Skip to main content

Modèles micro-macro pour les solides

  • Chapter
  • 818 Accesses

Part of the book series: Mathématiques et Applications ((MATHAPPLIC,volume 47))

This is a preview of subscription content, log in via an institution.

Buying options

eBook
USD   19.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   29.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

1.6 Bibliographie

  1. G. Allaire, Analyse numérique et optimisation, Cours à l’Ecole Polytechnique.

    Google Scholar 

  2. A. Askar, Lattice dynamical foundations of continuum theories, World Scientific.

    Google Scholar 

  3. J. M. Ball, Singularities and computation of miminizers for variational problems, In: Foundations of Computational Mathematics, R. DeVore, A. Iserles and E. Suli Eds., London Mathematical Society Lecture Note Series, Vol. 284, pp 1–20. Cambridge University Press, 2001.

    Google Scholar 

  4. J. M. Ball, Some open problems in elasticity, in Geometry, Mechanics, and Dynamics, pp 3–59, Springer, 2002.

    Google Scholar 

  5. Y. Bamberger, Mécanique de l’ingénieur, Hermann.

    Google Scholar 

  6. F. Bethuel, G; Huisken, S. Müller, K. Steffen, Variational models for microstructures and phase transition, Calculus of variations and geometric evolution problems, Springer Lecture notes in Mathematics, volume 1713, 1999, p 85–210.

    Google Scholar 

  7. X. Blanc, C. Le Bris et P.L. Lions, From molecular models to continuum mechanics, Archives for Rational Mechanics and Analysis, 164, pp 341–381, 2002.

    Article  MATH  MathSciNet  Google Scholar 

  8. H. Brézis, Analyse Fonctionnelle, 2ème Edition, Masson, 1994.

    Google Scholar 

  9. VV. Bulatov et coll., Multiscale modelling of materials, MRS, 1999

    Google Scholar 

  10. G. Buttazzo, M. Giaquinta, S. Hildebrandt, One-dimensional variational problems. An introduction, Oxford Lecture Series in Mathematics and its Applications, volume 15, 1998.

    Google Scholar 

  11. C. Carstensen Numerical Analysis of Microstructure, Chapter II of Theory and Numerics of Differential Equations, Editors J.F. Blowey, J.P. Coleman and A.W. Craig, 59–126, Springer, 2001.

    Google Scholar 

  12. M. Chipot, Elements of nonlinear analysis, Birkhäuser Advanced Texts, 2000.

    Google Scholar 

  13. Ph. G. Ciarlet, Elasticité tridimensionnelle, Masson, 1986, et Mathematical elasticity, volume 1, North Holland, 1993.

    Google Scholar 

  14. P. Deák, Th. Frauenheim, M. R. Pederson, Editeurs, Computer simulation of materials at atomic level, Wiley, 2000.

    Google Scholar 

  15. A. Ern & J.L. Guermond, Eléments finis: théorie, applications, mise en oeuvre, Springer, 2002.

    Google Scholar 

  16. L.C. Evans, Weak convergence methods for nonlinear PDE, Conference Board of the Mathematical Sciences, Regional Conference Series in Mathematics, 74, American Mathematical Society, 1988.

    Google Scholar 

  17. E. Giusti, Direct methods in the calculus of variations, World Scientific, 2003.

    Google Scholar 

  18. O. Kirchner, LP. Kubin, V. Pontikis, Editeurs, Computer simulation in materials science, Kluwer, 1996.

    Google Scholar 

  19. H. Kitagawa et al., Editeurs, Mesoscopic dynamics of fracture, Advances in Materials research, Springer, 1998.

    Google Scholar 

  20. J. Knap, M. Ortiz, An Analysis of the QuasiContinuum Method, J. Mech. Phys. Solids 49,9 (2001), p1899

    Article  MATH  Google Scholar 

  21. P. Le Tallec, Numerical methods for nonlinear tridimensional elasticity, dans le livre Handbook of numerical analysis, Ph. G. Ciarlet et J.-L. Lions Editeurs, Tome 5, North Holland.

    Google Scholar 

  22. R. Miller, E.B. Tadmor, R. Phillips, M. Ortiz, Quasicontinuum simulation of fracture at the atomic scale, Modelling Simul. Mater. Sci. Eng. 6 (1998), p607

    Article  Google Scholar 

  23. P. Pedregal, Variational methods in nonlinear elasticity., SIAM, 2000.

    Google Scholar 

  24. D. Raabe, Computational material science, Wiley, 1998.

    Google Scholar 

  25. P.A. Raviart & J.M. Thomas, Introduction à l’analyse numérique des équations aux dérivées partielles, Masson, 1992.

    Google Scholar 

  26. R. E. Rudd & J. Q. Broughton, Concurrent coupling of length scales in solid state system, pages 251–291, dans [27].

    Google Scholar 

  27. J. Salençon, Mécanique des milieux continus, Cours à l’Ecole Polytechnique.

    Google Scholar 

  28. V.B. Shenoy, R. Miller, E.B. Tadmor, R. Phillips, M. Ortiz, Quasicontinuum Models of Interfacial Structure and Deformation, Phys. Rev. Letters 80,4 (1998), p742

    Article  Google Scholar 

  29. V.B. Shenoy, R. Miller, E.B. Tadmor, D. Rodney, R. Phillips, M. Ortiz, An adaptative finite element approach to atomic-scale mechanics — the QuasiContinuum Method, J. Mech. Phys. Solids 47 (1999), p611

    Article  MATH  MathSciNet  Google Scholar 

  30. E.B. Tadmor, G.S. Smith, N. Bernstein, E. Kaxiras, Mixed finite element and atomistic formulation for complex crystals, Phys. Rev. B 59,1 (1999), p235

    Article  Google Scholar 

  31. E.B. Tadmor, R. Phillips, Mixed Atomistic and Continuum Models of Deformation in Solids, Langmuir 12 (1996), p4529

    Google Scholar 

  32. E.B. Tadmor, M. Ortiz, R. Phillips, Quasicontinuum analysis of defects in solids, Phil. Mag. A., 1996, 73, pp 1529–1563.

    Google Scholar 

Download references

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

(2005). Modèles micro-macro pour les solides. In: Systèmes multi-échelles. Mathématiques et Applications, vol 47. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-37671-2_1

Download citation

Publish with us

Policies and ethics