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Basics of Thermomechanics and Inelasticity

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Computational Geotechnics

Part of the book series: SpringerBriefs in Energy ((BRIESCMES))

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Abstract

Rock salt can undergo large inelastic deformations over extended periods of time. Many analyses, however, refer to time intervals and mechanical loads that cause deformations for which the small-strain assumption remains valid. Here, we restrict ourselves to such small-strain settings and postpone analyses under finite deformations to a follow-up contribution (compare also Fig. 2.1).

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Notes

  1. 1.

    https://doxygen.opengeosys.org/.

  2. 2.

    Other such coupling effects like heat of dissipation, thermoelastic or entropic effects are neglected here.

References

  • Bathe K (2014) Finite element procedures, 2nd edn. Klaus-Jürgen Bathe, Watertown

    MATH  Google Scholar 

  • Böttcher N, Görke U-J, Kolditz O, Nagel T (2017) Thermo-mechanical investigation of salt caverns for short-term hydrogen storage. Environ Earth Sci 76(3):98

    Article  Google Scholar 

  • de Borst R, Heeres OM (2002) A unified approach to the implicit integration of standard, non-standard and viscous plasticity models. Int J Numer Anal Methods Geomech 26(11):1059–1070

    Google Scholar 

  • Du C, Yang C, Yao Y, Li Z, Chen J (2012) Mechanical behaviour of deep rock salt under the operational conditions of gas storage. Int J Earth Sci Eng 5(6):1670–1676

    Google Scholar 

  • Forest S, Lorentz E et al (2004) Localization phenomena and regularization methods. Local approach to fracture. Les Presses de l’Ecole des Mines, Paris, pp 311–371

    Google Scholar 

  • Görke U-J, Günther H, Nagel T, Wimmer M (2010) A large strain material model for soft tissues with functionally graded properties. J Biomech Eng 132(7):074502

    Article  Google Scholar 

  • Görke U-J, Kaiser S, Bucher A, Kreißig R (2012a) A consistent mixed finite element formulation for hydro-mechanical processes in saturated porous media at large strains based on a generalized material description. Eur J Mech A Solids 32:88–102

    Google Scholar 

  • Haupt P (2002) Continuum mechanics and theory of materials. Springer, New York

    Book  MATH  Google Scholar 

  • Heeres OM, Suiker AS, de Borst R (2002) A comparison between the Perzyna viscoplastic model and the consistency viscoplastic model. Eur J Mech A Solids 21(1):1–12

    Google Scholar 

  • Heusermann S, Lux K-H, Rokahr R (1983) Entwicklung mathematisch-mechanischer Modelle zur Beschreibung des Stoffverhaltens von Salzgestein in Abhängigkeit von der Zeit und der Temperatur auf der Grundlage von Laborversuchen mit begleitenden kontinuumsmechanischen Berechnungen nach der Methode der finiten Elemente. Fachinformationszentrum Energie, Physik, Mathematik, Karlsruhe

    Google Scholar 

  • Heusermann S, Rolfs O, Schmidt U (2003) Nonlinear finite-element analysis of solution mined storage caverns in rock salt using the LUBBY2 constitutive model. Comput Struct 81(8–11):629–638; K.J Bathe 60th Anniversary Issue

    Google Scholar 

  • Holzapfel GA (2000) Nonlinear solid mechanics: a continuum approach for engineering. Wiley, New York

    MATH  Google Scholar 

  • Hunsche U, Schulze O (1994) Das Kriechverhalten von Steinsalz. Kali und Steinsalz 11(8/9): 238–255

    Google Scholar 

  • Hutter K, Jöhnk K (2004) Continuum methods of physical modeling: continuum mechanics, dimensional analysis, turbulence. Springer, Berlin

    Book  MATH  Google Scholar 

  • Itskov M (2009) Tensor algebra and tensor analysis for engineers: with applications to continuum mechanics, 2nd edn. Springer, Dordrecht

    Book  MATH  Google Scholar 

  • Jeremic B (2001) Line search techniques for elasto-plastic finite element computations in geomechanics. Commun Numer Methods Eng 17(2):115–126

