General Theory of Mechanical Material Behaviour

  • Peter Haupt
Part of the Advanced Texts in Physics book series (ADTP)


The theory of material behaviour (material theory) is a division of continuum mechanics. The aim of the material theory is to provide general principles and systematic methods for constructing mathematical models suitably representing the individual properties of material bodies. The modelling of material behaviour can be realised on three levels: constitutive equations, material symmetry properties and conditions of kinematic constraint.


Constitutive Equation Material Behaviour Internal Variable Reference Configuration Material Body 
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  1. 1.
    Truesdell & Noll [1965], Sect. 14; Leigh [1968], pp. 139. Cf. also Truesdell & Toupin [1960], Sect. 293.Google Scholar
  2. 2.
    See Müller [1976], eq. (4.7).Google Scholar
  3. 3.
    Truesdell & Toupin [1960], pp. 700.Google Scholar
  4. 4.
    Truesdell & Toupin [1960], pp. 704; Truesdell & Noll [1965], p. 359.Google Scholar
  5. 5.
    Truesdell & Noll [1965], Sect. 20.Google Scholar
  6. 6.
    Noll [1958]. An improved formulation of the general theory is found in Noll [1972].Google Scholar
  7. 7.
    Truesdell & Noll [1965], Sect. 26.Google Scholar
  8. 9.
    Noll [1958]; Truesdell & Noll [1965], Sect. 29.Google Scholar
  9. 10.
    However, a kinetic theory is capable of suggesting observer-invariant constitutive relations. This was shown by Müller [1976], p. 124. A theoretical investigation of frame-dependent constitutive relations is to be found in Muschik [1998a]. A physically interesting application of observer-invariant constitutive relations is provided in Sadiki & Hutter [1996]. A further example is mentioned in Balke [1998].Google Scholar
  10. 11.
    In this sense, two formulations of material frame-indifference are to be found in Leigh [1968], pp. 143. See also Bertram & Svendson [1997].Google Scholar
  11. 12.
    The presentation throughout this section follows Truesdell & Noll [1965], pp. 76.Google Scholar
  12. 13.
    Truesdell & Noll [1965], Sect. 32, 33.Google Scholar
  13. 14.
    Brauer [1965], Noll [1965].Google Scholar
  14. 15.
    Truesdell & Noll [1965], Sect. 30. A thermomechanical theory is found in Green et al. [1970]. See Bertram & Haupt [1976].Google Scholar
  15. 16.
    See, for example, Lockett [1972], p. 65.Google Scholar
  16. 17.
    Coleman & Gurtin [1967]; Lubliner [1973]. A comprehensive representation of the theory of internal variables is found in Maugin & Mushik [1994]. Cf. Maugin [1990].Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Peter Haupt
    • 1
  1. 1.Institute of MechanicsUniversity of KasselKasselGermany

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