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Articles

Nonlocal continuum mechanics structures: The virtual powers method vs the extra fluxes topic

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Pages 75-87 | Received 27 Jul 2022, Accepted 11 Nov 2022, Published online: 01 Dec 2022

References

  • R. Barretta, S. A. Faghidian, F. Marotti de Sciarra, et al., “Nonlocal strain gradient torsion of elastic beams: Variational formulation and constitutive boundary conditions,” Arch. Appl. Mech., vol. 90, no. 4, pp. 691–706, 2020. DOI: 10.1007/s00419-019-01634-w.
  • R. Barretta and F. Marotti de Sciarra, “Constitutive boundary conditions for nonlocal strain gradient elastic nano-beams,” Int. J. Eng. Sci., vol. 130, pp. 187–198, 2018. DOI: 10.1016/j.ijengsci.2018.05.009.
  • A. Krawietz, “Surface phenomena of gradient materials,” Continuum Mech. Thermodyn., vol. 33, no. 5, pp. 2203–2212, 2021. DOI: 10.1007/s00161-021-01022-2.
  • P. Germain, “The method of virtual power in the mechanics of continuous media I: Second-gradient theory,” Math. Mech. Compl. Sys., vol. 8, no. 2, pp. 153–190, 2020. DOI: 10.2140/memocs.2020.8.153.
  • M. Fabrizio, B. Lazzari and R. Nibbi, “Thermodynamics of non-local materials: Extra fluxes and internal powers,” Continuum Mech. Thermodyn., vol. 23, no. 6, pp. 509–525, 2011. DOI: 10.1007/s00161-011-0193-x.
  • J. E. Dunn and J. Serrin, “On the thermomechanics of interstitial working,” Arch. Rational Mech. Anal., vol. 88, no. 2, pp. 95–133, 1985. DOI: 10.1007/BF00250907.
  • I. Müller, Thermodynamics, Pitman Publishing Inc., Boston, 1985,
  • G. Amendola, M. Fabrizio and J. M. Golden, “Thermodynamics of a non-simple heat conductor with memory,” Quart. Appl. Math., vol. 69, no. 4, pp. 787–806, 2011. http://www.jstor.org/stable/43639008. DOI: 10.1090/S0033-569X-2011-01228-5.
  • G. Amendola, M. Fabrizio and J. M. Golden, “Second gradient viscoelastic fluids: Dissipation principle and free energies,” Meccanica, vol. 47, no. 8, pp. 1859–1868, 2012. DOI: 10.1007/s11012-012-9559-9.
  • A. Morro and M. Vianello, “Interstitial energy flux and stress-power for second-gradient elasticity,” Math. Mech. Solids, vol. 21, no. 4, pp. 403–412, 2016. DOI: 10.1177/1081286514522475.
  • J. M. Cardona, S. Forest and R. Sievert, “Towards a theory of second grade thermoelasticity,” Extract. Math., vol. 14, pp. 127–140, 1999. http://eudml.org/doc/38597.
  • M. Aouadi, B. Lazzari and R. Nibbi, “Exponential decay in thermoelastic materials with voids and dissipative boundary without thermal dissipation,” Z. Angew. Math. Phys, vol. 63, no. 5, pp. 961–973, 2012. DOI: 10.1007/s00033-012-0201-4.
  • S. Bargmann, A. Favata and P. Podio-Guidugli, “A revised exposition of the Green-Naghdi theory of heat propagation,” J Elast, vol. 114, no. 2, pp. 143–154, 2014. DOI: 10.1007/s10659-013-9431-8.
  • B. A. Hamidi, S. A. Hosseini, R. Hassannejad and F. Khosravi, “An exact solution on gold microbeam with thermoelastic damping via generalized Green-Naghdi and modified couple stress theories,” J. Therm. Stress., vol. 43, no. 2, pp. 157–174, 2020. DOI: 10.1080/01495739.2019.1666694.
  • B. A. Hamidi, S. A. Hosseini, R. Hassannejad and F. Khosravi, “Theoretical analysis of thermoelastic damping of silver nanobeam resonators based on Green-Naghdi via nonlocal elasticity with surface energy effects,” Eur. Phys. J. Plus., vol. 135, pp. 35, 2020. DOI: 10.1140/epjp/s13360-019-00037-8.
  • V. A. Eremeyev, F. S. Alzahrani, A. Cazzani, et al., “On existence and uniqueness of weak solutions for linear pantographic beam lattices models,” Continuum Mech. Thermodyn., vol. 31, no. 6, pp. 1843–1861, 2019. DOI: 10.1007/s00161-019-00826-7.
