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Nonlinear response for a general form of thermoelasticity equation in mediums under the effect of temperature-dependent properties and short-pulse heating

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Abstract

This article presents an algorithm for nonlinear transient response of an elastic body with temperature-dependent material features in a large deformation domain exposed to short-pulse heating. The principal target of this paper is employing a general form of thermoelasticity equation, including temperature and strain rate-dependent model using finite strain theory (FST). A thermally nonlinear study is conducted considering a significant gradient of temperature in comparison with the reference temperature. Based on FST, to present the couple equations of energy and motion in the reference medium, the second Piola–Kirchhoff stress and the Lagrangian strain–displacement are used. The obtained equations improved integrating temperature and strain rate-dependent technique and then solved using a Hermitian transfinite element technique. Wave propagation analysis under impulsive thermal loadings is also discussed in this work. Analyzing the phase lag in second sound waves and the impacts of temperature dependency of the medium properties are conducted. Based on the obtained results, the temperature dependency of the materials features has a significant influence on the thermoelastic transient responses. Results illustrate an absorbing feature of wave propagation. In addition, it is observed that there is a remarkable difference in the results obtained from using the general form of thermoelasticity and that of obtained from classic model.

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Abbreviations

\(C_{\text{T}}\) :

Specific heat coefficient

E :

Strain function

h :

Heat convection

K :

Phase lag of the Fourier equation

K″:

Thermal conduction

\({\mathsf{N}}({\mathsf{r}})\) :

Shap function

r :

Length

T :

Temperature

t :

Time

W :

Displacement

\(\alpha_{\text{T}}\) :

Thermal expansion

\(\Delta t\) :

Time increment

\(\rho_{\text{T}}\) :

Density

\(\mu_{\text{T}}\) :

Shear coefficient

\(\lambda_{\text{T}}\) :

Lame coefficient

\(\alpha_{1 \ldots 4}\) :

Relaxation time

\(\zeta ,\psi ,\eta\) :

Temperature dependency coefficient

\(\sigma\) :

Stress

\(\chi\) :

MGL coefficient

References

  1. Shamshuddin MD, Mishra SR, Beg O, et al. Numerical study of heat transfer and viscous flow in a dual rotating extendable disk system with a non-Fourier heat flux model. Heat Transf Asian Res. 2018;48:435–59.

    Article  Google Scholar 

  2. Hashimoto T, Morikawa J, Sawatari C. Relaxation behavior of ultradrawn poly(ethylene) film by temperature wave analysis. J Therm Anal Calorim. 2002;70:693–701.

    Article  CAS  Google Scholar 

  3. Sheikholeslami M, Rezaeianjouybari B, Darzi M, et al. Application of nano-refrigerant for boiling heat transfer enhancement employing an experimental study. Int J Heat Mass Transf. 2019;141:974–80.

    Article  CAS  Google Scholar 

  4. Ski P, Szparaga Ł, Kamasa P, et al. Application of dilatometry with modulated temperature for thermomechanical analysis of anti-wear coating/substrate systems. J Therm Anal Calorim. 2015;120:1609. https://doi.org/10.1007/s10973-015-4552-x.

    Article  CAS  Google Scholar 

  5. Sheikholeslami M, Farshad A, Shafee A, et al. Numerical modeling for nanomaterial behavior in a solar unit analyzing entropy generation. J Taiwan Inst Chem Eng. 2020. https://doi.org/10.1016/j.jtice.2020.06.005.

    Article  Google Scholar 

  6. Abouelregal AE. On Green and Naghdi thermoelasticity model without energy dissipation with higher order time differential and phase-lags. J Appl Comput Mech. 2020;3:445–56.

    Google Scholar 

  7. Sheikholeslami M, Jafaryar M, Shafee A, et al. Acceleration of discharge process of clean energy storage unit with insertion of porous foam considering nanoparticle enhanced paraffin. J Clean Prod. 2020. https://doi.org/10.1016/j.jclepro.2020.121206.

    Article  Google Scholar 

  8. Li Z, Sarafraz MM, Mazinani A, et al. Pool boiling heat transfer to CuO–H2O nanofluid on finned surfaces. Int J Heat Mass Transf. 2020. https://doi.org/10.1016/j.ijheatmasstransfer.2020.119780.

    Article  Google Scholar 

  9. Li Z, Hayat MT, Rashed A, et al. Transient pool boiling and particulate deposition of copper oxide nano-suspensions. Int J Heat Mass Transf. 2020. https://doi.org/10.1016/j.ijheatmasstransfer.2020.119743.

