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A Review of Methods for Studying the Elastic Characteristics of Nanoobjects

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Abstract

This work is an overview of studies on the determination of the elastic characteristics of nanomaterials published over the past 20 years in peer-reviewed Russian journals. It is known from the literature that changes in the characteristic size of nanomaterials lead to multiple changes in their properties, which must be taken into account when creating specific nanoparticle-filled structures.

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REFERENCES

  1. Goldstein, R.V. and Morozov, N.F., Mechanics of Deformation and Fracture of Nanomaterials and Nanotechnology, Phys. Mesomech., 2007, vol. 10, no. 5–6, pp. 235–246.

    Article  Google Scholar 

  2. Hall, E.O., The Deformation and Ageing of Mild Steel: II. Characteristics of the Lüders Deformation, Proc. Phys. Soc. B, 1951, vol. 64, no. 9, pp. 742–747.

    Article  ADS  Google Scholar 

  3. Petch, N.J., The Cleavage Strength of Polycrystals, J. Iron Steel Inst., 1953, vol. 174, pp. 25–28.

    Google Scholar 

  4. Koch, C.C., Ovid’ko, I.A., Seal, S., and Veprek, S., Structural Nanocrystalline Materials, Cambridge: Cambridge University Press, 2007.

  5. Golovin, Yu.I., Dub, S.N., Ivolgin, V.I., Korenkov, V.V., and Tyurin, Kinetic Features of the Deformation of Solids in Nano- and Microscopic Volumes, Phys. Solid State, 2005, vol. 47, no. 6, pp. 995–1007.

    Article  ADS  Google Scholar 

  6. Malygin, G.A., Strength and Plasticity of Nanocrystalline Materials and Nanosized Crystals, Phys.-Usp., 2011, vol. 54, no. 11, pp. 1091–1116.

    Article  ADS  Google Scholar 

  7. Malygin, G.A., Plasticity and Strength of Micro- and Nanocrystalline Materials, Phys. Solid State, 2007, vol. 49, no. 6, pp. 1013–1033.

    Article  ADS  Google Scholar 

  8. Andrievski, R.A. and Glezer, A.M., Strength of Nanostructures, Phys.-Usp., 2009, vol. 52, no. 4, pp. 315–334.

    Article  ADS  Google Scholar 

  9. Glezer, A.M., Structural Classification of Nanomaterials, Russian Metallurgy (Metally), 2011, vol. 2011, no. 4, pp. 263–269.

    Article  ADS  Google Scholar 

  10. Kozlov, G.V., Structure and Properties of Particulate-Filled Polymer Nanocomposites, Phys.-Usp., 2015, vol. 58, no. 1, pp. 33–60.

    Article  ADS  Google Scholar 

  11. Zel’dovich, Ya.B. and Raizer, Yu.P., Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena, Mineola, N.Y.: Dover Publications, 2002.

  12. Trunin, R.F., Collected Papers of the Institute of Experimental Gas Dynamics and Detonation Physics Published in Physics-Uspekhi Journal, Sarov: RFNC-VNIIEF, 2012.

  13. Kustov, E.F., Kustov, M.E., Miroshnichenko, A.Yu., and Shemetova, V.K., Elasticity of Solids in a Double Layer Model, Bulletin MPEI, 2013, no. 5, pp. 162–168.

    Google Scholar 

  14. Kustov, E.F., Kustov, D.M., and Antonov, V.A., About Ideal and Real Strength of Solids, Eng. Phys., 2018, no. 2, pp. 21–24.

    Google Scholar 

  15. Kustov, E.F. and Kustov, M.E., Surface Tension of Inorganic Melts, Bulletin MPEI, 2013, no. 4, pp. 216–221.

    Google Scholar 

  16. Kustov, M.E. and Solinov, V.F., Modulus of Elasticity and Tensile Strength of Inorganic Substances, News Academy Eng. Sci. A.M. Prokhorov, 2013, no. 9, pp. 19–25.

    Google Scholar 

  17. Kustov, M.E., The Surface Tension and Adhesion of Inorganic Substances, News Academy Eng. Sci. A.M. Prokhorov, 2013, no. 9, pp. 93–105.

    Google Scholar 

  18. Krivtsov, A.M. and Morozov, N.F., Anomalies in Mechanical Characteristics of Nanometer-Size Objects, Dokl. Phys., 2001, vol. 46, no. 11, pp. 825–827.

