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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the tendency of a substance to resist flow. Microscopically it is a diagnostic of the strength of the interactions between condensed matter’s constituents. The shear viscosity measures how disturbances in the system are transmitted to the rest of the system through interactions. If those interactions are strong, neighboring parts of the condensed matter more readily transmit the disturbances through the system. It was mentioned by Johnson et al. (2010) that there is paradox, that microscopically low shear viscosities indicate significant interaction strength. For instance, water, often cited as a low-viscosity liquid, in fact has a substantial viscosity as evidenced by its tendency to form eddies and whorls when faced with an obstacle. This paradox appears in the experimentally and theoretically determined viscosity-to-entropy ratio that is controlled by the temperature and the microscopic details are less important. This duality is illustrated by Kovtun et al. (2005) for the so-called KSS bound establishing the ratio limit in terms of fundamental constants B K s  ⋅ = π η 1 4 . Ordinary substances like water have s η ratios that lie well above the KSS value. The power universality of the SWF reflects the anomaly of the energy absorption within the characteristic length S L of the SWF. The front of blow-up structure separates the initial matter constituents and comminuted area, provides the universal momentum transfer related to the strain rate 1 ~ − c FW t ε  at the failure wave front. This macroscopically stress free state at failure wave front gives the vanishingly small value of viscosity in the acoustic limit. It is naturally to assume the blow-up damaged area, associated with Failure Wave, has extremely high entropy corresponding to the set of complex blow-up structures consisting the simple blow-up modes. The driving force for this limiting fragmentation is extremely high structural stresses (energy density) initiated by defects at the front of blow-up mode. Propagation of Failure Wave leads to the increase of dramatically comminuted area and the number of blow-up modes `that represents the internal degrees of freedom . This tendency in the entropy evolution is similar to the entropy definition by Bekenstein (1975) and the value of this area can be considered as the entropy measure. Acknowledgements The research was supported by the Russian Science Foundation (project n. 21-79-30041). References Baggioli, M., Vasin, M., Brazhkin, V., Trachenko, K., 2020. Gapped momentum states. Physics Reports 865, 1–44. Bannikova, I. A. , Uvarov, S. V. , Bayandin, Yu. V., Naimark, O. B. , 2014. An experimental study of non-Newtonian properties of water under electroexplosive loading. Technical Physics Letters, 40, 9, 766-768 ( DOI: 10.1134/S1063785014090041). Bannikova, I.A., Zubareva, A.N., Utkin, A.V., Uvarov, S.V., Naimark, O.B., 2016. Metastable States, Relaxation Mechanisms, and Liquid Fractures under Intensive Loading. Physical Mesomechanics, 16, 3, 69–77. Barker, L.M., Behavior of Dense Media under High Pressures, New York: Gordon and Breach, 1968 Bayandin Yu.V. , Naimark, О.B., 2004. Experimental and theoretical investigation of the self -similar structure of the plastic front of shock waves in condensed media. Physical mesomechanics, 7, 1, 305-308. Bekenstein, J.D., 1975. Statistical black-hole thermodynamics. Phys.Rev. D 12, 3077 Bourne, N., Millett, J., Rosenberg, Z., and Murray, N., 1998. On the Shock Induced Failure of Brittle Solids. J. Mech. Phys. Solids, 46, 1887– 1908. Budaev, U.B., Derjaguin, B.V., Lamazhapova ., Kh.D. 1990.On low-frequency shear elasticity of liquids. Sov. Phys. Dokl, 15, 3, 595-599. Cullis, I., and Andrews, T.D., The Failure Front in Silica Glasses, in Behavior of Dense Media under High Dynamic Pressures, Dulpech, A., ed., Cambridge: Cambridge University, 2003, vol. 2, pp. 65–74. Derjaguin, B.V. , Bazaron, U.B. , Lamazhapova, Kh.D. , Tsidypov, B.D., 1992. Shear elasticity of low-viscosity liquids at low frequencies. Progress in Surface Science, 40, 1-4, 462–465. Frenkel, J., Kinetic Theory of Liquids, Oxford University Press, 1947. Johnson, C.V., Steinberg, P. , 2010. What black holes teach about strongly coupled particles. Phys. Today, 63, 5, 29-33. Kovtun, P.K., Son, D. T., Starinets, A. O., 2005. Viscosity in strongly interacting quantum field theories from black hole physics. Phys. Rev. Lett. 94, 111601. Kurdyumov, S.P., 1988. Evolution and Self-Organization Laws of Complex Systems. Int. J. Mod. Phys., 1, 4, 299–327. Naimark, O.B., 2003. Collective Properties of Defect Ensembles and Some Nonlinear Problems of Plasticity and Fracture. Physical Mesomechanics, 6, 4, 39–63. Naimark, O.B., 2010. Structural-scaling transitions in solids with defects and some symmetry aspects of field.Physical mesomechanics, 13, 5, 113-126.