  • V. A. Eremeyev and F. Dell‘Isola, “Weak solutions within the gradient-incomplete strain-gradient elasticity,” Lobachevskii J. Math., vol. 41, no. 10, pp. 1992–1998, 2020. DOI: 10.1134/S1995080220100078.
  • V. A. Eremeyev, L. P. Lebedev and M. J. Cloud, “On weak solutions of boundary value problems within the surface elasticity of Nth order,” Z. Angew. Math. Mech., vol. 101, pp. e202000378, 2021. DOI: 10.1002/zamm.202000378.
  • O. R. Hrytsyna, “Applications of the local gradient elasticity to the description of the size effect of shear modulus,” SN Appl. Sci., vol. 2, no. 8, pp. 1453, 2020. DOI: 10.1007/s42452-020-03217-9.
  • L. Nazarenko, R. Glüge and H. Altenbach, “Uniqueness theorem in coupled strain gradient elasticity with mixed boundary conditions,” Continuum Mech. Thermodyn., vol. 34, no. 1, pp. 93–106, 2022. DOI: 10.1007/s00161-021-01048-6.
  • R. Zaera, Ò. Serrano and J. Fernández-Sáez, “Non-standard and constitutive boundary conditions in nonlocal strain gradient elasticity,” Meccanica., vol. 55, no. 3, pp. 469–479, 2020. DOI: 10.1007/s11012-019-01122-z.
  • A. Cutolo, V. Mallardo, M. Fraldi and E. Ruocco, “Third-order nonlocal elasticity in buckling and vibration of functionally graded nanoplates on Winkler-Pasternak media,” Ann. Solid Struct. Mech., vol. 12, no. 1–2, pp. 141–154, 2020. DOI: 10.1007/s12356-020-00059-3.
  • F. Ebrahimi, E. Salari and S. A. H. Hosseini, “Thermomechanical vibration behavior of FG nanobeams subjected to linear and non-linear temperature distributions,” J. Therm. Stress., vol. 38, no. 12, pp. 1360–1386, 2015. DOI: 10.1080/01495739.2015.1073980.
  • S. A. H. Hosseini and O. Rahmani, “Thermomechanical vibration of curved functionally graded nanobeam based on nonlocal elasticity,” J. Therm. Stress., vol. 39, no. 10, pp. 1252–1267, 2016. DOI: 10.1080/01495739.2016.1215731.
  • I. Müller, “The coldness, a universal function in thermoelastic bodies,” Arch. Rational Mech. Anal., vol. 41, no. 5, pp. 319–332, 1971. DOI: 10.1007/BF00281870.
  • S. Forest and E. C. Aifantis, “Some links between recent gradient thermo-elasto-plasticity theories and the thermomechanics of generalized continua,” Int. J. Solids Struct., vol. 47, no. 25-26, pp. 3367–3376, 2010. DOI: 10.1016/j.ijsolstr.2010.07.009.
  • E. C. Aifantis, 2016, “Chapter one – Internal length gradient (ILG) material mechanics across scales and disciplines,” in Advances in Applied Mechanics, Stéphane P.A. Bordas, Daniel S. Balint, Eds. Elsevier 49, pp. 1–110. DOI: 10.1016/bs.aams.2016.08.001.
  • E. Fried and M. E. Gurtin, “Tractions, balances, and boundary conditions for nonsimple materials with application to liquid flow at small-length scales,” Arch. Rational Mech. Anal., vol. 182, no. 3, pp. 513–554, 2006. DOI: 10.1007/s00205-006-0015-7.
  • F. dell’Isola, G. Sciarra and S. Vidoli, “Generalized Hooke’s law for isotropic second gradient materials,” Proc. R. Soc. A., vol. 465, no. 2107, pp. 2177–2196, 2009. DOI: 10.1098/rspa.2008.0530.
  • E. C. Aifantis, “A concise review of gradient models in mechanics and physics,” Front. Phys., vol. 7, pp. 239, 2020. DOI: 10.3389/fphy.2019.00239.
  • M. Caputo and M. Fabrizio, “Applications of new time and spatial fractional derivatives with exponential kernels,” Progr. Fract. Differ. Appl., vol. 2, no. 1, pp. 1–11, 2016. DOI: 10.12785/pfda/01020.
  • K. Parisis, V. Dimosthenis, L. Kouris, A. Konstantinidis and E. C. Aifantis, “A note on gradient/fractional one-dimensional elasticity and viscoelasticity,” Fractal. Fract., vol. 6, no. 2, pp. 84, 2022. DOI: 10.3390/fractalfract6020084.
  • V. E. Tarasov and E. C. Aifantis, “On fractional and fractal formulations of gradient linear and nonlinear elasticity,” Acta Mech., vol. 230, no. 6, pp. 2043–2070, 2019. DOI: 10.1007/s00707-019-2373-x.

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