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Coleman–Noll Procedure for Classical and Generalized Continuum Theories

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Encyclopedia of Continuum Mechanics

Synonyms

Constitutive equations; Entropy principle; Micromorphic theory; Strain gradient theory; Theory of materials; Theory of microforces

Definitions

Based on the second law of thermodynamics (entropy principle), the Coleman-Noll procedure provides a framework for formulating constitutive equations of simple materials. For the latter, the constitutive equations for the stress depend on the strain, as the objective part as the first gradient of the displacement, and on temperature. In generalized theories of continuum mechanics, the constitutive equations incorporate further gradient terms.

The Coleman-Noll Procedure

Within the continuum theory of thermomechanics, a set of balances are formulated (balances of energy, entropy, mass, linear, and angular momentum) which are considered to hold independent of the material under consideration. The behavior of a particular material is described by additional constitutive equations. Coleman and Noll (1963) proposed a procedure which combines...

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References

  • Coleman BD, Noll W (1963) The thermodynamics of elastic materials with heat conduction and viscosity. Arch Ration Mech Anal 13(1):167–178

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  • Eringen AC (1980) Mechanics of continua, 2nd edn. Wiley, New York/London/Sydney

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  • Truesdell C, Noll W (2004) The non-linear field theories of mechanics, 3rd edn. Springer, Berlin/Heidelberg

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Author information

Authors and Affiliations

  1. Institute of Mechanics and Fluid Dynamics, TU Bergakademie Freiberg, 09596, Lampadiusstr. 4, Freiberg, Germany

    Geralf Hütter

Authors
  1. Geralf Hütter
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Correspondence to Geralf Hütter .

Editor information

Editors and Affiliations

  1. Institut für Mechanik, Otto-von-Guericke-Universität Institut für Mechanik, Magdeburg, Germany

    Holm Altenbach

  2. Griffith University (Gold Coast Campus), Griffith School of Engineering Griffith University (Gold Coast Campus), Southport, Queensland, Australia

    Andreas Öchsner

Section Editor information

  1. Department of Theoretical Mechanics, Institute of Applied Mathematics and Mechanics, Peter the Great St. Petersburg Polytechnic University, Polytechnicheskaya 29, 195251, St. Petersburg, Russia

    Elena Ivanova

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Hütter, G. (2018). Coleman–Noll Procedure for Classical and Generalized Continuum Theories. In: Altenbach, H., Öchsner, A. (eds) Encyclopedia of Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53605-6_57-1

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  • DOI: https://doi.org/10.1007/978-3-662-53605-6_57-1

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-53605-6

  • Online ISBN: 978-3-662-53605-6

  • eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering

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