Nonlocal thermoelasticity based on nonlocal heat conduction and nonlocal elasticity

European Journal of Mechanics - A/Solids - Tập 60 - Trang 238-253 - 2016
Yajun Yu1, Xiaogeng Tian1, Qi-lin Xiong2
1State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi'an Jiaotong University, Xi'an 710049, PR China
2Department of Civil Engineering & Mechanics, Huazhong University of Science & Technology, 1037 Luoyu Road, Wuhan 430074, PR China

Tóm tắt

Từ khóa


Tài liệu tham khảo

Aifantis, 1999, Gradient deformation models at nano, micro, and macro scales, J. Eng. Mater. Technol., 121, 189, 10.1115/1.2812366

Alvarez, 2009, Phonon hydrodynamics and phonon-boundary scattering in nanosystems, J. Appl. Phys., 105, 014317, 10.1063/1.3056136

Ansari, 2010, Nonlocal plate model for free vibrations of single-layered graphene sheets, Phys. Lett. A, 375, 53, 10.1016/j.physleta.2010.10.028

Biot, 1956, Thermoelasticity and irreversible thermo-dynamics, J. Appl. Phys., 27, 240, 10.1063/1.1722351

Brancik, 1999, Programs for fast numerical inversion of laplace transforms in MATLAB language environment

Cao, 2007, Equation of motion of a phonon gas and non-Fourier heat conduction, J. Appl. Phys., 102, 053503, 10.1063/1.2775215

Cattaneo, 1958, A form of heat equation which eliminates the paradox of instantaneous propagation, CR Acad. Sci., 247, 431

Chan, 2008, Dynamics of femtosecond laser-induced melting of silver, Phys. Rev. B, 78, 214107, 10.1103/PhysRevB.78.214107

Chen, 2009, A hybrid Green's function method for the hyperbolic heat conduction problems, Int. J. Heat Mass Transf., 52, 4273, 10.1016/j.ijheatmasstransfer.2009.04.026

Cuenot, 2000, Elastic modulus of Polypyrrole nanotubes, Phys. Rev. Lett., 85, 1690, 10.1103/PhysRevLett.85.1690

Cuenot, 2004, Surface tension effect on the mechanical properties of nanomaterials measured by atomic force microscopy, Phys. Rev. B, 69, 165410, 10.1103/PhysRevB.69.165410

Dong, 2014, Size dependent thermal conductivity of Si nanosystems based on phonon gas dynamics, Phys. E, 56, 256, 10.1016/j.physe.2013.10.006

Duan, 2007, Exact solutions for axisymmetric bending of micro/nanoscale circular plates based on nonlocal plate theory, Nanotechnology, 18, 385704, 10.1088/0957-4484/18/38/385704

Duan, 2007, Calibration of nonlocal scaling effect parameter for free vibration of carbon nanotubes by molecular dynamics, J. Appl. Phys., 101, 10.1063/1.2423140

Eringen, 1974, Theory of nonlocal thermoelasticity, Int. J. Eng. Sci., 12, 1063, 10.1016/0020-7225(74)90033-0

Eringen, 1983, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, J. Appl. Phys., 54, 4703, 10.1063/1.332803

Eringen, 2002

Ezzat, 2011, Magneto-thermoelasticity with thermoelectric properties and fractional derivative heat transfer, Phys. B Condens. Matter, 406, 30, 10.1016/j.physb.2010.10.005

Forest, 2012, Stress gradient continuum theory, Mech. Res. Comm., 40, 16, 10.1016/j.mechrescom.2011.12.002

Green, 1972, Thermoelasticity, J. Elast., 2, 1, 10.1007/BF00045689

Guo, 2010, Thermal wave based on the thermomass model, J. Heat Transf., 132, 072403, 10.1115/1.4000987

Guo, 2005, The size-dependent elastic properties of nanofilms with surface effects, J. Appl. Phys., 98, 074306, 10.1063/1.2071453

Guo, 2015, Phonon hydrodynamics and its applications in nanoscale heat transfer, Phys. Rep., 595, 1, 10.1016/j.physrep.2015.07.003

Guyer, 1966, Solution of the linearized phonon boltzmann equation, Phys. Rev., 148, 765, 10.1103/PhysRev.148.766

Jou, 2010

Jou, 2010, Variational principles for thermal transport in nanosystems with heat slip flow, Phys. Rev. E, 82, 031128, 10.1103/PhysRevE.82.031128

Kovacs, 2015, Generalized heat conduction in heat pulse experiments, Int. J. Heat Mass Transf., 83, 613, 10.1016/j.ijheatmasstransfer.2014.12.045

Kuang, 2009, Variational principles for generalized dynamical theory of thermopiezoelectricity, Acta Mech., 203, 1, 10.1007/s00707-008-0039-1

