QC Publications — A list of articles on QC theory and applications


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2017

  1. A comparative study of nanovoid growth in FCC metals
    M. Ponga, M. Ortiz and M. P. Ariza
    Philosophical Magazine, 97, 2985–3007 (2017).
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  2. Review Article: Case studies in future trends of computational and experimental nanomechanics
    W. Gerberich, E. B. Tadmor, J. Kysar, A. M. Minor, I. Szlufarska, J. Amodeo, B. Devincre, E. Hintsala and R. Ballarini
    Journal of Vacuum Science & Technology A, 35, 060801 (2017).
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  3. Modeling and simulation of nanoindentation
    S. Huang and C. Zhou
    JOM, 69, 2256–2263 (2017).
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  4. Quasicontinuum method extended to irregular lattices
    K. Mikes and M. Jirasek
    Computers & Structures, 192, 50–70 (2017).
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  5. Benchmarking, validation and reproducibility of concurrent multiscale methods are still needed
    E. B. Tadmor and R. E. Miller
    Modelling and Simulation in Materials Science and Engineering, 25, 071001 (2017).
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  6. eXtended variational quasicontinuum methodology for lattice networks with damage and crack propagation
    O. Rokos, R. H. J. Peerlings and J. Zeman
    Computer Methods in Applied Mechanics and Engineering, 320, 769–792 (2017).
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  7. An adaptive variational Quasicontinuum methodology for lattice networks with localized damage
    O. Rokos, R. H. J. Peerlings, J. Zeman and L. A. A. Beex
    International Journal for Numerical Methods in Engineering, 112, 174–300 (2017).
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  8. Edge dislocations interacting with a Sigma 11 symmetrical grain boundary in copper upon mixed loading: A quasicontinuum method study
    W. S. Yu, Z. Q. Wang and S. P. Shen
    Computational Materials Science, 137, 162–170 (2017).
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  9. Accelerated quasicontinuum: a practical perspective on hyper-QC with application to nanoindentation
    W. K. Kim and E. B. Tadmor
    Philosophical Magazine, 97, 2284–2316 (2017).
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  10. Quasicontinuum simulations of geometric effect on onset plasticity of nano-scale patterned lines
    J. F. Jin, J. Y. Cao, S. Y. Zhou, P. J. Yang and Z. X. Guo
    Modelling and Simulation in Materials Science and Engineering, 25, 065012 (2017).
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  11. A Hessian-free Newton-Raphson method for the configuration of physics systems featured by numerically asymmetric force field
    Y. Liang, Z. Shi and W. P. Chung
    Mathematics and Computers in Simulation, 140, 1–23 (2017).
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  12. Automatic adaptivity in the fully nonlocal quasicontinuum method for coarse-grained atomistic simulations
    I. Tembhekar, J. S. Amelang, L. Munk and D. M. Kochmann
    International Journal for Numerical Methods in Engineering, 110, 878–900 (2017).
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  13. Material removal mechanism of copper chemical mechanical polishing with different particle sizes based on quasi-continuum method
    Z. B. Zhu, D. Y. He, S. L. He and W. C. Luo
    Friction, 5, 99–107 (2017).
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  14. The crack growth and expansion characteristics of Fe and Ni using quasi-continuum method
    R.-Z. Qiu, Y.-C. Lin, T.-H. Fang and L.-R. Tsai
    Materials Research Express, 4, 035019 (2017).
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  15. Quasicontinuum simulation of brittle cracking in single-crystal material
    T. L. Xu, J. H. Fan, R. Stewart, X. Zheng and A. Yao
    Crystal Research and Technology, 52, 1600247 (2017).
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2016

  1. A variational formulation of dissipative quasicontinuum methods
    O. Rokos, L. A. A. Beex, J. Zeman and R. H. J. Peerlings
    International Journal of Solids and Structures, 102, 214–229 (2016).