    Article  MATH  Google Scholar 

  • Kolditz O, Görke U-J, Shao H, Wang W (eds) (2012) Thermo-hydro-mechanical-chemical processes in porous media. Lecture notes in computational science and engineering. Springer, Berlin

    Google Scholar 

  • Kolditz O, Shao H, Wang W, Bauer S (eds) (2014) Thermo-hydro-mechanical-chemical processes in fractured porous media: modelling and benchmarking. Closed form solutions. Terrestrial environmental sciences. Springer, Cham

    Google Scholar 

  • Kolditz O, Görke U-J, Shao H, Wang W, Bauer S (eds) (2016) Thermo-hydro-mechanical-chemical processes in fractured porous media: modelling and benchmarking. Benchmarking initiatives. Terrestrial environmental sciences. Springer, Cham

    Google Scholar 

  • Lewis RW, Schrefler BA (1998) The finite element method in the static and dynamic deformation and consolidation of porous media, 2nd edn. Wiley, Chichester

    MATH  Google Scholar 

  • Markert B (2013) A survey of selected coupled multifield problems in computational mechanics. J Coupled Syst Multiscale Dyn 1(1):22–48

    Article  Google Scholar 

  • Mehrabadi MM, Cowin SC (1990) Eigentensors of linear anisotropic elastic materials. Q J Mech Appl Math 43(1):15–41.

    Article  MathSciNet  MATH  Google Scholar 

  • Minkley W, Mühlbauer J (2007) Constitutive models to describe the mechanical behavior of salt rocks and the imbedded weakness planes. In: Wallner M, Lux K, Minkley W, Hardy H (eds) The mechanical behaviour of salt – understanding of THMC processes in salt: 6th conference (SaltMech6), Hannover, Germany, pp 119–127

    Google Scholar 

  • Minkley W, Menzel W, Konietzky H, te Kamp L (2001) A visco-elasto-plastic softening model and its application for solving static and dynamic stability problems in potash mining. In: Billaux D et al (ed) FLAC and numerical modeling in geomechanics – 2001 (Proceedings of the 2nd international FLAC conference, Lyon, France), pp 27–27

    Google Scholar 

  • Nagel T, Görke U-J, Moerman KM, Kolditz O (2016) On advantages of the Kelvin mapping in finite element implementations of deformation processes. Environ Earth Sci 75(11):1–11

    Article  Google Scholar 

  • Nagel T, Minkley W, Böttcher N, Naumov D, Görke U-J, Kolditz O (2017) Implicit numerical integration and consistent linearization of inelastic constitutive models of rock salt. Comput Struct 182:87–103

    Article  Google Scholar 

  • Niazi M, Wisselink H, Meinders T (2013) Viscoplastic regularization of local damage models: revisited. Comput Mech 51(2):203–216

    Article  Google Scholar 

  • Seifert T, Schmidt I (2008) Line-search methods in general return mapping algorithms with application to porous plasticity. Int J Numer Methods Eng 73(10):1468–1495

    Article  MathSciNet  MATH  Google Scholar 

  • Simo JC, Hughes TJR (1998) Objective integration algorithms for rate formulations of elastoplasticity. In: Computational inelasticity. Interdisciplinary applied mathematics, vol. 7. Springer, New York, pp 276–299

    Google Scholar 

  • Wang W, Sluys L, De Borst R (1997) Viscoplasticity for instabilities due to strain softening and strain-rate softening. Int J Numer Methods Eng 40(20):3839–3864

    Google Scholar 

  • Zienkiewicz OC, Taylor RL, Zhu JZ (2005–2006) The finite element method set, 6th edn. Elsevier Butterworth-Heinemann, Oxford

    Google Scholar 

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Nagel, T., Böttcher, N., Görke, UJ., Kolditz, O. (2017). Basics of Thermomechanics and Inelasticity. In: Computational Geotechnics. SpringerBriefs in Energy(). Springer, Cham. https://doi.org/10.1007/978-3-319-56962-8_2

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  • DOI: https://doi.org/10.1007/978-3-319-56962-8_2

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