Abstract
The paper proposes the classical and the non-classical models of changes in the Young’s modulus of a geomaterial under the effect of an alternating load. The classical model is based on the Newton’s equation and the Jaeger’s idealized “mass-on-spring” model. The non-classical model is based on the gradient theory, which takes into account the internal heterogeneous structure (scale) of a geomaterial.
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References
Tutuncu AN, Podio AL, Gregory AR, Sharma MM (1998) Nonlinear viscoelastic behavior of sedimentary rocks, Part I: Effect of frequency and strain amplitude, Geophysics 63:184–194. https://doi.org/10.1190/1.1444311
Bauer A, Bhuiyan MH, Fjaer E, Holt RM, Lozovyi S, Pohl M, Szewczyk D. (2016) Frequency-dependent wave velocities in sediments and sedimentary rocks: Laboratory measurements and evidences, The Leading Edge 35:474–560. https://doi.org/10.1190/tle35060490.1
Kotsanis D, Nomikos P, Rozos D (2021) Comparison of static and dynamic Young’s modulus of prasinites, Mater. Proc. 2021(5):54. https://doi.org/10.3390/materproc2021005054
Borgomano JVM, Gallagher A, Sun C, Fortin J (2020) An apparatus to measure elastic dispersion and attenuation using hydrostatic- and axial-stress oscillations under undrained conditions, Review of Scientific Instruments 91(3):034502. https://doi.org/10.1063/1.5136329
Waqas U, Ahmed MF (2020) Prediction modeling for the estimation of dynamic elastic Young’s modulus of thermally treated sedimentary rocks using linear–nonlinear regression analysis, regularization, and ANFIS, Rock Mech. Rock Eng. 53:5411–5428. https://doi.org/10.1007/s00603-020-02219-8
Zhang QB, Zhao J (2014) A review of dynamic experimental techniques and mechanical behaviour of rock materials. Rock Mech. Rock Eng. 47:1411–1478. https://doi.org/10.1007/s00603-013-0463-y
Jaeger JC, Cook NGW, Zimmerman RW(2007) Laboratory testing of rocks. In: Fundamentals of Rock Mechanics, 4th ed., Blackwell Publishing, Malden, MA, USA, pp 145–167.
Forest S, Sievert R (2003) Elastoviscoplastic constitutive frameworks for generalized continua, Acta Mechanica 160(1–2):71–111, https://doi.org/10.1007/s00707-002-0975-0
Smolin IY (2005) On the application of the Cosserat model to the description of plastic deformation at the mesoscale, Fizicheskaya Mezomekhanika (3):49–62.
Bazant ZP, Jirasek M (2002) Nonlocal integral formulations of plasticity and damage: Survey of progress, Journal of Engineering Mechanics 128(11):1119–1149. https://doi.org/10.1061/(ASCE)0733-9399(2002)128:11(1119)
Lurie SA, Kalamkarov AL, Solyaev YO, Volkov AV (2021) Dilatation gradient elasticity theory, European Journal of Mechanics, A/Solids 88:104258. https://doi.org/10.1016/j.euromechsol.2021.104258
Placidi L, Misra A, Barchiesi E (2019) Simulation results for damage with evolving microstructure and growing strain gradient moduli, Continuum Mechanics and Thermodynamics 31(4):1143–1163. https://doi.org/10.1007/s00161-018-0693-z
Zhang G, Zheng C, Mi C, Gao X-L (2021) A microstructure-dependent Kirchhoff plate model based on a reformulated strain gradient elasticity theory, Mechanics of Advanced Materials and Structures 29(17):2521–2530. https://doi.org/10.1080/15376494.2020.1870054
Nazarenko L, Glüge R, Altenbach H (2021) Positive definiteness in coupled strain gradient elasticity, Continuum Mechanics and Thermodynamics 33(3):713–725. https://doi.org/10.1007/s00161-020-00949-2
Sidhardh S, Ray MC (2018) Element-free Galerkin model of nano-beams considering strain gradient elasticity, Acta Mechanica 229(7):2765–2786. https://doi.org/10.1007/s00707-018-2139-x
Mindlin RD (1964) Micro-structure in linear elasticity, Archive for Rational Mechanics and Analysis 16(1):51–78. https://doi.org/10.1007/BF00248490
Aifantis EC (2012) A note on gradient elasticity and nonsingular crack fields, Journal of the Mechanical Behavior of Materials 20(4–5):103–105. https://doi.org/10.1515/jmbm-2012-0002
Parisis K, Konstantopoulos I, Aifantis EC (2018) Nonsingular solutions of GradEla models for dislocations: An extension to fractional GradEla, Journal of Micromechanics and Molecular Physics 3(3–4):1840013. https://doi.org/10.1142/S2424913018400131
Guzev MA Non-classical solutions of a continuum model for rock descriptions, Journal of Rock Mechanics and Geotechnical Engineering 6(3):180–185. https://doi.org/10.1016/j.jrmge.2014.03.001
Qi CZ, Li KR, Bai JP, Chanyshev AI, Liu P. (2017) Strain gradient model of zonal disintegration of rock mass near deep-level tunnels, Journal of Mining Science 53:21–33. https://doi.org/10.1134/S1062739117011808
Lavrikov SV, Revuzhenko AF (2019) Mathematical modeling of deformation of self-stress rock mass surrounding a tunnel, Im: Wu W (ed) Desiderata Geotechnica, Springer Series in Geomechanics and Geoengineering pp 79–85. https://doi.org/10.1007/978-3-030-14987-1_9
Guzev M, Kozhevnikov, E, Turbakov M, Riabokon E, Poplygin V (2020) Experimental studies of the influence of dynamic loading on the elastic properties of sandstone, Energies 2020(13):6195. https://doi.org/10.3390/en13236195
Goldstein H, Poole Jr C, Safko J (2002) Classical Mechanics, 3rd ed, Addison Wesley, San Francisco.
Guzev M, Riabokon E, Turbakov M, Kozhevnikov E, Poplygin V (2020) Modelling of the dynamic Young’s modulus of a sedimentary rock subjected to nonstationary loading, Energies 2020(13):6461. https://doi.org/10.3390/en13236461
Lomakin EV, Lurie SA, Rabinskiy LN, Solyaev YO (2019) On the refined stress analysis in the applied elasticity problems accounting of gradient effects, Doklady Physics 489(6):585–591. https://doi.org/10.1134/S1028335819120103
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Guzev, M.A., Riabokon, E.P., Turbakov, M.S., Poplygin, V.V., Kozhevnikov, E.V., Gladkikh, E.A. (2023). Classical and Non-Classical Models of Changes in the Young Modulus of Geomaterials Under Alternating Loads. In: Altenbach, H., Berezovski, A., dell'Isola, F., Porubov, A. (eds) Sixty Shades of Generalized Continua. Advanced Structured Materials, vol 170. Springer, Cham. https://doi.org/10.1007/978-3-031-26186-2_21
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