Computational Mechanics

, Volume 40, Issue 4, pp 771–789

Numerical inversion of the Laplace–Carson transform applied to homogenization of randomly reinforced linear viscoelastic media

  • Martin Lévesque
  • Michael D. Gilchrist
  • Nicolas Bouleau
  • Katell Derrien
  • Didier Baptiste
Original Paper

DOI: 10.1007/s00466-006-0138-6

Cite this article as:
Lévesque, M., Gilchrist, M.D., Bouleau, N. et al. Comput Mech (2007) 40: 771. doi:10.1007/s00466-006-0138-6

Abstract

Homogenization of linear viscoelastic materials is possible using the viscoelastic correspondence principle (VCP) and homogenization solutions obtained for linear elastic materials. The VCP involves a Laplace–Carson Transform (LCT) of the material phases constitutive theories and in most cases, the time domain solution must be obtained through numerical inversion of the LCT. The objective of this paper is to develop and test numerical algorithms to invert LCT which are encountered in the context of homogenization of linear viscoelastic materials. The homogenized properties, as well as the stress concentration and strain localization tensors, are considered. The algorithms suggested have the following two key features: (1) an acceptance criterion which allows to reject solutions of unacceptable accuracy and (2) some algorithms lead to solutions for the homogenized properties where the thermodynamics restrictions imposed on linear viscoelastic materials are encountered. These two features are an improvement over the previous algorithms. The algorithms are tested on many examples and the accuracy of the inversion is excellent in most cases.

Keywords

Homogenization Viscoelasticity Numerical inversion Laplace transform 

Copyright information

© Springer Verlag 2006

Authors and Affiliations

  • Martin Lévesque
    • 1
  • Michael D. Gilchrist
    • 2
  • Nicolas Bouleau
    • 3
  • Katell Derrien
    • 4
  • Didier Baptiste
    • 4
  1. 1.CREPEC, Department of Mechanical EngineeringÉcole Polytechnique de MontréalMontréalCanada
  2. 2.School of Electrical, Electronic and Mechanical EngineeringUniversity College DublinBelfield, Dublin 4Ireland
  3. 3.Ecole Nationale des Ponts et ChausséesMarne-la-Vallée Cedex 2France
  4. 4.Laboratoire LIM - ENSAM - ParisParisFrance

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