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中文核心期刊
Volume 54 Issue 10
Oct.  2022
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Wu Hua, Zou Shaohua, Xu Chenghui, Yu Yajun, Deng Zichen. Thermodynamic basis and transient response of generalized thermoelasticity. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(10): 2796-2807 doi: 10.6052/0459-1879-22-225
Citation: Wu Hua, Zou Shaohua, Xu Chenghui, Yu Yajun, Deng Zichen. Thermodynamic basis and transient response of generalized thermoelasticity. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(10): 2796-2807 doi: 10.6052/0459-1879-22-225

THERMODYNAMIC BASIS AND TRANSIENT RESPONSE OF GENERALIZED THERMOELASTICITY

doi: 10.6052/0459-1879-22-225
  • Received Date: 2022-05-27
  • Accepted Date: 2022-09-16
  • Available Online: 2022-09-17
  • Publish Date: 2022-10-18
  • The rapid development of micro/nano technology and the wide application of ultrashort pulsed laser technology have put forward an urgent need for generalized heat conduction and thermoelastic coupling theory to describe ultrafast thermal shock at micro/nano scale. Based on extended thermodynamic principle, a generalized thermoelastic coupling theory considering the dual-phase-lagging effect of heat conduction and the rate of higher order heat flux is established. Inspired by Green-Naghdi (GN) generalized heat conduction model, thermal "elastic" and "viscous" element models are proposed, which are similar to the series and parallel models of viscoelastic constitutive relations in the field of mechanics. The Cattanoe-Vernotte (CV), GN, dual-phase-lag (DPL) and Moore-Gibson-Thompson (MGT) heat conduction models were obtained by series and parallel methods. Theoretical derivation further shows that the newly formulated model corresponds to the Burgers model of heat conduction. In these models, the proportional relationship between the relaxation time of each phase lag is also obtained. Laplace transform method is used to study the transient response of one-dimensional structure under thermal shock and moving heat source. The results show that the present model overcomes the paradox of infinite thermal wave velocity. When the boundary thermal shock load is applied, the results obtained by the new model have higher peak and the smallest affected region. And under the effect of moving heat source, the new model can generate a larger peak response. The new model could coupled with the classical elastic theory and built a generalized thermoelasticity. With this theory, the jump of stress at wavefront of thermal wave and elastic wave can be clearly observed. Theoretically, this paper promotes the combination of extended thermodynamics and continuum mechanics, which is of enlightening significance to the study of fundamental theoretical problems far from equilibrium of extreme mechanics. For applications, this work can provide theoretical basis and numerical method for the transient response analysis under the moving heat sources.

     