    Article  ADS  Google Scholar 

  19. Krivtsov, A.M. and Morozov, N.F., On Mechanical Characteristics of Nanocrystals, Phys. Solid State, 2002, vol. 44, no. 12, pp. 2260–2265.

    Article  ADS  Google Scholar 

  20. Golovnev, I.F., Golovneva, E.I., Konev, A.A., and Fomin, V.M., Physical Mesomechanics and Molecular-Dynamic Modeling, Phys. Mesomech., 1998, vol. 1, no. 2, pp. 19–30.

    Google Scholar 

  21. Golovneva, E.I., Golovnev, I.F., and Fomin, V.M., Molecular Dynamics Analysis of Dynamic Fracture of Nanostructures, Phys. Mesomech., 2003, vol. 6, no. 3, pp. 37–45.

    Google Scholar 

  22. Ivanova, E.A., Krivtsov, A.M., and Morozov, N.F., Peculiarities of the Bending-Stiffness Calculation for Nanocrystals, Dokl. Phys., 2002, vol. 47, no. 8, pp. 620–622.

    Article  ADS  Google Scholar 

  23. Prinz, V.Y., Seleznev, V.A., Gutakovsky, A.K., Chehoskiy, A.V., Preobrazhenskii, V.V., Putyato, M.A., and Gavrilova, T.A., Free-Standing and Overgrown InGaAs/GaAs Nanotubes, Nanohelices and Their Arrays, Physica E. Low Dimens. Syst. Nanostruct., 2000, vol. 6, no. 1, pp. 828–831.

    Article  ADS  Google Scholar 

  24. Prinz, V.Y., Grutzmacher, D., Beyer, A., David, C., Ketterer, B., and Deckardt, E., A New Technique for Fabricating Three-Dimensional Micro- and Nanostructures of Various Shapes, Nanotechnology, 2001, vol. 12, no. 4, pp. 399–402.

    Article  ADS  Google Scholar 

  25. Golod, S.V., Prinz, V.Ya., Mashanov, V.I., and Gutakovsky, A.K., Fabrication of Conducting GeSi/Si Micro- and Nanotubes and Helical Microcoils, Semicond. Sci. Technol., 2001, vol. 16, no. 3, pp. 181–185.

    Article  ADS  Google Scholar 

  26. Vorob’ev, A.B. and Prinz, V.Y., Directional Rolling of Strained Heterofilms, Semicond. Sci. Technol., 2002, vol. 17, no. 6, pp. 614–616.

    Article  ADS  Google Scholar 

  27. Tersoff, J., Modeling Solid-State Chemistry: Interatomic Potentials for Multicomponent Systems, Phys. Rev. B, 1989, vol. 39, no. 8, pp. 5566–5568.

    Article  ADS  Google Scholar 

  28. Nordlund, K., Nord, J., Frantz, J., and Keinonen, J., Strain-Induced Kirkendall Mixing at Semiconductor Interfaces, Comput. Mater. Sci., 2000, vol. 18, no. 3–4, pp. 283–294.

    Article  Google Scholar 

  29. Bolesta, A.V., Golovnev, I.F., and Fomin, V.M., Molecular Dynamics Simulations of InGaAs/GaAs Nanotubes Synthesis, Fiz. Mezomekh., 2004, vol. 7, spec. iss., part 2, pp. 8–10.

    Google Scholar 

  30. Bolesta, A.V., Golovnev, I.F., and Fomin, V.M., InGaAs/GaAs Nanotubes Simulation: Comparison between Continual and Molecular Dynamics Approaches, Comput. Mater. Sci., 2006, vol. 36, no. 1–2, pp. 147–151.

    Article  Google Scholar 

  31. Morozov, N.F., Semenov, B.N., and Tovstik, P.E., Simulation of Nanoobject Formation by Methods of Continuum Mechanics, Phys. Mesomech., 2002, vol. 5, no. 3–4, pp. 5–8.

    Google Scholar 

  32. Ivanova, E.A., Krivtsov, A.M., Morozov, N.F., and Firsova, A.D., Inclusion of the Moment Interaction in the Calculation of the Flexural Rigidity of Nanostructures, Dokl. Phys., 2003, vol. 48, no. 8, pp. 455–458.

    Article  ADS  Google Scholar 

  33. Berinskii, I.E., Ivanova, E.A., Krivtsov, A.M., and Morozov, N.F., Application of Moment Interaction to the Construction of a Stable Model of Graphite Crystal Lattice, Mech. Solids, 2007, vol. 42, no. 5, pp. 663–671.

