Skip to main content
SpringerLink
Log in

Fine Description of Materials

  • Chapter
  • First Online:
Book cover PGD-Based Modeling of Materials, Structures and Processes

Part of the book series: ESAFORM Bookseries on Material Forming ((EBMF))

  • 644 Accesses

Abstract

Nano-science and nano-technology, as well as fine modeling of the structure and mechanics of materials from nanometric to micrometric scales use descriptions ranging from the quantum to statistical mechanics.

[On quantum mechanics] I don’t like it, and I’m sorry I ever had anything to do with it.

—Erwin Schroedinger.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover 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

Institutional subscriptions

References

  1. E. Cancès, M. Defranceschi, W. Kutzelnigg, C. Le Bris, Y. Maday, in Computational Quantum Chemistry: a Primer. Handbook of Numerical Analysis, vol 10 (Elsevier, Amsterdam, 2003), p. 3–270

    Google Scholar 

  2. C. Le Bris (ed.), Handbook of Numerical Analysis. Computational Chemistry, Vol. 10 (Elsevier, Amsterdam, 2003)

    Google Scholar 

  3. V. Gavini, K. Bhattacharya, M. Ortiz, Quasi-continuum orbital-free density-functional theory: a route to multi-million atom non-periodic DFT calculation. J. Mech. Phys. Solids 55(4), 697–718 (2007)

    Article  MathSciNet  Google Scholar 

  4. C. Le Bris, P.L. Lions, From atoms to crystals: a mathematical journey. Bull. Am. Math. Soc. 42(3), 291–363 (2005)

    Article  MATH  Google Scholar 

  5. C. Le Bris, Computational chemistry from the perspective of numerical analysis. Acta Numerica 14, 363–444 (2005)

    Google Scholar 

  6. C. Le Bris, in Mathematical and Numerical Analysis for Molecular Simulation: Accomplishments and Challenges. Proceedings of the International Congress of Mathematicians, (Madrid, Spain, 2003), pp. 1507–1522

    Google Scholar 

  7. V.B. Shenoy, R. Millera, E.B. Tadmor, D. Rodney, R. Phillips, M. Ortiz, An adaptive fnite element approach to atomic-scale mechanics—the quasicontinuum method. J. Mech. Phys. Solids 36, 500–531 (1999)

    Google Scholar 

  8. G.J. Wagner, W.K. Liu, Coupling of atomistic and continuum simulations using a bridging scale decomposition. J. Comput. Phys. 190, 249–274 (2003)

    Article  MATH  Google Scholar 

  9. H. Ben Dhia, Multiscale mechanical problems: the Arlequin method. C. R. Acad. Sci., Paris 326, Ser-II b. 326, 899–904 (1998)

    Google Scholar 

  10. S.P. Xiao, T. Belytschko, A bridging domain method for coupling continua with molecular dynamics. Comput. Methods Appl. Mech. Eng. 193, 1645–1669 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  11. H.C. Öttinger, M. Laso, in Smart Polymers in Finite Element Calculation, ed. by P. Moldanaers, R. Keunings. Theoretical and Applied Rheology. Proceedings of the XIth International Congress on Rheology, vol 1 (Elsevier, 1992), pp. 286–288

    Google Scholar 

  12. M.A. Martinez, E. Cueto, I. Alfaro, M. Doblare, F. Chinesta, Updated Lagrangian free surface flow simulations with the natural neighbour Galerkin methods. Int. J. Numer. Meth. Eng. 60(13), 2105–2129 (2004)

    Article  MATH  Google Scholar 

  13. D. Gonzalez, E. Cueto, F. Chinesta, M. Doblare, An updated Lagrangian strategy for free-surface fluid dynamics. J. Comput. Phys. 223, 127–150 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  14. M.A. Martinez, E. Cueto, M. Doblare, F. Chinesta, Natural element meshless simulation of injection processes involving short fiber suspensions. J. Nonnewton. Fluid Mech. 115, 51–78 (2003)

    Article  MATH  Google Scholar 

  15. A. Ammar, B. Mokdad, F. Chinesta, R. Keunings, A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids. J. Nonnewton. Fluid Mech. 139, 153–176 (2006)

    Article  MATH  Google Scholar 

  16. F. Chinesta, A. Ammar, A. Falco, M. Laso, On the reduction of stochastic kinetic theory models of complex fluids. Model. Simul. Mater. Sci. Eng. 15, 639–652 (2007)

    Article  Google Scholar 

  17. B.B. Bird, C.F. Curtiss, R.C. Armstrong, O. Hassager, in Dynamics of Polymeric Liquids. Kinetic Theory, vol 2 (John Wiley and Sons, Chichester, 1987)

    Google Scholar 

  18. R.G. Larson, The Structure and Rheology of Complex Fluids (Oxford University Press, New York, 1999)

    Google Scholar 

  19. H.J. Bungartz, M. Griebel, Sparse grids. Acta Numerica 13, 1–123 (2004)

    Article  MathSciNet  Google Scholar 

  20. Y. Achdou, O. Pironneau, Computational Methods for Option Pricing, SIAM Frontiers in Applied Mathematics (SIAM Publishers, Philadelphia, 2005)

    Google Scholar 

  21. A. Ammar, F. Chinesta, in Circumventing Curse of Dimensionality in the Solution of Highly Multidimensional Models Encountered in Quantum Mechanics Using Meshfree Separated Representations. Lecture Notes on Computational Science and Engineering, (Springer, 2008), pp. 1–17

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. UMR CNRS, Ecole Centrale de Nantes, Nantes, France

    Francisco Chinesta

  2. Aragon Institute of Engineering Research, Universidad de Zaragoza, Zaragoza, Spain

    Elías Cueto

Authors
  1. Francisco Chinesta
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Elías Cueto
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Francisco Chinesta .

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Chinesta, F., Cueto, E. (2014). Fine Description of Materials. In: PGD-Based Modeling of Materials, Structures and Processes. ESAFORM Bookseries on Material Forming. Springer, Cham. https://doi.org/10.1007/978-3-319-06182-5_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-06182-5_2

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-06181-8

  • Online ISBN: 978-3-319-06182-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation