References
- Guo JG, Zhao YP. The size-dependent elastic properties of nanofilms with surface effects. J Appl Phys. 2005;98:074306. doi: https://doi.org/10.1063/1.2071453
- Govindjee S, Sackman JL. On the use of continuum mechanics to estimate the properties of nanotubes. Solid State Commun. 1999;110:227–223. doi: https://doi.org/10.1016/S0038-1098(98)00626-7
- Eringen AC, Edelen DBG. On nonlocal elasticity. Int J Eng Sci. 1972;10:233–248. doi: https://doi.org/10.1016/0020-7225(72)90039-0
- Eringen AC. Nonlocal continuum filed theories. New York: Springer; 2002.
- Eringen AC. On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J Appl Phys. 1983;54:4703–4710. doi: https://doi.org/10.1063/1.332803
- Janghorban M. Two different types of differential quadrature methods for static analysis of microbeams based on nonlocal thermal elasticity theory in thermal environment. Arch Appl Mech. 2012;82:669–675. doi: https://doi.org/10.1007/s00419-011-0582-4
- Nami MR, Janghorban M, Damadam M. Thermal buckling analysis of functionally graded rectangular nanoplates based on nonlocal third-order shear deformation theory. Aerosp Sci Technol. 2015;41:7–15. doi: https://doi.org/10.1016/j.ast.2014.12.001
- Li CL, Guo HL, Tian XG, et al. Size-dependent thermo-electromechanical responses analysis of multi-layered piezoelectric nanoplates for vibration control. Compos Struct. 2019;225:111112. doi: https://doi.org/10.1016/j.compstruct.2019.111112
- Mindlin RD. Second gradient of strain and surface-tension in linear elasticity. Int J Solids Struct. 1965;1:414–438.
- Aifantis EC. On the role of gradients in the localization of deformation and fracture. Int J Eng Sci. 1992;30:1279–1299. doi: https://doi.org/10.1016/0020-7225(92)90141-3
- Yang F, Chong ACM, Lam DCC, et al. Couple stress based strain gradient theory for elasticity. Int J Solids Struct. 2002;39:2731–2743. doi: https://doi.org/10.1016/S0020-7683(02)00152-X
- Polizzotto C. Stress gradient versus strain gradient constitutive models within elasticity. Int J Solids Struct. 2014;51:1809–1818. doi: https://doi.org/10.1016/j.ijsolstr.2014.01.021
- Lim CW, Zhang G, Reddy J. A higher-order nonlocal elasticity and strain gradient theory and its application in wave propagation. J Mech Phys Solids. 2015;78:298–313. doi: https://doi.org/10.1016/j.jmps.2015.02.001
- Li L, Hu YJ. Buckling analysis of size-dependent nonlinear beams based on a nonlocal strain gradient theory. Int J Eng Sci. 2015;97:84–94. doi: https://doi.org/10.1016/j.ijengsci.2015.08.013
- Ebrahimi F, Dabbagh A. Viscoelastic wave propagation analysis of axially motivated double-layered graphene sheets via nonlocal strain gradient theory. Wave Random Complex. 2020; 1–20.
- Joseph DD, Preziosi L. Heat waves. Rev Mod Phys. 1989;61:41–73. doi: https://doi.org/10.1103/RevModPhys.61.41
- Sobolev SL. Nonlocal diffusion models: application to rapid solidification of binary mixtures. Int J Heat Mass Transf. 2014;71:295–302. doi: https://doi.org/10.1016/j.ijheatmasstransfer.2013.12.048
- Peshkov V. Second sound in helium II. J Phys. 1944;8:381–382.
- Sherief HH, Hamza FA, Saleh HA. The theory of generalized thermoelastic diffusion. Int J Eng Sci. 2004;42:591–608. doi: https://doi.org/10.1016/j.ijengsci.2003.05.001
- Kumar R, Kansal T. Propagation of Lamb waves in transversely isotropic thermoelastic diffusive plate. Int J Solids Struct. 2008;45:5890–5913. doi: https://doi.org/10.1016/j.ijsolstr.2008.07.005
- Suo YH, Shen SP. Dynamical theoretical models and variational principles for coupled temperature-diffusion-mechanics. Acta Mech. 2012;223:29–41. doi: https://doi.org/10.1007/s00707-011-0545-4
- Sherief HH, Saleh HA. A half-space problem in the theory of generalized thermoelastic diffusion. Int J Solids Struct. 2005;42:4484–4493. doi: https://doi.org/10.1016/j.ijsolstr.2005.01.001
- Aouadi M. A problem for an infinite elastic body with a spherical cavity in the theory generalized thermoelastic diffusion. Int J Solids Struct. 2007;44:5711–5722. doi: https://doi.org/10.1016/j.ijsolstr.2007.01.019
- Li CL, Guo HL, Tian XG. Transient responses of generalized magnetothermoelasto-diusive problems with rotation using Laplace transform–finite element method. J Therm Stress. 2017;40:1152–1165. doi: https://doi.org/10.1080/01495739.2017.1312722
- Hosseini SM, Sladek J, Sladek V. Two-dimensional transient analysis of coupled non-Fick diffusion-thermoelasticity based on Green-Naghdi theory using the meshless local Petrov-Galerkin (MLPG) method. Int J Mech Sci. 2014;82:74–80. doi: https://doi.org/10.1016/j.ijmecsci.2014.03.009
- Li CL, Guo HL, Tian XG. Time-domain finite element analysis to nonlinear transient responses of generalized diffusion-thermoelasticity with variable thermal conductivity and diffusivity. Int J Mech Sci. 2017;131(132):234–244. doi: https://doi.org/10.1016/j.ijmecsci.2017.07.008
- Ezzat MA, Fayik MA. Fractional order theory of thermoelastic diffusion. J Therm Stress. 2011;34:851–872. doi: https://doi.org/10.1080/01495739.2011.586274
- EI-Karamany AS, Ezzat MA. Thermoelastic diffusion theory with memory-dependent derivative. J Therm Stress. 2016;39:1035–1050. doi: https://doi.org/10.1080/01495739.2016.1192847
- Li CL, Guo HL, Tian XG. A size-dependent generalized thermoelastic diffusion theory and its application. J Therm Stress. 2017;40:603–626. doi: https://doi.org/10.1080/01495739.2017.1300786
- Li CL, He TH, Tian XG. Transient responses of nanosandwich structure based on size-dependent generalized thermoelastic diffusion theory. J Therm Stress. 2019;42:1171–1191. doi: https://doi.org/10.1080/01495739.2019.1623140
- Jou D, Lebon G, Criado-Sancho M. Variational principles for thermal transport in nanosystems with heat slip flow. Phys Rev E. 2010;82:031128. doi: https://doi.org/10.1103/PhysRevE.82.031128
- Tzou DY, Guo ZY. Nonlocal behavior in thermal lagging. Int J Therm Sci. 2010;49:1133–1137. doi: https://doi.org/10.1016/j.ijthermalsci.2010.01.022
- Sobolev SL. Equations of transfer in nonlocal media. Int J Heat Mass Transf. 1994;37:2175–2182. doi: https://doi.org/10.1016/0017-9310(94)90319-0
- Wang GX, Prasad V. Microscale heat and mass transfer and non-equilibrium phase change in rapid solidification. Mat Sci Eng A. 2000;292:142–148. doi: https://doi.org/10.1016/S0921-5093(00)01003-0
- Sellitto A, Alvarez FX, Jou D. Geometrical dependence of thermal conductivity in elliptical and rectangular nanowires. Int J Heat Mass Transf. 2012;55:3114–3120. doi: https://doi.org/10.1016/j.ijheatmasstransfer.2012.02.045
- Guyer RA, Krumhansl JA. Solution of the linearized phonon Boltzmann equation. Phys Rev. 1966;148:765–778.
- Dong Y, Cao BY, Guo ZY. Size dependent thermal conductivity of Si nanosystems based on phonon gas dynamics. Phys E. 2014;56:256–262. doi: https://doi.org/10.1016/j.physe.2013.10.006
- Chen G. Ballistic-diffusive heat-conduction equations. Phys Rev Lett. 2001;86:2297–2300. doi: https://doi.org/10.1103/PhysRevLett.86.2297
- Hoogeboom-Pot KM, Hernandez-Charpak JN, Gu XK, et al. A new regime of nanoscale thermal transport: collective diffusion increases dissipation efficiency. PNAS. 2015;112:4846–4851. doi: https://doi.org/10.1073/pnas.1503449112
- Li CL, Guo HL, Tian XG, et al. Nonlocal diffusion-elasticity based on nonlocal mass transfer and nonlocal elasticity and its application in shock-induced responses analysis. Mech Adv Mater Struct. 2019: 1–12.
- Reddy JN. Nonlocal theories for bending, buckling and vibration of beams. Int J Eng Sci. 2007;45:288–307. doi: https://doi.org/10.1016/j.ijengsci.2007.04.004
- Shen HS, Xu YM, Zhang CL. Prediction of nonlinear vibration of bilayer graphene sheets in thermal environments via molecular dynamics simulations and nonlocal elasticity. Comput Methods Appl Mech Eng. 2013;267:458–470. doi: https://doi.org/10.1016/j.cma.2013.10.002
- Yu YJ, Tian XG, Liu XR. Size-dependent generalized thermoelasticity using Eringen’s nonlocal model. Eur J Mech A-Solid. 2015;51:96106. doi: https://doi.org/10.1016/j.euromechsol.2014.12.005
- Ma Y. Size-dependent thermal conductivity in nanosystems based on non-Fourier heat transfer. Appl Phys Lett. 2012;101:211905. doi: https://doi.org/10.1063/1.4767337
- Sudak LJ. Column buckling of multiwalled carbon nanotubes using nonlocal continuum mechanics. J Appl Phys. 2003;94:7281. doi: https://doi.org/10.1063/1.1625437
- Lu JP. Elastic properties of carbon nanotubes and nanoropes. Phys Rev Lett. 1997;79:1297–1300. doi: https://doi.org/10.1103/PhysRevLett.79.1297
- Li CL, Tian XG, He TH. Nonlocal thermo-viscoelasticity and its application in size-dependent responses of bi-layered composite viscoelastic nanoplate under nonuniform temperature for vibration control. Mech Adv Mater Struct. 2020: 1–15.
- Brancik L. Programs for fast numerical inversion of Laplace transforms in MATLAB language environment. Proc Seventh Prague Conference MATLAB. 1999;99:27–39.
- Yu YJ, Tian XG, Xiong QL. Nonlocal thermoelasticity based on nonlocal heat conduction and nonlocal elasticity. Eur J Mech A-Solid. 2016;60:238–253. doi: https://doi.org/10.1016/j.euromechsol.2016.08.004