Size-dependent thermoelasticity of a finite bi-layered nanoscale plate based on nonlocal dual-phase-lag heat conduction and Eringen's nonlocal elasticity

doi:10.1007/s10483-021-2692-5

Abstract

Abstract: The size effects on heat conduction and elastic deformation are becoming significant along with the miniaturization of the device and wide application of ultrafast lasers. In this work, to better describe the transient responses of nanostructures, a size-dependent thermoelastic model is established based on nonlocal dual-phase-lag (N-DPL) heat conduction and Eringen's nonlocal elasticity, which is applied to the one-dimensional analysis of a finite bi-layered nanoscale plate under a sudden thermal shock. In the numerical part, a semi-analytical solution is obtained by using the Laplace transform method, upon which the effects of size-dependent characteristic lengths and material properties of each layer on the transient responses are discussed systematically. The results show that the introduction of the elastic nonlocal parameter of Medium 1 reduces the displacement and compressive stress, while the thermal nonlocal parameter of Medium 1 increases the deformation and compressive stress. These findings may be beneficial to the design of nano-sized and multi-layered devices.

Key words: thermoelasticity, size effect, multi-layered nanostructure

2010 MSC Number:

35L35

Zhangna XUE, Gongqi CAO, Jianlin LIU. Size-dependent thermoelasticity of a finite bi-layered nanoscale plate based on nonlocal dual-phase-lag heat conduction and Eringen's nonlocal elasticity. Applied Mathematics and Mechanics (English Edition), 2021, 42(1): 1-16.

