Experimental and numerical study of shock-induced processes show that the accepted ideas of elastic-plastic transition within concepts of continuum mechanics cannot explain mechanical and physical properties of the shocked material related to defective structures occurring on a sub-continuum scale. New trend in mechanics called mesomechanics describes the deformation and destruction of the material as the multiscale process that defines a change in mechanisms of momentum and energy transport in a deformable solid depending on the strain rate, boundary and initial conditions. However, the physical processes on different scales associated with high-rate deformation are not well understood till present because experimental diagnostics does not allow us to obtain reliable data on deformation processes on the mesoscale in real time. Computer simulations as a tool for probing details of the deformation process also run into unresolved problems related to the choice of the closing relations embedded into the computer complex package or the unknown interaction laws between the mesostructure elements. It became clear that in order to develop predictive mathematical models, it is necessary to critically examine the fundamental postulates used to interpret shock compression phenomena and to develop first-principle approach capable to describe a whole complex of non-equilibrium processes in a deformable medium.
In this chapter, the presented in Chapter 5 approach, being suitable for any non-equilibrium conditions, is used to describe the processes of high-rate deformation of solids. The response of any condensed medium to external loading goes through all relaxation stages from elastic to hydrodynamic one. In contrast to the hydrodynamic limit, the processes occurring near the elastic limit have wave nature when spatial and temporal correlations cannot be separated. The specific feature of the response of a solid to shock loading is a very strong interaction of atoms with each other that corresponds to a very high degree of spatial correlation and memory about the initial state of the system. Shock on a solid breaks correlations into mesoscopic parts moving at different speeds like a wave packet. Similar to the generation of turbulence in liquids, strong shears cause the formation of rotational structures inside the propagating waveform. An irreversible part of the mesoscopic structures remain frozen into material after the wave when the solid state is restored. The synergistic formation of vortex-wave structures on the mesoscale defines the medium response to high-rate deformation (Section 7.4). Within the framework of the developed approach, we proposed a new mathematical model of the propagating waveform generated by mesoscopic structures evolving over time. The integral formulation of the problem of the planar shock-induced wave propagation in a solid with the closing relationship for the relaxing stress tensor is given in sections 7.6-7.7. The explicit approximate solution to the problem obtained in section 7.8 allowed us to decipher the information on the stress relaxation involved in the waveform evolution during its propagation along the material. The processing of experimental waveforms obtained at different distances from the impact surface for different materials in a wide range of impact velocities revealed the general laws of the relaxation processes taking into account the specificity of various materials (Sections 7.9-7.11).
In the first sections of this chapter, we provide a brief summary of the physical and thermodynamic properties of solids that are necessary to understand the new approach to describing shock-induced processes. More information can be found in books [1-6].