PSI - Issue 32

O.B. Naimark et al. / Procedia Structural Integrity 32 (2021) 144–151 Author name / Structural Integrity Procedia 00 (2019) 000–000

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characteristic delay time c t . The H L - area reveals the blow-up GMS dissipation-momentum scenario with anomalous dispersion properties in the presence of defects induced criticality. 3. Results and discussion Non-equilibrium viscoelastic effects due to the liquid structure was supported by Derjaguin et al. (1992) studying relaxation spectra at oscillatory loads applied to simple liquids, when shear elasticity effects were observed at . It was assumed that the spectral regions with times s 5 10 − ≈ τ is related to coordinated motion and rearrangement of molecules on larger characteristic time scales than the molecular diffusion time. The physical mechanisms leading to the development of instabilities in condensed media indicate the possibility of describing instabilities in liquids on the basis of an analysis by Bannikova et al. (2016) of the kinetics of fluctuations, if the latter are viewed as defects in the structure of the liquids. In the case of liquid the mesoscopic defects, being by their nature the fluctuation of the displacement field in solids, can be also regarded as real structural defects which are produced during collective motion of groups of molecules. This mechanism of motion does not correspond to the conventional diffusion mechanism of momentum transfer in simple liquids. Generation of the collective solitary and blow-up modes follows to the scenario of the energy absorption at the vicinity of critical points and localized on characteristic lengths S L and ... ) ( 1,2 Ι , L = iL i = c H for the characteristic times t L V S S = and c t consequently. These times can be identified with the effective relaxation time and have to estimate as s t S 5 ~ 10 − and s t c 7 6 10 ~ 10 − − − . The existence of characteristic lengths S L and H L as the parameters of the self-similar solutions (6) and (7) characterizes two slits of wave numbers S S k L 1 = and H H k L 1 = , where the system reveals GMS with new mechanisms of dissipation and momentum transfer. Initiation of the Failure Wave represents the acoustic limit of the GMS dynamics and is the analogous to the phonon field describing collective excitations of a crystal lattice in the low-temperature limit of the theory. Similar idea was discussed by Sakharov (1968) for entropy determination of gravity systems in the presence of collective excitation of the mass field. This similarity follows from statistical thermodynamics of matter with defects, which reveals universality in the global symmetry properties caused by the collective modes of defects without influence of matter constituents. Thus, the considered scenarios of fragmentation of a matter can be presumably be extended to arbitrary energy density, which are not necessarily bounded by the acoustic limit in solid. The minimal length of fragments in the “acoustic limit” was estimated by Naimark (2010) using the natural parameters with independent dimensions: elastic modulus G , material density ρ and Plank’s constant h The length ξ corresponds to the acoustic limit of fragments for the energy density C , C ρ G= 2 is the sound speed. Failure Wave is the limit case of fragmentation in intensive shock with initiation of extremely damaged area of length c L with particle sizes close to acoustic limit size m ξ 9 ~ 10 − . Excitation of Failure Wave in a certain characteristic volume at a certain threshold elastic energy density (as a shock wave passes through) owes to the existence of a minimum volume in which the matter fragmentation is subject to blow-up defects dynamics. 4. Conclusion There is conceptual duality in the understanding of the shear viscosity, the momentum diffusion parameter, and underlying micro- and mesoscopic mechanisms. Macroscopically the shear viscosity is a property associated with ( ρ G ρ h / ) )m ( ~ 10 = ξ 10 9 − − 1/ 4 1/ 2 10 −       .