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  2. Mechanical Property Evaluation on the Bending and Compressing Behaviour of Nano-beam
    Q. S. Bai, X. He, X. Q. Zhang, R. Q. Shen and Y. C. Liang
    Journal of Wuhan University of Technology -- Materials Science Edition, 31, 903–906 (2016).
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  3. Nanoindentation simulation on single crystal copper by quasi-continuum method
    A. B. Zhu, D. Y. He, R. J. He and C. Zou
    Materials Science and Engineering A, 674, 76–81 (2016).
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  4. Microscopic properties of a nanocrystal aluminum thin film during nanoimprint using quasi-continuous method
    T. H. Fang, W. J. Chang, D. J. Yu and C. C. Huang
    Thin Solid Films, 612, 237–242 (2016).
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  5. Microscopic properties of a nanocrystal aluminum thin film during nanoimprint using quasi-continuous method
    T.-H. Fang, W.-J. Chang, D.-J. Yu and C.-C. Huang
    Thin Solid Films, 612, 237–242 (2016).
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  6. Quasicontinuum investigation of the feedback effects on friction behavior of an abrasive particle over a single crystal aluminum substrate
    C. C. Fang, X. H. Meng, Y. B. Xie, and B. Zhao
    Tribology International, 98, 48–58 (2016).
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  7. Atomistic/continuum blending with ghost force correction
    C. Ortner and L. Zhang
    SIAM Journal of Scientific Computing, 38, A346–A375 (2016).
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  8. Nanoindentation simulation of coated aluminum thin film using quasicontinuum method
    O. Alizadeh, G. T. Eshlaghi and S. Mohammadi
    Computational Materials Science, 111, 12–22 (2016).
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2015

  1. Multiscale simulation of incipient plasticity and dislocation nucleation on nickel film during tilted flat-ended nanoindentation
    F. L. Zeng, B. Zhao and Y. Sun
    Acta Mechanica Solida Sinica, 28, 484–496 (2015).
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  2. Analysis of Transition State Theory rates upon spatial coarse-graining
    A. Binder, M. Luskin, D. Perez and A. F. Voter
    Mutliscale Modeling & Simulation, 13, 890–915 (2015).
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  3. Indenter size effect on the reversible incipient plasticity of Al (001) surface: Quasicontinuum study
    Dan Tang, Yu-Fei Shao, Jiu-Hu Li, Xing Zhao and Yang Qi
    Chinese Physics B, 24, 086805 (2015).
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  4. An atomistic/continuum coupling method using enriched bases
    J. R. Chen, C. J. Garcia-Cervera and X. T. Li
    Multiscale Modeling & Simulation, 13, 766–789 (2015).
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  5. Mechanical Property Evaluation on the Bending and Compressing Behaviour of Nano-beam
    Q. S. Bai, X. He, X. Q. Zhang, R. Q. Shen and Y. C. Liang
    Journal of Wuhan University Technology -- Materials Science Edition, 31, 903–909 (2015).
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  6. Finite-temperature non-equilibrium quasi-continuum analysis of nanovoid growth in copper at low and high strain rates
    M. Ponga, M. Ortiz and M. P. Ariza
    Mechanics of Materials, 90, 253–267 (2015).
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  7. Surface effects in nanoscale structures investigated by a fully-nonlocal energy-based quasicontinuum method
    J. S. Amelang and D. M. Kochmann
    Mechanics of Materials, 90, 166–184 (2015).
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  8. Summation rules for a fully-nonlocal energy-based quasicontinuum method
    J. S. Amelang, G. N. Venturini and D. M. Kochmann
    Journal of the Mechanics and Physics of Solids, 82, 378–413 (2015).
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  9. Higher-order quasicontinuum methods for elastic and dissipative lattice models: uniaxial deformation and pure bending
    L. A. A. Beex, O. Rokos, J. Zeman, and S. P. A. Bordas
    Gesellschaft fuer Angewandte Mathematik und Mechanik (GAMM-Mitt.), 38, 344–368 (2015).