    Article  Google Scholar 

  10. Shishesaz M, Zakipour A, Jafarzadeh A. Magneto-elastic analysis of an annular FGM plate based on classical plate theory using GDQ method. Latin Am J Solids Struct. 2016;13:2736–62.

    Article  Google Scholar 

  11. Othman MIA, Mondal S. Memory-dependent derivative effect on 2D problem of generalized thermoelastic rotating medium with Lord–Shulman model. Indian J Phys. 2019;94:1169–81.

    Article  Google Scholar 

  12. Yueqiua L, Long L, Peijun W, et al. Reflection and refraction of thermoelastic waves at an interface of two couple-stress solids based on Lord–Shulman thermoelastic theory. Appl Math Model. 2018;55:536–50.

    Article  Google Scholar 

  13. Lord HW, Shulman Y. A generalized dynamical theory of thermoelasticity. J Mech Phys Solids. 1967;15:299–309.

    Article  Google Scholar 

  14. Zhang D, Starzewsk MO. Thermoelastic waves in helical strands with Maxwell–Cattaneo heat conduction. Theor Appl Mech Lett. 2019;9:30–307.

    CAS  Google Scholar 

  15. Green AE, Lindsay KA. Thermoelasticity. J Elast. 1972;2:1–7.

    Article  Google Scholar 

  16. Green AE, Naghdi PM. Thermoelasticity without energy dissipation. J Elast. 1993;31:189–208.

    Article  Google Scholar 

  17. Nikolarakis AM, Theotokoglou EE. Transient analysis of a functionally graded ceramic/metal layer considering Lord-Shulman theory. Math Probl Eng. 2018;2018:1–11.

    Article  Google Scholar 

  18. El-Attar SI, Hendy MH, Ezzat MA. On phase-lag Green-Naghdi theory without energy dissipation for electro-thermoelasticity including heat sources. Mech Based Des Struct Mach. 2019. https://doi.org/10.1080/15397734.2019.1610971.

    Article  Google Scholar 

  19. Kiani Y, Eslami MR. Nonlinear generalized thermoelasticity of an isotropic layer based on Lord–Shulman theory. Eur J Mech A Solids. 2017. https://doi.org/10.1016/j.euromechsol.2016.10.004.

    Article  Google Scholar 

  20. Yu YJ, Xue ZN, Tian XG. A modified Green–Lindsay thermoelasticity with strain rate to eliminate the discontinuity. Meccanica. 2018;53:2543–54.

    Article  Google Scholar 

  21. Shivay ON, Mukhopadhyay S. A complete Galerkin’s type approach of finite element for the solution of a problem on modified Green–Lindsay thermoelasticity for a functionally graded hollow disk. Eur J Mech A Solids. 2020. https://doi.org/10.1016/j.euromechsol.2019.103914.

    Article  Google Scholar 

  22. Kumar R, Vohra R, Gorla MG. Variational principle and plane wave propagation in thermoelastic medium with double porosity under Lord–Shulman theory. J Solid Mech. 2017;9:423–33.

    Google Scholar 

  23. Marin M, Craciun EM, Pop N. Some results in Green–Lindsay thermoelasticity of bodies with dipolar structure. Mathematics. 2020. https://doi.org/10.3390/math8040497.

    Article  Google Scholar 

  24. Alshorbagy EA. Temperature effects on the vibration characteristics of a functionally graded thick beam. Ain Shams Eng J. 2013;4:455–64.

    Article  Google Scholar 

  25. Zenkour AM. Refined two-temperature multi-phase-lags theory for thermomechanical response of microbeams using the modified couple stress analysis. Acta Mech. 2018;299:3671–92.

    Article  Google Scholar 

  26. Kumar R, Devi S. Response of thermoelastic functionally graded beam due to ramp type heating in modified couple stress with dual-phase-lag model. Multidiscip Model Mater Struct. 2017;13:471–88.

    Article  Google Scholar 

  27. Sheikholeslami M, Jafaryar M, Abohamzeh E, et al. Energy and entropy evaluation and two-phase simulation of nanoparticles within a solar unit with impose of new turbulator. Sustain Energy Technol Assess. 2020. https://doi.org/10.1016/j.seta.2020.100727.

    Article  Google Scholar 

  28. Manh TD, Salehi F, Shafee A, et al. Role of magnetic force on the transportation of nanopowders including radiation. J Therm Anal Calorim. 2019. https://doi.org/10.1007/s10973-019-09182-9.

    Article  Google Scholar 

  29. Sheikholeslami M, Abohamzeh E, Jafaryar M, et al. CuO nanomaterial two-phase simulation within a tube with enhanced turbulator. Powder Technol. 2020;373:1–13.