Lebon, 1995, A non-local thermodynamic analysis of second sound propagation in crystalline dielectrics, J. Phys. Condens. Matter, 7, 1461, 10.1088/0953-8984/7/7/025

Lebon, 2011, An extended thermodynamic model of transient heat conduction at sub-continuum scales, Proc. R. Soc. A, 467, 3241, 10.1098/rspa.2011.0087

Lebon, 2012, Beyond the Fourier heat conduction law and the thermal no-slip boundary condition, Phys. Lett. A, 376, 2842, 10.1016/j.physleta.2012.09.034

Lim, 2015, A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation, J. Mech. Phys. Solids, 78, 298, 10.1016/j.jmps.2015.02.001

Lord, 1967, A generalized dynamical theory of thermoelasticity, J. Mech. Phys. Solids, 15, 299, 10.1016/0022-5096(67)90024-5

Ma, 2012, Size-dependent thermal conductivity in nanosystems based on non-Fourier heat transfer, Appl. Phys. Lett., 101, 211905, 10.1063/1.4767337

Polizzotto, 2001, Nonlocal elasticity and related variational principles, Int. J. Solids Struct., 38, 7359, 10.1016/S0020-7683(01)00039-7

Polizzotto, 2003, Unified thermodynamic framework for nonlocal/gradient continuum theories, Eur. J. Mech. A Solids, 22, 651, 10.1016/S0997-7538(03)00075-5

Polizzotto, 2014, Stress gradient versus strain gradient constitutive models within elasticity, Int. J. Solids Struct., 51, 1809, 10.1016/j.ijsolstr.2014.01.021

Polizzotto, 2015, A unifying variational framework for stress gradient and strain gradient elasticity theories, Eur. J. Mech. A Solids, 49, 430, 10.1016/j.euromechsol.2014.08.013

Polizzotto, 2016, Variational formulations and extra boundary conditions within stress gradient elasticity with extensiuons to beam and plate models, Int. J. Solids Struct., 80, 415, 10.1016/j.ijsolstr.2015.09.015

Reddy, 2007, Nonlocal theories for bending, buckling and vibration of beams, Int. J. Eng. Sci., 45, 288, 10.1016/j.ijengsci.2007.04.004

Salvadori, 2003, Measurement of the elastic modulus of nanostructured gold and platinum thin films, Phys. Rev. B, 67, 153404, 10.1103/PhysRevB.67.153404

Sellitto, 2010, Second law of thermodynamics and phonon-boundary conditions in nanowires, J. Appl. Phys., 107, 064302, 10.1063/1.3309477

Shen, 2013, Prediction of nonlinear vibration of bilayer graphene sheets in thermal environments via molecular dynamics simulations and nonlocal elasticity, Comput. Methods Appl. Mech. Eng., 267, 458, 10.1016/j.cma.2013.10.002

Sherief, 2010, Fractional order theory of thermoelasticity, Int. J. Solids Struct., 47, 269, 10.1016/j.ijsolstr.2009.09.034

Soboley, 1994, Equations of transfer in non-local media, Int. J. Heat Mass Transf., 37, 2175, 10.1016/0017-9310(94)90319-0

Tzou, 1996

Tzou, 2010, Nonlocal behavior in thermal lagging, Int. J. Therm. Sci., 49, 1133, 10.1016/j.ijthermalsci.2010.01.022

Vernotte, 1958, Paradoxes in the continuous theory of the heat conduction, CR Acad. Sci., 246, 3154

Wang, 2006, Buckling analysis of micro-and nano-rods/tubes based on nonlocal Timoshenko beam theory, J. Phys. D Appl. Phys., 39, 3904, 10.1088/0022-3727/39/17/029

Wang, 2014, A generalized theory of thermoelasticity based on thermomass and its uniqueness theorem, Acta Mech., 225, 797, 10.1007/s00707-013-1001-4

Yang, 2002, Couple stress based strain gradient theory for elasticity, Int. J. Solids Struct., 39, 2731, 10.1016/S0020-7683(02)00152-X

Yu, 2014, A novel generalized thermoelasticity model based on memory-dependent derivative, Int. J. Eng. Sci., 81, 123, 10.1016/j.ijengsci.2014.04.014

Yu, 2016, The dilemma of hyperbolic heat conduction and its settlement by incorporating spatially nonlocal effect at nanoscale, Phys. Lett. A, 380, 255, 10.1016/j.physleta.2015.09.030

Yu, 2013, Fractional order generalized electro-magneto-thermo-elasticity, Eur. J. Mech. A Solids, 42, 188, 10.1016/j.euromechsol.2013.05.006

Yu, 2015, Size-dependent generalized thermoelasticity using Eringen's nonlocal model, Eur. J. Mech. A Solids, 51, 96, 10.1016/j.euromechsol.2014.12.005

Youssef, 2010, Theory of fractional order generalized thermoelasticity, J. Heat Transf., 132, 061301, 10.1115/1.4000705