TrendMD

References

[1] EDELSTEIN, A. S. and CAMMARATA, R. C. Nanomaterials:Synthesis, Properties and Applications, Institute of Physics Publishing, Bristol (1996)
[2] HAMID, M. S., MARYAM, K., and MOHAMADREZA, A. Modified continuum model for stability analysis of asymmetric FGM double-sided NEMS:corrections due to finite conductivity, surface energy and nonlocal effect. Composites Part B, 83, 117-133(2015)
[3] KAMBALI, P. N., NIKHIL, V. S., and PANDEY, A. K. Surface and nonlocal effects on response of linear and nonlinear NEMS devices. Applied Mathematical Modelling, 43, 252-267(2017)
[4] GUO, J. G. and ZHAO, Y. P. The size-dependent elastic properties of nanofilms with surface effects. Journal of Applied Physics, 98(7), 074306(2005)
[5] LI, X. F., ZHANG, H., and LEE, K. Y. Dependence of Young's modulus of nanowires on surface effect. International Journal of Mechanical Sciences, 81, 120-125(2014)
[6] SOBOLEY, S. L. Equations of transfer in non-local media. International Journal of Heat and Mass Transfer, 37(14), 2175-2182(1994)
[7] CHAN, W. L., AVERBACK, R. S., CAHILL, D. G., and LAGOUTCHEV, A. Dynamics of femtosecond laser-induced melting of silver. Physical Review B, 78, 214107(2008)
[8] XU, M. T., GUO, J. F., WANG, L. Q., and CHENG, L. Thermal wave interference as the origin of the overshooting phenomenon in dual-phase-lagging heat conduction. International Journal of Thermal Sciences, 50(5), 825-830(2011)
[9] JOSEPH, D. D. and PREZIOSI, L. Heat waves. Reviews of Modern Physics, 61, 41-73(1989)
[10] CHESTER, M. Second sound in solids. Physical Review, 131, 2013-2015(1963)
[11] CATTANEO, C. A form of heat conduction equation which eliminates the paradox of instantaneous propagation. Compte Rendus, 247(4), 431-433(1958)
[12] VERNOTTE, P. Paradoxes in the continuous theory of the heat conduction. Compte Rendus, 246, 3154-3155(1958)
[13] TZOU, D. Y. A unified field approach for heat conduction from macro-to micro-scales. Journal of Heat Transfer-Transactions of the ASME, 117(1), 8-16(1995)
[14] TZOU, D. Y. Experimental support for the lagging behavior in heat propagation. Journal of Thermophysics and Heat Transfer, 9(4), 686-693(1995)
[15] TZOU, D. Y. and GUO, Z. Y. Nonlocal behavior in thermal lagging. International Journal of Thermal Sciences, 49, 1133-1137(2010)
[16] TZOU, D. Y. Nonlocal behavior in phonon transport. International Journal of Heat and Mass Transfer, 54, 475-481(2011)
[17] MARANGANTI, R. and SHARMA, P. Length scales at which classical elasticity breaks down for various materials. Physical Review Letters, 98(19), 195504-1-4(2007)
[18] FARAJI-OSKOUIE, M., NOROUZZADEH, A., ANSARI, R., and ROUHI, H. Bending of small-scale Timoshenko beams based on the integral/differential nonlocal-micropolar elasticity theory:a finite element approach. Applied Mathematics and Mechanics (English Edition), 40(6), 767-782(2019) https://doi.org/10.1007/s10483-019-2491-9
[19] AIFANTIS, E. Strain gradient interpretation of size effects. International Journal of Fracture, 95, 299-314(1999)
[20] SAHMANI, S. and FATTAHI, A. M. Small scale effects on buckling and postbuckling behaviors of axially loaded FGM nanoshells based on nonlocal strain gradient elasticity theory. Applied Mathematics and Mechanics (English Edition), 39(4), 561-580(2018) https://doi.org/10.1007/s10483-018-2321-8
[21] HADJESFANDIARI, A. R. and DARGUSH, G. F. Couple stress theory for solids. International Journal of Solids and Structures, 48, 2496-2510(2011)
[22] YANG, F., CHONG, A., LAM, D., and TONG, P. Couple stress based strain gradient theory for elasticity. International Journal of Solids and Structures, 39, 2731-2743(2002)
[23] ERINGEN, A. C. Nonlocal Continuum Field Theories, Springer-Verlag, New York (2002)
[24] POLIZZOTTO, C. Stress gradient versus strain gradient constitutive models within elasticity. International Journal of Solids and Structures, 51(9), 1809-1818(2014)
[25] TAUPIN, V., GBEMOU, K., FRESSENGEAS, C., and CAPOLUNGO, L. Nonlocal elasticity tensors in dislocation and disclination cores. Journal of the Mechanics and Physics of Solids, 100, 62-84(2017)
[26] CHANG, D. M. and WANG, B. L. Surface thermal shock cracking of a semi-infinite medium:a nonlocal analysis. Acta Mechanica, 226(12), 4139-4147(2015)
[27] GUVEN, U. General investigation for longitudinal wave propagation under magnetic field effect via nonlocal elasticity. Applied Mathematics and Mechanics (English Edition), 36(10), 1305-1318(2015) https://doi.org/10.1007/s10483-015-1985-9
[28] YU, Y. J., TIAN, X. G., and XIONG, Q. L. Nonlocal thermoelasticity based on nonlocal heat conduction and nonlocal elasticity. European Journal of Mechanics A/Solids, 60, 238-253(2016)
[29] YANG, W. Z. and CHEN, Z. T. Nonlocal dual-phase-lag heat conduction and the associated nonlocal thermal-viscoelastic analysis. International Journal of Heat and Mass Transfer, 156, 119752(2020)
[30] GUYER, R. A. and KRUMHANSL, J. A. Solution of the linearized phonon boltzmann equation. Physical Review, 148, 766-778(1966)
[31] GUYER, R. A. and KRUMHANSL, J. A. Thermal conductivity, second sound, and phonon hydrodynamic phenomena in nonmetallic crystals. Physical Review, 148, 778-788(1966)
[32] CAO, B. Y. and GUO, Z. Y. Equation of motion of a phonon gas and non-Fourier heat conduction. Journal of Applied Physics, 102(5), 053503(2007)
[33] GUO, Z. Y. and CAO, B. Y. A general heat conduction law based on the concept of motion of thermal mass. Acta Physica Sinica, 57(7), 4273-4281(2008)
[34] BRORSON, S. D., FUJIMOTO, J. G., and IPPEN, E. P. Femtosecond electronic heat-transport dynamics in thin gold films. Physical Review Letters, 59, 1962-1965(1987)
[35] BRANCIK, L. Programs for fast numerical inversion of Laplace transforms in MATLAB language environment. Proceedings of the 7th Conference MATLAB' 99, Czech Republic, Prague, 27-39(1999)
[36] XIONG, Q. L. and TIAN, X. G. Modeling of non-equilibrium deformation in a double-layered thin film during ultrashort laser heating. Journal of Thermal Stresses, 36, 387-404(2013)
[37] QIU, T. Q., JUHASZ, T., SUAREZ, C., BRON, W. E., and TIEN, C. L. Femtosecond laser heating of multi-layered metals Ⅱ, experiments. International Journal of Heat and Mass Transfer, 37(17), 2799-2808(1994)
[38] XUE, Z. N., YU, Y. J., and TIAN, X. G. Transient responses of bi-layered structure based on generalized thermoelasticity:interfacial conditions. International Journal of Mechanical Sciences, 99, 179-186(2015)