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Continuum Mechanics and Thermodynamics

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14-06-2021 | Review Article

Relative Lagrangian formulation in thermo-viscoelastic solid bodies

Authors: Marcello Goulart Teixeira, Gabriel Thomaz Aquino Pereira, I-Shih Liu

Published in: Continuum Mechanics and Thermodynamics | Issue 6/2021

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

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

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

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)CrossRef

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

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)MathSciNetCrossRef

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)ADSCrossRef

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)

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

Title: Relative Lagrangian formulation in thermo-viscoelastic solid bodies
Authors: Marcello Goulart Teixeira
Gabriel Thomaz Aquino Pereira
I-Shih Liu
Publication date: 14-06-2021
Publisher: Springer Berlin Heidelberg
Published in: Continuum Mechanics and Thermodynamics / Issue 6/2021
Print ISSN: 0935-1175
Electronic ISSN: 1432-0959
DOI: https://doi.org/10.1007/s00161-021-01028-w

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