    Article  ADS  Google Scholar 

  34. Ivanova, E.A., Morozov, N.F., Semenov, B.N., and Firsova, A.D., Determination of Elastic Moduli of Nanostructures: Theoretical Estimates and Experimental Techniques, Mech. Solids, 2005, vol. 40, no. 4, pp. 60–68.

    Google Scholar 

  35. Kizuka, T., Direct Atomistic Observation of Deformation in Multiwalled Carbon Nanotubes, Phys. Rev. B Condens. Matter Mater. Phys., 1999, vol. 59, no. 7, pp. 4646–4649.

    Article  ADS  Google Scholar 

  36. Eremeyev, V.A. and Morozov, N.F., The Effective Stiffness of a Nanoporous Rod, Dokl. Phys., 2010, vol. 55, no. 6, pp. 279–282.

    Article  ADS  Google Scholar 

  37. Loboda, O.S. and Krivtsov, A.M., The Influence of the Scale Factor on the Elastic Moduli of a 3D Nanocrystal, Mech. Solids, 2005, vol. 40, no. 4, pp. 20–32.

    Google Scholar 

  38. Golovneva, E.I., Golovnev, I.F., and Fomin, V.M., Research of Nanoclusters Size Effect on the Molecular-Dynamic Modeling Results, Fiz. Mezomekh., 2004, vol. 7, spec. iss., part 2, pp. 11–13.

    Google Scholar 

  39. Zubko, I.Yu. and Trusov, P.V., Determination of Elastic Constants of FCC Single Crystals Using the Interatomic Interaction Potential, Vestnik Perm. Univ. Phys., 2011, vol. 17, no. 2, pp. 147–169.

    Google Scholar 

  40. Sanditov, D.S., Transverse Strain and Nonlinearity of the Force of Interatomic Interaction of Solids, Dokl. Phys., 2019, vol. 64, no. 5, pp. 206–209.

    Article  Google Scholar 

  41. Galashev, A.E., Polukhin, V.A., Izmodenov, I.A., and Galasheva, O.A., Elastic Properties and Stability of Crystalline Silicon Nanoparticles. Computer Experiment, J. Surf. Invest.: X-Ray, Synchrotron Neutron Tech., 2007, no. 10, pp. 60–67.

    Google Scholar 

  42. Utkin, A.V. and Fomin, V.M., Molecular Dynamic Calculation of the Bulk Modulus for Silicon and Silicon Carbide, Dokl. Phys., 2020, vol. 65, no. 5, pp. 174–177.

    Article  Google Scholar 

  43. Krivtsov, A.M. and Morozov, N.F., Two Reasons for Introducing the Scale Factor into the Description of the Mechanical Properties of Nanostructures, in Problems of Mechanics, Klimov, D.M., Ed., Moscow: Fizmatlit, 2003, pp. 485–488.

  44. Barenblatt, G.I., Golitsyn, G.S., Eremin, N.N., and Urusov, V.S., Universality of the Linear Nanoscale, Dokl. Phys., 2014, vol. 59, no. 10, pp. 446–448.

    Article  ADS  Google Scholar 

  45. Barenblatt, G.I. and Monteiro, P.J.M., Scaling Laws in Nanomechanics, Phys. Mesomech., 2010, vol. 13, no. 5–6, pp. 245–248.

    Article  Google Scholar 

  46. Golovin, Yu.I., Nanoindentation and Its Potential, Moscow: Mashinostroenie, 2009.

  47. Sneddon, I.N., The Relation between Load and Penetration in the Axisymmetric Boussinesq Problem for a Punch of Arbitrary Profile, Int. J. Eng. Sci. Pergamon, 1965, vol. 3, no. 1, pp. 47–57.

    Article  Google Scholar 

  48. Oliver, W.C. and Pharr, G.M., An Improved Technique for Determining Hardness and Elastic Modulus Using Load and Displacement Sensing Indentation Experiments, J. Mater. Res., 1992, vol. 7, no. 6, pp. 1564–1583.

    Article  ADS  Google Scholar 

  49. GOST R 8.748: Metals and Alloys. Hardness and Other Characteristics of Materials at Instrumental Indentation Test, 2011.

  50. Fedosov, S.A. and Pešek, L., Determining Mechanical Properties of Materials by Microindentation: Modern Foreign Methods, Moscow: Faculty of Physics of MSU, 2004.

  51. Bulychev, S.I. and Alekhin, V.P., Testing of Materials by Continuous Indentation, Moscow: Mashinostroenie, 1990.

  52. Pharr, G.M., Measurement of Mechanical Properties by Ultra-Low Load Indentation, Mater. Sci. Eng. A, 1998, vol. 253, no. 1–2, pp. 151–159.