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  • [1]
    Zhmakin AI. Heat conduction beyond the Fourier law. Technical Physics, 2021, 66(1): 1-22 doi: 10.1134/S1063784221010242
    [2]
    李吉伟, 何天虎. 考虑应变率的广义压电热弹理论及其应用. 力学学报, 2020, 52(5): 1267-1276 (Li Jiwei, He Tianhu. A generalized piezoelectric-thermoelastic theory with strain rate and its application. Chinese Journal of Theoreticaland and Applied Mechanics, 2020, 52(5): 1267-1276 (in Chinese) doi: 10.6052/0459-1879-20-120
    [3]
    李妍, 何天虎, 田晓耕. 超短激光脉冲加热薄板的广义热弹扩散问题. 力学学报, 2020, 52(5): 1255-1266 (Li Yan, He Tianhu, Tian Xiaogeng. A generalized thermoelastic diffusion problem of thin plate heated by the ultrashort laser pulses. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(5): 1255-1266 (in Chinese) doi: 10.6052/0459-1879-20-118
    [4]
    张培, 何天虎. 考虑非局部效应和记忆依赖微分的广义热弹问题. 力学学报, 2018, 50(3): 508-516 (Zhang Pei, He Tianhu. A generalized thermoelastic problem with nonlocal effect and memory-dependent derivative. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(3): 508-516 (in Chinese) doi: 10.6052/0459-1879-18-079
    [5]
    Li SN, Cao BY. Anomalous heat diffusion from fractional Fokker–Planck equation. Applied Mathematics Letters, 2020, 99: 105992 doi: 10.1016/j.aml.2019.07.023
    [6]
    Yu YJ, Deng ZC. New insights on microscale transient thermoelastic responses for metals with electron-lattice coupling mechanism. European Journal of Mechanics-A/Solids, 2020, 80: 103887 doi: 10.1016/j.euromechsol.2019.103887
    [7]
    Cattaneo C. A form of heat equation which eliminates the paradox of instantaneous propagation. Compete Rendus, 1958, 247: 431-433
    [8]
    Vernotte P. Paradoxes in the continuous theory of the heat conduction. Compte Rendus, 1958, 246: 3154-3155
    [9]
    Tzou DY. The generalized lagging response in small-scale and high-rate heating. International Journal of Heat and Mass Transfer, 1995, 38(17): 3231-3240
    [10]
    Green AE, Naghdi PM. On undamped heat waves in an elastic solid. Journal of Thermal Stresses, 1992, 15(2): 253-264
    [11]
    Green AE, Naghdi PM. Thermoelasticity without energy dissipation. Journal of Elasticity, 1993, 31(3): 189-208
    [12]
    Quintanilla RXFN. Instability and non-existence in the nonlinear theory of thermoelasticity without energy dissipation. Continuum Mechanics and Thermodynamics, 2001, 13(2): 121-129
    [13]
    Quintanilla R. Moore−Gibson−Thompson thermoelasticity. Mathematics and Mechanics of Solids, 2019, 24(12): 4020-4031 doi: 10.1177/1081286519862007
    [14]
    Cao BY, Guo ZY. Equation of motion of a phonon gas and non-Fourier heat conduction. Journal of Applied Physics, 2007, 102(5): 053503 doi: 10.1063/1.2775215
    [15]
    Kuang Z. Variational principles for generalized dynamical theory of thermopiezoelectricity. Acta Mechanica, 2009, 203(1-2): 1-11 doi: 10.1007/s00707-008-0039-1
    [16]
    Lord HW, Shulman Y. A generalized dynamical theory of thermoelasticity. Journal of the Mechanics and Physics of Solids, 1967, 15(5): 299-309 doi: 10.1016/0022-5096(67)90024-5
    [17]
    Bazarra N, Fernández JR, Quintanilla R. Lord−Shulman thermoelasticity with microtemperatures. Applied Mathematics & Optimization, 2021, 84(2): 1667-1685
    [18]
    El-Karamany AS, Ezzat MA. On the phase−lag Green–Naghdi thermoelasticity theories. Applied Mathematical Modelling, 2016, 40(9-10): 5643-5659
    [19]
    Alizadeh Hamidi B, Hosseini SA, Hassannejad R, et al. An exact solution on gold microbeam with thermoelastic damping via generalized Green-Naghdi and modified couple stress theories. Journal of Thermal Stresses, 2020, 43(2): 157-174 doi: 10.1080/01495739.2019.1666694
    [20]
    Tzou DY. Experimental support for the lagging behavior in heat propagation. Journal of Thermophysics and Heat Transfer, 1995, 9(4): 686-693
    [21]
    Tzou DY. Macro-to Microscale Heat Transfer: The Lagging Behavior. John Wiley & Sons, 2014: 388-391
    [22]
    Singh B. Wave propagation in dual-phase-lag anisotropic thermoelasticity. Continuum Mechanics and Thermodynamics, 2013, 25(5): 675-683 doi: 10.1007/s00161-012-0261-x
    [23]
    Quintanilla R. Moore-Gibson-Thompson thermoelasticity with two temperatures. Applications in Engineering Science, 2020, 1: 100006 doi: 10.1016/j.apples.2020.100006
    [24]
    Youssef HM. A novel theory of generalized thermoelasticity based on thermomass motion and two-temperature heat conduction. Journal of Thermal Stresses, 2021, 44(2): 133-148 doi: 10.1080/01495739.2020.1838247
    [25]
    Green AE, Lindsay KA. Thermoelasticity. Journal of Elasticity, 1972, 2(1): 1-7 doi: 10.1007/BF00045689
    [26]
    Yu YJ, Xue ZN, Tian XG. A modified Green–Lindsay thermoelasticity with strain rate to eliminate the discontinuity. Meccanica, 2018, 53(10): 2543-2554 doi: 10.1007/s11012-018-0843-1
    [27]
    Marin M, Craciun EM, Pop N. Some results in Green–Lindsay thermoelasticity of bodies with dipolar structure. Mathematics, 2020, 8(4): 497 doi: 10.3390/math8040497
    [28]
    Yu YJ, Zhao LJ. Fractional thermoelasticity revisited with new definitions of fractional derivative. European Journal of Mechanics-A/Solids, 2020, 84: 104043 doi: 10.1016/j.euromechsol.2020.104043
    [29]
    Yu YJ, Deng ZC. Fractional order theory of Cattaneo-type thermoelasticity using new fractional derivatives. Applied Mathematical Modelling, 2020, 87: 731-751 doi: 10.1016/j.apm.2020.06.023
    [30]
    Yu YJ, Deng ZC. Fractional order thermoelasticity for piezoelectric materials. Fractals, 2021, 29(4): 2150082 doi: 10.1142/S0218348X21500821
    [31]
    Yu YJ, Li SS, Deng ZC. Unified theory of 2n + 1 order size-dependent beams: Mathematical difficulty for functionally graded size-effect parameters solved. Applied Mathematical Modelling, 2020, 79: 314-340 doi: 10.1016/j.apm.2019.10.038
    [32]
    Abouelregal AE. A novel model of nonlocal thermoelasticity with time derivatives of higher order. Mathematical Methods in the Applied Sciences, 2020, 43(11): 6746-6760 doi: 10.1002/mma.6416
    [33]
    Yu YJ, Tian XG, Xiong QL. Nonlocal thermoelasticity based on nonlocal heat conduction and nonlocal elasticity. European Journal of Mechanics-A/Solids, 2016, 60: 238-253 doi: 10.1016/j.euromechsol.2016.08.004
    [34]
    Machrafi H, Lebon G. General constitutive equations of heat transport at small length scales and high frequencies with extension to mass and electrical charge transport. Applied Mathematics Letters, 2016, 52: 30-37
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