Quasicontinuum Method Documentation

QC Code

The QC code is available for download here. The following documentation for the QC code is available:

• QC Tutorial Guide version 1.4 (October 2011)
• QC Reference Manual version 1.4 (October 2011)

QC Theory

The QC theory has been extensively docmumented in a variety of formats. The following sources are good places to start:

• Key articles describing major milestones in QC method development include:
• E. B. Tadmor, M. Ortiz and R. Phillips, "Quasicontinuum analysis of defects in solids", Phil. Mag. A, 73, 1529-1563 (1996). Available online for subscribers here.
• V. B. Shenoy, R. Miller, E. B. Tadmor, D. Rodney, R. Phillips and M. Ortiz, "An adaptive finite element approach to atomic-scale mechanics the quasicontinuum method", J. Mech. Phys. Solids, 47, 611-642 (1999). Available online for subscribers here.
• E. B. Tadmor, G. S. Smith, N. Bernstein and E. Kaxiras, "Mixed finite element and atomistic formulation for complex crystals", Phys. Rev. B, 59, 235-245 (1999). Available online for subscribers here.
• L. M. Dupuy, E. B. Tadmor, R. E. Miller and R. Phillips, "Finite-temperature quasicontinuum: Molecular dynamics without all the atoms", Phys. Rev. Lett., 95, 060202 (2005). Available online for subscribers here.
• Key review articles and overviews of QC include:
  • R. E. Miller and E. B. Tadmor, "The quasicontinuum method: Overview, applications and current directions", J. Comp.-Aided Mater. Des., 9, 203-239 (2002). Reprint available here with permission of publisher.
  • E. B. Tadmor and R. E. Miller, "The theory and implementation of the quasicontinuum method", in the Handbook of Materials Modeling, Part A - Methods, edited by S. Yip, Springer-Verlag, New York, 2005. Preprint available here.
• Articles reviewing and comparing multiscale methods similar to QC:
  • W. A. Curtin and R. E. Miller, "Atomistic/continuum coupling in computational materials science", Modell. Simul. Mater. Sci. Eng., 11, R33-R68 (2003). Available online for subscribers here.
  • R. E. Miller and E. B. Tadmor, "Hybrid continuum mechanics and atomistic methods for simulating materials deformation and failure", MRS Bulletin, 32, 920-926 (2007). Available online for subscribers here.
  • R. E. Miller and E. B. Tadmor, "A unified framework and performance benchmark of fourteen multiscale atomistic/continuum coupling methods", Model. Simul. Mater. Sci. Eng., 17, 053001 (2009). Preprint available here.
• A graduate-level textbook discussing the theoretical foundations of the QC method and other multiscale methods:
  • E. B. Tadmor and R. E. Miller, Modeling Materials: Continuum, Atomistic and Multiscale Techniques, Cambridge University Press (2011).
  More information on this book and a companion book written by the same authors together with Ryan S. Elliott on Continuum Mechanics and Thermodynamics is available at http://modelingmaterials.org.