    Article  Google Scholar 

  53. Adaskin, A.M. and Sapronov, I.Yu., Interdependence of Macro- and Microhardness of Materials at Indentation by Vickers Pyramid, Strength. Coatings, 2018, no. 11, pp. 489–495.

    Google Scholar 

  54. Useinov, S., Soloviev, V., Gogolinsky, K., Useinov, A., and Lvova, N., Measurement of Mechanical Properties of Materials with Nanometer Spatial Resolution, Nanoindustria, 2010, vol. 2, pp. 30–35.

    Google Scholar 

  55. Díez-Pascual, A.M., Gomez-Fatou, M.A., Ania, F., and Flores, A., Nanoindentation in Polymer Nanocomposites, Prog. Mater. Sci., 2015, vol. 67, pp. 1–94.

    Article  Google Scholar 

  56. Poon, B., Rittel, D., and Ravichandran, G., An Analysis of Nanoindentation in Linearly Elastic Solids, Int. J. Solids Struct., 2008, vol. 45, no. 24, pp. 6018–6033.

    Article  Google Scholar 

  57. Goldstein, R.V., Mechanics of Micro- and Nanostructures. Nanoindentation, Moscow: MPK, 2011.

  58. Derjaguin, B.V., Muller, V.M., and Toporov, Y.P., Effect of Contact Deformation on the Adhesion of Elastic Solids, J. Colloid Interface Sci., 1975, vol. 53, no. 2, pp. 314–326.

    Article  ADS  Google Scholar 

  59. Maugis, D., Adhesion of Spheres: The JKR-DMT Transition Using a Dugdale Model, J. Colloid Interface Sci., 1992, vol. 150, no. 1, pp. 243–269.

    Article  Google Scholar 

  60. Johnson, K.L., Kendall, K., and Roberts, A.D., Surface Energy and the Contact of Elastic Solids, Proc. R Soc. London. A Math. Phys. Sci., 1971, vol. 324, no. 1558, pp. 301–313.

    ADS  Google Scholar 

  61. Cappella, B. and Dietler, G., Force-Distance Curves by Atomic Force Microscopy, Surf. Sci. Rep., 1999, vol. 34, pp. 1–104.

    Article  ADS  Google Scholar 

  62. Butt, H.J., Cappella, B., and Kappl, M., Force Measurements with the Atomic Force Microscope: Technique, Interpretation and Applications, Surf. Sci. Rep., 2005, vol. 59, no. 1–6, pp. 1–152.

    Article  ADS  Google Scholar 

  63. Jee, A.Y. and Lee, M., Comparative Analysis on the Nanoindentation of Polymers Using Atomic Force Microscopy, Polym. Test., 2010, vol. 29, no. 1, pp. 95–99.

    Article  Google Scholar 

  64. Wang, Y., Dou, S., Shang, L., Zhang, P., Yan, X., Zhang, K., Zhao, J., and Li, Y., Effects of Microsphere Size on the Mechanical Properties of Photonic Crystals, Crystals, 2018, vol. 8, no. 12, pp. 1–11.

    Google Scholar 

  65. Cuenot, S., Fretigny, C., Demoustier-Champagne, S., and Nysten, B., Measurement of Elastic Modulus of Nanotubes by Resonant Contact Atomic Force Microscopy, J. Appl. Phys., 2003, vol. 93, no. 9, pp. 5650–5655.

    Article  ADS  Google Scholar 

  66. Nysten, B., Fretigny, C., and Cuenot, S., Elastic Modulus of Nanomaterials: Resonant Contact-AFM Measurement and Reduced-Size Effects (Invited Paper), in Testing, Reliability, and Application of Micro- and Nano-Material Systems III, Geer, R.E., et al., Eds., 2005, vol. 5766, p. 78.

  67. Beilstein, J., Maharaj, D., and Bhushan, B., Scale Effects of Nanomechanical Properties and Deformation Behavior of Au Nanoparticle and Thin Film Using Depth Sensing Nanoindentation, Nanotechnology, 2014, vol. 5, no. 1, pp. 822–836.

    Google Scholar 

  68. Mook, W.M., Nowak, J.D., Perrey, C.R., Carter, C.B., Mukherjee, R., Girshick, S.L., McMurry, P.H., and Gerberich, W.W., Compressive Stress Effects on Nanoparticle Modulus and Fracture, Phys. Rev. B. Condens. Matter Mater. Phys., 2007, vol. 75, no. 21, pp. 1–10.