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  10. A goal-oriented adaptive procedure for the quasi-continuum method with cluster approximation
    A. Memarnahavandi, F. Larsson and K. Runesson
    Computational Mechanics, 55, 617–642 (2015).
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  11. The mechanical reliability of an electronic textile investigated using the virtual-power-based quasicontinuum method
    L. A. A. Beex, R. H. J. Peerlings, K. van Os and M. G. D. Geers
    Mechanics of Materials, 80, 52–66 (2015).
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2014

  1. Theory-based benchmarking of the blended force-based quasicontinuum method
    X. H. Li, M. Luskin, C. Ortner and A. V. Shapeev
    Computer Methods in Applied Mechanics and Engineering, 268, 763–781 (2014).
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  2. Central summation in the quasicontinuum method
    L. A. A. Beex, R. H. J. Peerlings and M. G. D. Geers
    Journal of the Mechanics and Physics of Solids, 70, 242–261 (2014).
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  3. Quasicontinuum-based multiscale approaches for plate-like beam lattices experiencing in-plane and out-of-plane deformation
    L. A. A. Beex, P. Kefriden, T. Rabezuk and S. P. A. Bordas
    Computer Methods in Applied Mechanics and Engineering, 279, 348–378 (2014).
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  4. A posteriori error control for a quasi-continuum approximation of a periodic chain
    C. Ortner and H. Wang
    IMA Journal of Numerical Analysis, 34, 977–1001 (2014).
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  5. Effect of initial contact location on multiasperity nanocontact: Quasicontinuum Simulation
    W. G. Jiang, S. Xu and Z. W. Wang
    NANO, 9, 1450004 (2014).
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  6. Interactions between edge lattice dislocations and Sigma 11 symmetrical tilt grain boundary: comparisons among several FCC metals and interatomic potentials
    W. S. Yu and Z. Q. Wang
    Philosophical Magazine, 94, 2224–2246 (2014).
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  7. A local quasicontinuum method for 3D multilattice crystalline materials: Application to shape-memory alloys
    V. Sorkin, R. S. Elliott and E. B. Tadmor
    Modelling and Simulation in Materials Science and Engineering, 22, 055001 (2014).
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  8. Study of nanocontact and incipient nanoscratch process using the quasicontinuum method
    C. C. Fang and X. J. Yang
    Materials Science and Engineering A, 600, 221–230 (2014).
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  9. A multiscale quasicontinuum method for dissipative lattice models and discrete networks
    L. A. A. Beex, R. H. J. Peerlings and M. G. D. Geers
    Journal of the Mechanics and Physics of Solids, 64, 154–169 (2014).
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  10. Quasicontinuum study of the shear behavior of defective tilt grain boundaries in Cu
    V. Peron-Luhrs, F. Sansoz and L. Noels
    Acta Materialia, 64, 419–428 (2014).
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  11. Hyper-QC: An accelerated finite-temperature quasicontinuum method using hyperdynamics
    W. K. Kim, M. Luskin, D. Perez, A. F. Voter and E. B. Tadmor
    Journal of the Mechanics and Physics of Solids, 63, 94–112 (2014).
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  12. On the Effect of Ghost Force in the Quasicontinuum Method: Dynamic Problems in One Dimension
    X. T. Li and P. B. Ming
    Communications in Computational Physics, 15, 647–676 (2014).
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  13. A multiscale quasicontinuum method for lattice models with bond failure and fiber sliding
    L.A.A. Beex, R.H.J. Peerlings and M.G.D. Geers
    Computer Methods in Applied Mechanics and Engineering, 269, 108–122 (2014).
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2013

  1. The effect of ghost forces for a quasicontinuum method in three dimension
    L. Cui and P. B. Ming
    Science China-Mathematics, 56, 2571–2589 (2013).
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  2. Comparison of concurrent multiscale methods in the application of fracture in nickel
    V. Iacobellis and K. Behdinan
    Journal of Applied Mechanics, 80, 051003 (2013).
