Advertisement

Advanced Continuum-Atomistic Model of Materials Based on Coupled Boundary Element and Molecular Approaches

  • Tadeusz Burczyński
  • Waclaw Kuś
  • Adam Mrozek
  • Radoslaw Górski
  • Grzegorz Dziatkiewicz
Part of the IUTAM Bookseries book series (IUTAMBOOK, volume 13)

Abstract

The paper contains a description of a multiscale algorithm based on the boundary element method (BEM), coupled with a discrete atomistic model. The discrete model uses empirical pair-wise potentials and the Embedded Atom Method (EAM) to compute interaction forces between atoms. The Newton—Raphson method with the backtracking algorithm is applied to solve a nonlinear system of equations of the nanoscale model. The continuum domain is modeled using BEM with subregions. Some numerical results of simulations at the nanoscale are shown to examine the presented technique.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Burczyński, T.: The Boundary Element Method in Mechanics, WNT, Warsaw (1995).Google Scholar
  2. 2.
    Burczyński,T., Mrozek, A., Kuś, W.: A computational continuum-discrete model of materials. Bulletin of the Polish Academy of Sciences, Technical Sciences 55(1), 85–89 (2007).Google Scholar
  3. 3.
    Girifalco, L.A., Weizer, V.G.: Application of the Morse potential function to cubic metals. Physical Review 114(3), 687–690 (1959).CrossRefADSGoogle Scholar
  4. 4.
    Górski, R., Fedelinski, P.: Analysis, optimization and identification of composite structures using boundary element method. Journal of Computational and Applied Mechanics 6(1), 53– 65 (2005).zbMATHGoogle Scholar
  5. 5.
    Liu, K., Karpov, E.G., Zhang S., Park, H.S.: An introduction to computational nanomechanics and materials. Computer Methods in Applied Mechanics and Engineering 193, 1529–1578 (2004).zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Mishin, Y., Farkas, D.: Interatomic potentials for monoatomic metals from experimental data and ab initio calculations. Physical Review 59(5), 3393–3407 (1999).ADSCrossRefGoogle Scholar
  7. 7.
    Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flanery, B.P.: Numerical Recipes. The Art of Scientific Computing, Cambridge University Press, Cambridge (2007).zbMATHGoogle Scholar
  8. 8.
    Sunyk, R., Steinmann, P.: On higher gradients in continuum-atomistic modeling. International Journal of Solids and Structures 40, 6877–6896 (2002).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, B.V. 2009

Authors and Affiliations

  • Tadeusz Burczyński
    • 1
    • 2
  • Waclaw Kuś
    • 1
  • Adam Mrozek
    • 1
  • Radoslaw Górski
    • 1
  • Grzegorz Dziatkiewicz
    • 1
  1. 1.Department for Strength of Materials and Computational MechanicsSilesian University of TechnologyGliwicePoland
  2. 2.Department of Artificial Intelligence, Institute of Computer ModellingCracow University of TechnologyCracowPoland

Personalised recommendations