    Article  Google Scholar 

  69. Gerberich, W.W., Mook, W.M., Perrey, C.R., Carter, C.B., Baskes, M.I., Mukherjee, R., Gidwani, A., Heberlein, J., McMurry, P.H., and Girshick, S.L., Superhard Silicon Nanospheres, J. Mech. Phys. Solids, 2003, vol. 51, no. 6, pp. 979–992.

    Article  ADS  Google Scholar 

  70. Mordehai, D., Kazakevich, M., Srolovitz, D.J., and Rabkin, E., Nanoindentation Size Effect in Single-Crystal Nanoparticles and Thin Films: A Comparative Experimental and Simulation Study, Acta Mater., 2011, vol. 59, no. 6, pp. 2309–2321.

    Article  ADS  Google Scholar 

  71. Nowak, J.D., Mook, W.M., Minor, A.M., Gerberich, W.W., and Carter, C.B., Fracturing a Nanoparticle, Philos. Mag., 2007, vol. 87, no. 1, pp. 29–37.

    Article  ADS  Google Scholar 

  72. Taloni, A., Vodret, M., Costantini, G., and Zapperi, S., Size Effects on the Fracture of Microscale and Nanoscale Materials, Nat. Rev. Mater., 2018, vol. 3, no. 7, pp. 211–224.

    Article  ADS  Google Scholar 

  73. Jang, D., Gross, C.T., and Greer, J.R., Effects of Size on the Strength and Deformation Mechanism in Zr-Based Metallic Glasses, Int. J. Plasticity, 2011, vol. 27, no. 6, pp. 858–867.

    Article  Google Scholar 

  74. Dimiduk, D.M., Uchic, M.D., and Parthasarathy, T.A., Size-Affected Single-Slip Behavior of Pure Nickel Microcrystals, Acta Mater., 2005, vol. 53, no. 15, pp. 4065–4077.

    Article  ADS  Google Scholar 

  75. Chen, C.Q., Pei, Y.T., and De Hosson, J.T.M., Effects of Size on the Mechanical Response of Metallic Glasses Investigated through in Situ TEM Bending and Compression Experiments, Acta Mater., 2010, vol. 58, no. 1, pp. 189–200.

    Article  ADS  Google Scholar 

  76. Zhu, Y., Qin, Q., Xu, F., Fan, F., Ding, Y., Zhang, T., Wiley, B.J., and Wag, Z.L., Size Effects on Elasticity, Yielding, and Fracture of Silver Nanowires: In Situ Experiments, Phys. Rev. B, 2012, vol. 85, no. 4, p. 045443.

    Article  ADS  Google Scholar 

  77. Han, J.H. and Saif, M.T.A., In Situ Microtensile Stage for Electromechanical Characterization of Nanoscale Freestanding Films, Rev. Sci. Instrum., 2006, vol. 77, no. 4, p. 045102.

    Article  Google Scholar 

  78. Kizuka, T., Takatani, Y., Asaka, K., and Yoshizaki, R., Measurements of the Atomistic Mechanics of Single Crystalline Silicon Wires of Nanometer Width, Phys. Rev. B, 2005, vol. 72, no. 3, p. 035333.

    Article  ADS  Google Scholar 

  79. Shushkov, A.A. and Vakhrushev, A.V., Methods for Determination of Mechanical Properties of Nanostructures, Khimich. Fiz. Mezoskopia, 2018, vol. 20, no. 1, pp. 57–71.

    Google Scholar 

  80. Vakhrushev, A.V., Vakhrusheva, L.L., and Shushkov, A.A., Numerical Analysis of the Change in the Elastic Modulus of Crystalline Metal Nanoparticles under Different Loading Conditions, Izv. TulGU. Estestv. Nauki, 2011, no. 3, pp. 137–150.

    Google Scholar 

  81. Vakhrushev, A.A., Fedotov, A.Yu., Shushkov, A.A., and Shushkov, A.V., Modeling the Formation of Metal Nanoparticles, Study of the Structural, Physical and Mechanical Properties of Nanoparticles and Nanocomposites, Izv. TulGU. Estestv. Nauki, 2011, no. 2, pp. 241–253.

    Google Scholar 

  82. Andrievskii, R.A., Kalinnikov, G.V., Hellgren, N., Sandstrom, P., and Shtanskii, D.V., Nanoindentation and Strain Characteristics of Nanostructured Boride/Nitride Films, Phys. Solid State, 2000, vol. 42, pp. 1671–1674.

