Regimes of interscale momentum exchange in shock deformed solids

Quantum Effects on the Mesoscale

“…The emergence of various turbulent structures at the intermediate between macro and micro scale levels, as shown by experimental data, accompanies non-equilibrium processes of mass, momentum, and energy transfer in media of various nature. It was experimentally discovered [11,12] that multi-scale and multi-stage energy exchange is a mechanism of the structural evolution of a physical system far from thermodynamic equilibrium. The description of such processes requires solving a whole complex of fundamental problems of modern science: the creation of a theory of turbulence, thermodynamics of highly non-equilibrium processes, and non-equilibrium statistical mechanics of open systems.…”

“…In this paper, on the basis of the integral model of elastic-plastic waves (12) propagating in a dispersive medium, we formulate the problem of the spectrum of relaxation and delay times that evolve when the wave packet spreads. On the basis of the theory of a special type nonlinear operators depending on parameters [35,36], a variant of the iterative procedure sweeping along the system evolution path is proposed, which can make it possible to calculate the dynamics of turbulent structures in media of different nature at different scale levels.…”

“…The observed formation of local inhomogeneities at mesoscopic scale, such as the localized shear bands, microcracks, traces of microflows and rotational structures significantly change the macroscopic properties of the medium. In experiments on shock loading of solid materials [12,22,23], it was found that the formation of dynamic structures inside the propagating waveform is of resonant origin when the wave length coincides with the size of spatial internal structure of the medium. It is impossible to detect if they are reversible or not until behind the wave a part of them remained frozen into the medium.…”

“…Equation (12) and its approximate form (21) describe the wave packet spreading during its propagation. The set ( 19)- (20) describes the evolution of the discrete internal structure of the packet during its spreading.…”

“…Experimental results, obtained in the study of non-equilibrium processes in different branches of mechanics (hydrodynamics of turbulent flows, multi-phase flows, shock-induced processes in solids, biomechanical processes), show many similar features of the non-classical system response to external perturbations. Far from equilibrium processes are often accompanied by self-organization of new dynamic structures [8][9][10][11][12][13][14][15][16] such as boundary layers, mass velocity pulsations, vortex structures, various localized inhomogeneities, etc. The observable self-organization effects are characterized not only by the medium properties (composition, phase state) but also by the loading and boundary conditions and the system geometry.…”