Free access
Issue
ESAIM: M2AN
Volume 39, Number 4, July-August 2005
Page(s) 797 - 826
DOI http://dx.doi.org/10.1051/m2an:2005035
Published online 15 August 2005
  1. G. Alberti and C. Mantegazza, A note on the theory of SBV functions. Bollettino U.M.I. Sez. B 7 (1997) 375–382.
  2. L. Ambrosio, L. Fusco and D. Pallara, Functions of bounded variation and free discontinuity problems. Oxford Mathematical Monographs, The Clarendon Press Oxford University Press, New York (2000).
  3. X. Blanc, C. Le Bris and F. Legoll, work in preparation, and Analysis of a prototypical multiscale method coupling atomistic and continuum mechanics, Preprint, Laboratoire Jacques-Louis Lions, Université Paris 6 (2004), available at http://www.ann.jussieu.fr/publications/2004/R04029.html
  4. X. Blanc, C. Le Bris and P.-L. Lions, From molecular models to continuum mechanics. Arch. Rational Mech. Anal. 164 (2002) 341–381. [CrossRef] [MathSciNet]
  5. A. Braides, G. Dal Maso and A. Garroni, Variational formulation of softening phenomena in fracture mechanics: the one-dimensional case. Arch. Rational Mech. Anal. 146 (1999) 23–58. [CrossRef] [MathSciNet]
  6. S.C. Brenner and L.R. Scott, The Mathematical Theory of Finite Element Methods. Springer (1991).
  7. J.Q. Broughton, F.F. Abraham, N. Bernstein and E. Kaxiras, Concurrent coupling of length scales: Methodology and application. Phys. Rev. B 60 (1999) 2391–2403. [CrossRef]
  8. P.G. Ciarlet, An O(h²) method for a non-smooth boundary value problem. Aequationes Math. 2 (1968) 39–49. [CrossRef] [MathSciNet]
  9. P.G. Ciarlet, Mathematical Elasticity, Vol. I: Three-Dimensional Elasticity. Studies in Mathematics and its Applications, North Holland (1988).
  10. P.G. Ciarlet, Basic Error Estimates for Elliptic Problems, in Handbook of Numerical Analysis, Vol. II, P.G. Ciarlet, J.-L. Lions, Eds., North-Holland (1991) 17–351.
  11. W. E and P. Ming, private communication.
  12. J. Knap and M. Ortiz, An analysis of the Quasicontinuum method. J. Mech. Phys. Solids 49 (2001) 1899–1923. [CrossRef]
  13. P. Le Tallec, Numerical Methods for nonlinear three-dimensional elasticity, in Handbook of Numerical Analysis, Vol. III, P.G. Ciarlet, J.-L. Lions, Eds., North-Holland (1994) 465–622.
  14. F. Legoll, Méthodes moléculaires et multi-échelles pour la simulation numérique des matériaux (Molecular and multiscale methods for the numerical simulation of materials), Ph.D. Thesis, Université Pierre et Marie Curie (France), 2004, available at http://cermics.enpc.fr/~legoll/these_Legoll.pdf
  15. J.E. Marsden and T.J.R. Hugues, Mathematical foundations of Elasticity. Dover (1994).
  16. R. Miller, E.B. Tadmor, R. Phillips and M. Ortiz, Quasicontinuum simulation of fracture at the atomic scale. Model. Simul. Mater. Sci. Eng. 6 (1998) 607–638. [CrossRef]
  17. A. Quarteroni and A. Valli, Numerical Approximation of Partial Differential Equations. Springer (1997).
  18. E.B. Tadmor, M. Ortiz and R. Phillips, Quasicontinuum analysis of defects in solids. Philos. Mag. A 73 (1996) 1529–1563. [CrossRef]
  19. E.B. Tadmor and R. Phillips, Mixed atomistic and continuum models of deformation in solids. Langmuir 12 (1996) 4529–4534. [CrossRef]
  20. E.B. Tadmor, G.S. Smith, N. Bernstein and E. Kaxiras, Mixed finite element and atomistic formulation for complex crystals. Phys. Rev. B 59 (1999) 235–245. [CrossRef]
  21. V.B. Shenoy, R. Miller, E.B. Tadmor, R. Phillips and M. Ortiz, Quasicontinuum models of interfacial structure and deformation. Phys. Rev. Lett. 80 (1998) 742–745. [CrossRef]
  22. V.B. Shenoy, R. Miller, E.B. Tadmor, D. Rodney, R. Phillips and M. Ortiz, An adaptative finite element approach to atomic-scale mechanics – the Quasicontinuum method, J. Mech. Phys. Solids 47 (1999) 611–642.
  23. C. Truesdell and W. Noll, The nonlinear field theories of mechanics theory of elasticity. Handbuch der Physik, III/3, Springer Berlin (1965) 1–602.
  24. L. Truskinovsky, Fracture as a phase transformation, in Contemporary research in mechanics and mathematics of materials, Ericksen's Symposium, R. Batra and M. Beatty, Eds., CIMNE, Barcelona (1996) 322–332.
  25. K.J. Van Vliet, J. Li, T. Zhu, S. Yip and S. Suresh, Quantifying the early stages of plasticity through nanoscale experiments and simulations. Phys. Rev. B 67 (2003) 104105. [CrossRef]
  26. P. Zhang, P.A. Klein, Y. Huang, H. Gao and P.D. Wu, Numerical simulation of cohesive fracture by the virtual-internal-bond model. Comput. Model. Engrg. Sci. 3 (2002) 263–289.

Recommended for you