In Chapter 7 we have obtained the explicit solution to the problem of the shock-induced waveforms propagation that allows us to describe the medium response both during the loading and post-shock effects. As experiments show [1], the model parameters depending on the distance travelled by the wave after impact evolve during the waveform propagation along the material. In the section 7.10 we have already traced the evolution of the parameters by using their experimental values obtained for the waveforms recorded at various distances from the impact surface (see Fig. 7.11). It is found out that all experimental points obtained by using the waveforms measured at different traveled distances fall down on the straight lines going at different angles for each material.
In Chapter 8, the integral model developed in Chapter 7 is applied to describe the shock-induced waveform evolution during its propagation inside the material through the evolution of the model parameters by methods developed in cybernetic physics and considered in Chapter 6. The goal function for the waveform evolution is determined by maximum of the total entropy production that pointes out the direction of the system evolution in accordance with MEP [2]. The speed gradient (SG) algorithm determines the fastest evolutionary paths to the goal. Comparison of the theoretical paths obtained in this way with the experimental results for quasi-stationary regime of the waveform propagation shows good agreement between them.
The parameters used in the integral model of the waveform, as it was found out, determine two limiting states inside the waveform. The observed decrease in the parameter during the so-called elastic precursor relaxation makes the material state less solid while the parameter defines the time interval needed for the restoration (at least partial) of the solid material state when the so-called plastic front reaches the plateau of the compression pulse. It means that the parameters evolve inside the waveform whereas the waveform evolution at rather large distance from the impact surface is adequately described by the integral model with the constant parameters over the waveform duration.
The described structure evolution inside the finite-duration waveform is an example of a process in which, as a result of the self-organization of new mesoscopic structures, the generalized integral entropy production after the unloading front can become negative.