Advertisement

About the Mathematical Modeling of Irreversibility Problems

  • P. Laborde
Conference paper
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 66)

Abstract

We are concerned with the modeling of irreversible behaviors in Solid Mechanics and the numerical solution of the associated free boundary problem. A general enough framework is presented which allows us to represent typical stress/strain diagrams in the study of damage processes. We state some mathematical results in order to prove the coherence of the model with respect to the given diagrams. Theoretic tools are discussed for the solution of the corresponding discrete finite element problem.

Keywords

Variational Inequality Free Boundary Problem Internal Parameter Tangent Stiffness Tangent Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Halphen, B. and Nguyen, Q.S. (1975) Sur les matériaux standard generalises, J. Mecan. Vol. 14, pp. 39–63zbMATHGoogle Scholar
  2. Laborde, P. (1992) Numerical solution of free boundary problems in Solids Mechanics, Int. Ser. Numer. Analysis Vol. 107, pp. 339–347MathSciNetGoogle Scholar
  3. Laborde, P. and Michrafy, A. (1991) On general constitutive equations involving damage, Eur. J. Mech., A/Solids Vol. 10 no. 2, pp. 213–237MathSciNetzbMATHGoogle Scholar
  4. Laborde, P. and Petitjean, F. (1996) Symétries materielles et comportements non-lineaires en Elasticité, C. R. Acad. Sci., Paris Vol. 323, Serie I, pp. 1147–1152MathSciNetzbMATHGoogle Scholar
  5. Laborde, P. and Petitjean, F. (1997) Computation of form-invariant response functions in Elasticity, Report MIP Google Scholar
  6. Laborde, P., Toson, B. and Pesque, J.J. (1997) On the consistent tangent operator algorithm for thermo-plastic problems, Comp. Meth. Appl. Mech. Eng., to appearGoogle Scholar
  7. Michrafy, A. (1988) Modélisation et calcul pour certains types de matériaux composites endommageables, Thesis, BordeauxGoogle Scholar
  8. Petitjean, F. (1996) Modélisation de comportements irreversibles en mécanique des structures, Thesis, ToulouseGoogle Scholar
  9. Simo, J.C. and Taylor, R.L. (1985) Consistent tangent operators for rate independent elasto-plasticity, Comp. Meth. Appl. Mech. Eng. Vol. 48, pp. 101–118CrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1999

Authors and Affiliations

  • P. Laborde
    • 1
  1. 1.Mathématiques pour l’Industrie et la PhysiqueCNRS/UPS/INSA, UMR 5640Toulouse Cedex 04France

Personalised recommendations