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  3. Analysis of an energy-based atomistic/continuum approximation of a vacancy in the 2D triangular lattice
    C. Ortner and A. V. Shapeev
    Mathematics of Computation, 82, 2191–2236 (2013).
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  4. A priori and posteriori W-1, W-infinity error analysis of a QC method for complex lattices
    A. Abdulle, P. Lin and A. V. Shapeev
    SIAM Journal on Numerical Analysis, 51, 2357–2379 (2013).
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  5. A Gamma convergence analysis of the quasicontinuum method
    M. I. Espanol, D. M. Kochmann, S. Conti and M. Ortiz
    Multiscale Modeling & Simulation, 11, 766–794 (2013).
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  6. A two-scale model predicting the mechanical behavior of nanocrystalline solids
    V. Peron-Louhrs, A. Jerusalem, F. Sansoz, L. Stainier and L. Noels
    Journal of the Mechanics and Physics of Solids, 61, 1895–1914 (2013).
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  7. Effect of the Sigma 5(310)/[001]theta=53.1 degrees grain boundary on the incipient yield of bicrystal copper: A quasicontinuum simulation and nanoindentation experiment
    D. B. Shan and L. M. Wang and L. Yuan
    Journal of Materials Research, 28, 766–773 (2013).
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  8. Quasi-Continuum Model for the Finite Deformation of Single-Layer Graphene Sheets Based on the Temperature-Related Higher Order Cauchy-Born Rule
    X. Y. Wang and X. Guo
    Journal of Computational and Theoretical Nanoscience, 10, 1540164 (2013).
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  9. Finite element analysis of Cauchy-Born Approximations to Atomistic Models
    C. Makridakis and E. Suli
    Archive for Rational Mechanics and Analysis, 207, 813–843 (2013).
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  10. Formulation and optimization of the energy-based blended quasicontinuum method
    M. Luskin, C. Ortner and B. Van Koten
    Computer Methods in Applied Mechanics and Engineering, 253, 160–168 (2013).
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  11. Lattice stability for atomistic chains modeled by local approximations of the embedded atom method
    X. H. Li and M. Luskin
    Computational Materials Science, 66, 96–103 (2013).
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  12. Multiscale simulations on the reversible plasticity of Al (001) surface under a nano-sized indenter
    Y. F. Shao, X. Zhao, J. H. Li and S. Q. Wang
    Computational Materials Science, 67, 346–352 (2013).
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  13. Convergence of a Force-Based Hybrid Method in Three Dimensions
    J. F. Lu and P. B. Ming
    Communications on Pure and Applied Mathematics, 66, 83–108 (2013).
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2012

  1. Ghost force influence of a quasicontinuum method in two dimension
    J. R. Chen and P. B. Ming
    Journal of Computational Mathematics, 30, 657–683 (2012).
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  2. Construction and sharp consistency estimates for atomistic/continuum coupling methods with general interfaces: A two-dimensional model problem
    C. Ortner and L. Zhang
    SIAM Journal on Numerical Analysis, 50, 2940–2965 (2012).
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  3. Objective quasicontinuum approach for rod problems
    Ye. Hakobyan, E. B. Tadmor and R. D. James
    Physical Review B, 86, 245435 (2012).
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  4. Positive definiteness of the blended force-based quasicontinuum method
    X. H. Li, M. Luskin and C. Ortner
    Multiscale Modeling and Simulation, 10, 1023–1045 (2012).
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  5. The spectrum of the force-based quasicontinuum operator for a homogeneous periodic chain
    M. Dobson, C. Ortner and A. V. Shapeev
    Multiscale Modeling and Simulation, 10, 744–765 (2012).
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  6. Numerical Methods for Multilattices
    A. Abdulle, P. Lin and A. V. Shapeev
    Multiscale Modeling and Simulation, 10, 696–726 (2012).
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  7. Brittle-ductile behavior of a nanocrack in nanocrystalline Ni: A quasicontinuum study
    Y. F. Shao, X. Yang, X. Zhao and S. Q. Wang
    Chinese Physics B, 21, 093104 (2012).
