Relative Lagrangian Formulation of Finite Thermoelasticity
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B. D. Coleman and W. Noll, “The thermodynamics of elastic materials with heat conduction and viscosity,” Arch. Ration. Mech. Anal., vol. 13, pp. 167–178, 1963.
I.-S. Liu, Continuum Mechanics. Berlin: Springer: Berlin Heidelberg, 2002.
C. Truesdell and W. Noll, The Non-Linear Field Theories of Mechanics. Berlin: Springer, 2004.
A. E. Green, R. S. Rivlin, and R. T. Shield, “General theory of small elastic defor-mations superposed on finite deformations,” Arch. Ration. Mech. Anal., vol. 211, pp. 128–154, 1952.
I.-S. Liu, “Successive linear approximation for boundary value problems of nonlinear elasticity in relative-descriptional formulation,” Int. J. Eng Sci., vol. 49, pp. 635–645, 2011.
M. E. Gurtin, E. Fried, and L. Anand, The Mechanics and Thermodynamics of Continua. Cambridge: Cambridge University Press, 2010.
I.-S. Liu, “Entropy flux relation for viscoelastic bodies,” Journal of Elasticity, vol. 90, pp. 259–270, 2008.
I. Müller, “On the entropy inequality,” Arch. Ration. Mech. Anal., vol. 26, pp. 118–141, 1967.
I.-S. Liu, “On entropy flux of transversely isotropic elastic bodies,” Journal of Elas-ticity, vol. 96, pp. 97–104, 2009.
I.-S. Liu, “General theory of small elastic deformations superposed on finite defor-mations,” Arch. Ration. Mech. Anal., vol. 46, pp. 131–148, 1972.
I.-S. Liu, “A note on the mooney–rivlin material model,” Continuum Mech. and Thermody, vol. 24, pp. 583–590, 2011.
I.-S. Liu, R. A. Cipolatti, and M. A. Rincon, “Successive linear approximation for finite elasticity,” Computational and Applied Mathematics, vol. 29, pp. 465–478, 2010.
I.-S. Liu, R. A. Cipolatti, M. A. Rincon, and L. A. Palermo, “Successive linear approximation for large deformation–instability of salt migration,” Journal of Elasticity, vol. 114, pp. 19–39, 2014.
R. A. Cipolatti, I.-S. Liu, and M. A. Rincon, “Mathematical analysis of successive linear approximation for mooney-rivlin material model in finite elasticity,” Journal of Applied Analysis and Computation, vol. 2, pp. 363–379, 2012.
R. A. Cipolatti, I.-S. Liu, L. A. Palermo, M. A. Rincon, and R. M. S. Rosa, “A boundary value problem arising from nonlinear viscoelasticity: mathematical analysis and numerical simulations,” Applied Mathematics and Computation, vol. 335, pp. 237–247, 2018.
R. M. S. Rosa, R. A. Cipolatti, I.-S. Liu, L. A. Palermo, and M. A. Rincon, “On the existence, uniqueness and regularity of solutions of a viscoelastic stokes problem modelling salt rocks,” Applied Mathematics and Optimization, vol. 78, p. 403–456, 2018.
P. Massimi, A. Quarteroni, F. E. Saleri, and G. Scrofani, “Modeling of salt tectonics,” Comput. Methods Appl. Mech. Eng., vol. 197, pp. 281–293, 2007.
C. I. Steefel and G. T. Y. et al., “Reactive transport codes for subsurface environmental simulation,” Computational Geosciences, vol. 19, p. 445–478, 2015.
G. T. Yeh, C. H. Tsai, and I.-S. Liu, A Geo-Mechanics Model for Finite Visco-Elastic Materials (GMECH 1.0): Theoretical Basis and Numerical Approximation. PhD thesis, Graduate Institute of Applied Geology, National Central University, Jhongli, Taoyuan 32001, Taiwan, 2013.
G. T. Yeh and C. H. Tsai, A Three-Dimensional Model of Coupled Fluid Flow,Thermal Transport, Hydrogeochemical Transport, and Geomechanics through Multiple Phase Systems (HYDROGEOCHEM 7.1): Theoretical Basis and Numerical Approximation. PhD thesis, Graduate Institute of Applied Geology, National Central University, Jhongli, Taoyuan 32001, Taiwan, 2015.
C. Colon and M. G. T. et al., “Surface salt in kuqa fold-thrust belt, northwestern china: time-lapse surface deformation and mechanical modelling,” in Proceedings of Fringe 2015 Workshop, vol. 1, European Space Agency, 2015.
DOI: https://doi.org/10.5540/tcam.2021.022.04.00609
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