Mechanics of Time-Dependent Materials

, Volume 12, Issue 2, pp 95–127 | Cite as

On the development and parameter identification of Schapery-type constitutive theories

  • Martin Lévesque
  • Katell Derrien
  • Didier Baptiste
  • Michael D. Gilchrist


Schapery-type constitutive theories for nonlinearly viscoelastic materials have been used extensively within the literature. Most of the applications are 1D but some 3D applications can be found. Most of the 3D applications are thermodynamically inconsistent extensions of the 1D constitutive theory. This paper shows and illustrates how thermodynamically admissible Schapery-type constitutive theories can be generated. In addition, a new 3D constitutive theory is introduced. A new data reduction procedure for obtaining the material parameters, which does not rely on creep–recovery tests, is introduced. The procedure leads to material parameters that are thermodynamically admissible and considers the whole mechanical response rather than particular values, as in most data reduction procedures. This procedure is tested on a thermoplastic material and the constitutive theory thus obtained is compared with data from other load histories.


Nonlinear viscoelasticity Schapery Parameter identification Thermodynamics 


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Copyright information

© Springer Science+Business Media, B. V. 2008

Authors and Affiliations

  • Martin Lévesque
    • 1
  • Katell Derrien
    • 2
  • Didier Baptiste
    • 2
  • Michael D. Gilchrist
    • 3
  1. 1.CREPEC, Département de Génie MécaniqueÉcole Polytechnique de MontréalMontréalCanada
  2. 2.Laboratoire d’Ingénierie des MatériauxUMR8006 CNRS, Ecole. Nat. Sup. Arts et MétiersParisFrance
  3. 3.School of Electrical, Electronic and Mechanical EngineeringUniversity College DublinBelfieldIreland

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