Probing the mechanism of ultrafast thermoelastic processes is becoming increasingly important with the development of laser-assisted micro/nano machining. Although thermoelastic models containing temperature rate have been historically proposed, the strain rate has not been considered yet. In this work, a generalized thermoelastic model is theoretically established by introducing the strain rate in Green–Lindsay (GL) thermoelastic model with the aid of extended thermodynamics. Numerically, a semi-infinite one-dimensional problem is considered with traction free at one end and subjected to a temperature rise. The problem is solved using the Laplace transform method, and the transient responses, i.e. displacement, temperature and stresses are graphically depicted. Interestingly, it is found that the strain rate may eliminate the discontinuity of the displacement at the elastic and thermal wave front. Also, the present model is compared with Green–Naghdi (GN) models. It is found that the thermal wave speed of the present model is faster than GN model without energy dissipation, and slower than GN model with energy dissipation. In addition, the thermoelastic responses from the present model are the largest. The present model based upon GL model is free of the jump of GL model in the displacement distribution, and is safer in engineering practices than GN model. The present work will benefit the theoretical modeling and numerical prediction of thermoelastic process, especially for those under extreme fast heating.
Green–Lindsay model Relaxation times Strain rate Transient responses Green–Naghdi model
This is a preview of subscription content, log in to check access.
This study was funded by National Key R&D Problem of China (No. 2017YFB1102801), National Natural Science Foundation of China (No. 11572237), and Fundamental Research Funds for the Central Universities (3102017OQD072).
Compliance with ethical standards
Conflict of interest
The authors declare that they have no conflict of interest.
Afrin N, Zhang Y, Chen JK (2014) Dual-phase lag behavior of a gas-saturated porous-medium heated by a short-pulsed laser. Int J Therm Sci 75:21–27CrossRefGoogle Scholar
Chen JK, Tzou DY, Beraun JE (2006) A semiclassical two-temperature model for ultrafast laser heating. Int J Heat Mass Transf 49(1–2):307–316CrossRefzbMATHGoogle Scholar
Hosoya N, Kajiwara I, Inoue T, Umenai K (2014) Non-contact acoustic tests based on nanosecond laser ablation: generation of a pulse sound source with a small amplitude. J Sound Vib 333(18):4254–4264ADSCrossRefGoogle Scholar
Abd-alla AN, Giorgio I, Galantucci L, Hamdan AM, Del Vescovo D (2016) Wave reflection at a free interface in an anisotropic pyroelectric medium with nonclassical thermoelasticity. Continuum Mech Thermodyn 28(1–2):67–84ADSMathSciNetCrossRefzbMATHGoogle Scholar
Partap G, Chugh N (2017) Thermoelastic damping in microstretch thermoelastic rectangular Plate. Microsyst Technol 23(12):5875–5886CrossRefGoogle Scholar
Hosseini SM (2017) Shock-induced nonlocal coupled thermoelasticity analysis (with energy dissipation) in a MEMS/NEMS beam resonator based on Green–Naghdi theory: a meshless implementation considering small scale effects. J Therm Stresses 40(9):1134–1151CrossRefGoogle Scholar
Hosseini SM (2018) Analytical solution for nonlocal coupled thermoelasticity analysis in a heat-affected MEMS/NEMS beam resonator based on Green–Naghdi theory. Appl Math Model 57:21–36MathSciNetCrossRefGoogle Scholar
Liu S, Sun Y, Ma J, Yang J (2018) Theoretical analysis of thermoelastic damping in bilayered circular plate resonators with two-dimensional heat conduction. Int J Mech Sci 135:114–123CrossRefGoogle Scholar
Peshkov V (1944) Second sound in helium II. J. Phys. 8:381–382Google Scholar
Xiao R, Sun H, Chen W (2016) An equivalence between generalized Maxwell model and fractional Zener model. Mech Mater 100:148–153CrossRefGoogle Scholar
Brancik L (1999) Programs for fast numerical inversion of Laplace transforms in MATLAB language environment. In: Proceedings of the 7th conference MATLAB’99, Czech Republic, Prague, pp 27–39Google Scholar
Yu YJ, Tian X-G, Xiong Q-L (2016) Nonlocal thermoelasticity based on nonlocal heat conduction and nonlocal elasticity. Eur J Mech A Solids 60:238–253MathSciNetCrossRefGoogle Scholar
Yu YJ et al (2016) The dilemma of hyperbolic heat conduction and its settlement by incorporating spatially nonlocal effect at nanoscale. Phys Lett A 380(1–2):255–261ADSCrossRefGoogle Scholar
Othman MIA, Zidan MEM, Hilal MIM (2015) The effect of initial stress on thermoelastic rotation medium with voids due to laser pulse heating with energy dissipation. J Therm Stresses 38(8):835–853CrossRefGoogle Scholar
Othman MIA, Zidan MEM, Hilal MIM (2014) Effect of magnetic field on a rotating thermoelastic medium with voids under thermal loading due to laser pulse with energy dissipation. Can J Phys 92(11):1359–1371ADSCrossRefGoogle Scholar