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Relative Lagrangian formulation in thermo-viscoelastic solid bodies

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Abstract

A model to a coupled thermal-viscoelastic finite deformation problem is presented. The nonlinearities are solved using the successive linear approximation method. This method uses the relative Lagrangian formulation and the idea of the superposed large deformation by small deformations. Furthermore, the constitutive equations are calculated at each state, with the reference configuration updated for each time step. After the problem is linearized, the finite element method is used. To exemplify the model a simulation of an oil well closure is presented.

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References

  1. Belytschko, T., Liu, W.K., Moran, B.: Nonlinear Finite Elements for Continua and Structures. Wiley, Chichester (2000)

    MATH  Google Scholar 

  2. Liu, I.-S.: Continuum Mechanics. Springer, Berlin, Heidelberg (2002)

    Book  Google Scholar 

  3. Liu, I.-S.: Entropy flux relation for viscoelastic bodies. J. Elasticity 90, 259–270 (2008)

    Article  MathSciNet  Google Scholar 

  4. Liu, I.-S., Cipolatti, R.A., Rincon, M.A.: Successive linear approximation for boundary value problems of nonlinear elasticity in relative-descriptional formulation. Int. J. Eng. Sci. 49, 635–645 (2011)

    Article  Google Scholar 

  5. Liu, I.-S.: Successive linear approximation for finite elasticity. Comp. Appl. Math. 29(3), 465–478 (2010)

    Article  MathSciNet  Google Scholar 

  6. Liu, I.-S., Cipolatti, R.A., Rincon, M.A., Palermo, L.A.: Successive linear approximation for large deformation—instability of salt migration. J. Elast. 114, 19–39 (2014)

    Article  MathSciNet  Google Scholar 

  7. Mazariegos, R.A., Andrews, M.J., Russel, J.E.: Modeling the evolution of salt structures using nonlinear rocksalt flow laws. Tectonophysics 256, 129–143 (1996)

    Article  ADS  Google Scholar 

  8. Teixeira, M., Liu, I.S., Rincon, M.A., Cipolatti, R.A., Palermo, L.A.: The influence of temperature on the formation of salt domes. Int. J. Model. Simul. Petrol. Ind. 8(2), 35–41 (2014)

    Google Scholar 

  9. Truesdell, C., Noll, W.: The Non-Linear Field Theories of Mechanics, 3rd edn. Springer, Berlin (2004)

    Book  Google Scholar 

Download references

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Authors and Affiliations

  1. Federal University of Rio de Janeiro, Rio de Janeiro, Brazil

    Marcello Goulart Teixeira & Gabriel Thomaz Aquino Pereira

  2. Intitute of Mathematics, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil

    I-Shih Liu

Authors
  1. Marcello Goulart Teixeira
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  2. Gabriel Thomaz Aquino Pereira
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  3. I-Shih Liu
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Corresponding author

Correspondence to Marcello Goulart Teixeira.

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Communicated by Andreas Öchsner.

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Teixeira, M.G., Pereira, G.T.A. & Liu, IS. Relative Lagrangian formulation in thermo-viscoelastic solid bodies. Continuum Mech. Thermodyn. 33, 2263–2277 (2021). https://doi.org/10.1007/s00161-021-01028-w

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  • DOI: https://doi.org/10.1007/s00161-021-01028-w

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