    Article  CAS  Google Scholar 

  30. Gupta M, Mukhopadhyay S. A study on generalized thermoelasticity theory based on non-local heat conduction model with dual-phase-lag. J Therm Stress. 2019;42:1123–35.

    Article  Google Scholar 

  31. Privalko VP, Korskanov VV, Privalko EG, et al. Composition-dependent properties of polyethylene/kaolin composites: VI. Thermoelastic behavior in the melt state. J Therm Anal Calorim. 2000;59:509–16.

    Article  CAS  Google Scholar 

  32. Shakeriaski F, Ghodrat M. The nonlinear response of Cattaneo-type thermal loading of a laser pulse on a medium using the generalized thermoelastic model. Theor Appl Mech Lett. 2020. https://doi.org/10.1016/j.taml.2020.01.030.

    Article  Google Scholar 

  33. Morikawa J, Hashimoto T. New technique for Fourier transform thermal analysis. J Therm Anal Calorim. 2001;64:403.

    Article  CAS  Google Scholar 

  34. Biswas S. Modeling of memory-dependent derivatives in orthotropic medium with three-phase-lag model under the effect of magnetic field. Mech Based Des Struct Mach. 2019;47:302–18.

    Article  Google Scholar 

  35. Touloukian YS. Thermophysical properties of high temperature solid materials. New York: McMillan; 1976.

    Google Scholar 

  36. Reddy JN, Chin C. Thermomechanical analysis of functionally graded cylinders and plates. J Therm Stress. 1998. https://doi.org/10.1080/01495739808956165.

    Article  Google Scholar 

  37. Hong K, Wang C, Xu F. Finite-element thermal analysis of flows on moving domains with application to modeling of a hydraulic arresting gear. J Therm Anal Calorim. 2020. https://doi.org/10.1007/s10973-020-09583-1.

    Article  Google Scholar 

  38. Zhao B, Chen H, Gao D, et al. Heat transfer simulation in cavity of twin screw compressor under coupling of clearance leakage-heat by utilizing fuzzy beamlet finite element model. J Therm Anal Calorim. 2020. https://doi.org/10.1007/s10973-020-09531-z.

    Article  PubMed  PubMed Central  Google Scholar 

  39. Mirparizi M, Fotuhi AR. Nonlinear coupled thermo-hyperelasticity analysis of thermal and mechanical wave propagation in a finite domain. Physica A. 2020. https://doi.org/10.1016/j.physa.2019.122755.

    Article  Google Scholar 

  40. Wiebe R, Stanciulescu I. Inconsistent Stability of Newmark’s method in structural dynamics applications. ASME Comput Nonlinear Dyn. 2015;10:051006–8.

    Article  Google Scholar 

  41. Matle S. Elastic wave propagation study in copper poly-grain sample using FEM. Theor Appl Mech Lett. 2017;7:1–5.

    Article  Google Scholar 

  42. Yang X, Liu Y. Picard iterative processes for initial value problems of singular fractional differential equations. Math Ann. 2014. https://doi.org/10.1186/1687-1847-2014-102.

    Article  Google Scholar 

  43. Yavuz S, Malgaca L, Karagülle H. Analysis of active vibration control of multi-degree-of-freedom flexible systems by Newmark method. Simul Model Pract Theory. 2016;69:136–48.

    Article  Google Scholar 

  44. Ting E, Chen H. A unified numerical approach for thermal stress waves. Comput Struct. 1982;15:165–75.

    Article  Google Scholar 

  45. Mirparizi M, Fotuhi M, Shariyat M. Nonlinear coupled thermoelastic analysis of thermal wave propagation in a functionally graded finite solid undergoing finite strain. J Therm Anal Calorim. 2020;139:2309–20.

    Article  CAS  Google Scholar 

  46. Shariyat M, Lavasani SMH, Khaghani M. Nonlinear transient thermal stress and elastic wave propagation analyses of thick temperature-dependent FGM cylinders, using a second-order point-collocation method. Appl Mathemat Modell. 2010;34(4):898–918.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, Shahid Bahonar University of Kerman, Kerman, Iran

    Farshad Shakeriaski

  2. School of Engineering and Information Technology, University of New South Wales Canberra, Canberra, 2610 ACT, Australia

    Maryam Ghodrat

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Shakeriaski, F., Ghodrat, M. Nonlinear response for a general form of thermoelasticity equation in mediums under the effect of temperature-dependent properties and short-pulse heating. J Therm Anal Calorim 147, 843–854 (2022). https://doi.org/10.1007/s10973-020-10290-0

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