, Volume 53, Issue 10, pp 2543–2554 | Cite as

A modified Green–Lindsay thermoelasticity with strain rate to eliminate the discontinuity

  • Y. Jun Yu
  • Zhang-Na Xue
  • Xiao-Geng Tian


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 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.


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Authors and Affiliations

  1. 1.Department of Engineering Mechanics, School of Mechanics, Civil Engineering and ArchitectureNorthwestern Polytechnical UniversityXi’anPeople’s Republic of China
  2. 2.State Key Laboratory for Strength and Vibration of Mechanical StructureXi’an Jiaotong UniversityXi’anPeople’s Republic of China

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