Encyclopedia of Continuum Mechanics

Living Edition
| Editors: Holm Altenbach, Andreas Öchsner

Coleman–Noll Procedure for Classical and Generalized Continuum Theories

  • Geralf HütterEmail author
Living reference work entry
DOI: https://doi.org/10.1007/978-3-662-53605-6_57-1



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...

This is a preview of subscription content, log in to check access.


  1. Coleman BD, Noll W (1963) The thermodynamics of elastic materials with heat conduction and viscosity. Arch Ration Mech Anal 13(1):167–178MathSciNetCrossRefzbMATHGoogle Scholar
  2. Eringen AC (1980) Mechanics of continua, 2nd edn. Wiley, New York/London/SydneyzbMATHGoogle Scholar
  3. Truesdell C, Noll W (2004) The non-linear field theories of mechanics, 3rd edn. Springer, Berlin/HeidelbergCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany 2018

Authors and Affiliations

  1. 1.Institute of Mechanics and Fluid DynamicsTU Bergakademie FreibergFreibergGermany

Section editors and affiliations

  • Elena Ivanova
    • 1
  1. 1.Department of Theoretical Mechanics, Institute of Applied Mathematics and MechanicsPeter the Great St. Petersburg Polytechnic UniversitySt. PetersburgRussia