material can be regarded as an experimental expression of the effect of micro-localization. This is also confirmed by our results of numerical simulation of the propagation of shock waves in a two-dimensional formulation and analytical estimations.

The one-dimensional impact problem in the case of Fung’s quasi-linear viscoelastic model is studied for the relaxation function of the standard solid model (or Zener model). Additionally, quasi-linear viscoelastic Maxwell and Kelvin–Voigt models are recovered as limit cases. The results of numerical simulations for some illustrative values of the dimensionless problem parameters are presented. The obtained results can be of interest for biomedical testing.

In the paper, a new phenomenological interpretation of some of the principal temporal effects of high-rate plastic deformation of metals from a united viewpoint is represented. A comparative analysis of some of the well-known dynamic plastic deformation models is given. Influence of strain rate on the stress-strain relation in a wide range of strain rates for different types of aluminum alloys and steels is described by the relaxation model of plasticity, by original and improved empirical Johnson-Cook models, and by the phenomenological Rusinek-Klepaczko model. It is shown that the structural-time model (“the relaxation model of plasticity”) is capable to effectively predict a wide spectrum of materials responses to fast and slow dynamic loading.