    Article  ADS  Google Scholar 

  83. Gogolinsky, K.V., Methods of Control of Geometric Parameters and Mechanical Properties of Solids with Micro- and Nanometer Spatial Resolution, Doct. Dissertation, St. Petersburg: Mining Univ., 2015.

  84. Vakhrushev, A.V. and Shushkov, A.A., Method for Calculating Elastic Parameters of Nanoelements, Khimich. Fiz. Mezoskopia, 2007, vol. 7, no. 3, pp. 277–285.

    Google Scholar 

  85. Vakhrushev, A.V., Fedotov, A.Yu., Vakhrushev, A.A., Shushkov, A.A., and Shushkov, A.V., A Study of the Formation of Metal Nanoparticles and Determination of Mechanical-Structural Characteristics of Nanoobjects and Composite Materials on Their Basis, Khimich. Fiz. Mezoskopia, 2010, vol. 12, no. 4, pp. 486–495.

    Google Scholar 

  86. Lipanov, A.M., Vakhrushev, A.V., Tenenev, V.A., and Fedotov, A.Yu., Mathematical Modeling of Dynamic Interaction of Solids. Part 1. Theoretical Foundations, Khimich. Fiz. Mezoskopia, 2014, vol. 16, no. 4, pp. 513–523.

    Google Scholar 

  87. Vakhrushev, A.V., Shushkov, A.A., Zykov, S.N., and Klekovkin, V.S., Determination of the Young’s Modulus of Nanoparticles by Numerical Modeling and Experimental Investigation. Part 1. Methodology of Numerical Modeling, Khimich. Fiz. Mezoskopia, 2014, vol. 16, no. 3, pp. 381–387.

    Google Scholar 

  88. Vakhrushev, A.V., Shushkov, A.A., Zykov, S.N., Vakhrusheva, L.L., and Klekovkin, V.S., Determination of the Young’s Modulus of Nanoparticles by Numerical Modeling and Experimental Investigation. Part 2. Method of Correlating the Results of Elastic Experiment and Numerical Simulation, Khimich. Fiz. Mezoskopia, 2015, vol. 17, no. 2, pp. 214–218.

    Google Scholar 

  89. Vakhrushev, A.V., Lipanov, A.M., and Shushkov, A.A., Patent C1 2296972 USA, Russia, Method for Determining the Young’s Modulus of Materials, Byull. Izobret., 2007, pp. 1–6.

  90. Vakhrushev, A.V., Lipanov, A.M., and Shushkov, A.A., Patent С1 2292029 USA, Method for Determining the Young’s Modulus of Micro- and Nanoparticles, Byull. Izobret., 2012, pp. 1–7.

  91. Vakhrushev, A.V., Lipanov, A.M., and Shushkov, A.A., Patent C1 2292029 USA, Russia, Method for Determining the Young’s Modulus of Materials, Byull. Izobret., 2007, pp. 1–7.

  92. Dremin, A.N. and Karpukhin, I.A., Method for Determination of Hugoniot Curves of Dispersed Substances, PMTF, 1960, no. 3, pp. 184–188.

    Google Scholar 

  93. Torquato, S., Yeong, C.L.Y., Rintoul, M.D., Milius, D.L., and Aksay, I.A., Elastic Properties and Structure of Interpenetrating Boron Carbide/Aluminum Multiphase Composites, J. Am. Ceram. Soc., 2004, vol. 82, no. 5, pp. 1263–1268.

    Article  Google Scholar 

  94. Fomin, V.M. and Filippov, A.A., A Theoretical and Experimental Method for Determining the Elastic Characteristics of Nanomaterials, Dokl. Phys., 2019, vol. 64, no. 12, pp. 466–469.

    Article  ADS  Google Scholar 

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Funding

The study was carried out with the financial support of the Russian Foundation for Basic Research (Project No. 19-11-50040).

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  1. Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    V. M. Fomin & A. A. Filippov

  2. Novosibirsk State University, 630090, Novosibirsk, Russia

    V. M. Fomin

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Correspondence to A. A. Filippov.

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Translated from in Fizicheskaya Mezomekhanika, 2020, Vol. 23, No. 5, pp. 5–19.

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Fomin, V.M., Filippov, A.A. A Review of Methods for Studying the Elastic Characteristics of Nanoobjects. Phys Mesomech 24, 117–130 (2021). https://doi.org/10.1134/S1029959921020016

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