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  8. Interactions between edge lattice dislocations and Sigma 11 symmetrical tilt grain boundaries in copper: A quasi-continuum method study
    W. S. Yu and Z. Q. Wang
    Acta Materialia, 60, 5010–5021 (2012).
    Abstract HTML Text
  9. Investigation of grain boundary activity in nanocrystalline Al under an indenter by using a multiscale method
    Y. F. Shao, X. Yang, X. Zhao and S. Q. Wang
    Chinese Physics B, 21, 083101 (2012).
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  10. Multiscale analysis of delay effect of dislocation nucleation with surface pit defect in nanoindentation
    Z. L. Zhang and Y. S. Ni
    Computational Materials Science, 62, 203–209 (2012).
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  11. Multiscale simulations of wedged nanoindentation on nickel
    F. L. Zeng, Y. Sun, Y. Z. Liu and Y. Zhou
    Computational Materials Science, 62, 47–54 (2012).
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  12. A generalized quasinonlocal atomistic-to-continuum coupling method with finite-range interaction
    X. H. Li and M. Luskin
    IMA Journal of Numerical Analysis, 32, 377–393 (2012).
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  13. Anisotropic plastic deformation beneath surface step during nanoindentation of FCC Al by multiscale analysis
    H. B. Lu, Y. S. Ni, J. F. Mei, J. W. Li and H. S. Wang
    Computational Materials Science, 58, 192–200 (2012).
    Abstract HTML Text
  14. HotQC simulation of nanovoid growth under tension in copper
    M. P. Ariza, I. Romero, I. Ponga and M. Ortiz
    International Journal of Fracture, 174, 75–85 (2012).
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  15. Analysis of the quasi-nonlocal quasicontinuum approximation of the embedded atom model
    X. H. Li and M. Luskin
    International Journal for Multiscale Computational Engineering, 10, 33–49 (2012).
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  16. Stress-based atomistic/continuum coupling: a new variant of the quasicontinuum approximation
    C. Makridakis, C. Ortner and E. Suli
    International Journal for Multiscale Computational Engineering, 10, 51–64 (2012).
    Abstract HTML Text
  17. Numerical simulation for finite deformation of single-walled carbon nanotubes at finite temperature using temperature-related higher order Cauchy-Born rule based quasi-continuum model
    X. Y. Wang and X. Guo
    Computational Materials Science, 55, 273–283 (2012).
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  18. Investigation of the thermo-mechanical properties of single-walled carbon nanotubes based on the temperature-related higher order Cauchy-Born rule
    X. Guo, J. Liao and X. Wang
    Computational Materials Science, 51, 445–454 (2012).
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2011

  1. Multiscale analysis of defect initiation on the atomistic crack tip in body-centered-cubic metal Ta
    H. B. Lu, J. W. Li, Y. S. Ni, J.-F. Mei and H.-S. Wang
    Acta Physica Sinica, 60, 106101 (2011).
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  2. A priori error estimates for energy-based quasicontinuum approximations of a periodic chain
    C. Ortner and H. Wang
    Mathematica Models & Methods in Applied Sciences, 21, 2491–2521 (2011).
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  3. Analysis of the quasi-nonlocal approximation of linear and circular chains in the plane
    P. Belik and M. Luskin
    SIAM Journal of Multiscale Modeling and Simulation, 9, 1495–1527 (2011).
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  4. Multiscale simulations of mixed-mode fracture in bcc-Fe
    I. R. Vatne, E. Ostby and C. Thaulow
    Modelling and Simulation in Materials Science and Engineering, 19, 085006 (2011).
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  5. Analysis of energy-based blended quasi-continuum approximations
    B. van Koten and M. Luskin
    SIAM Journal of Numerical Analysis, 49, 2182–2209 (2011).
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  6. Quasicontinuum study the influence of misfit dislocation interactions on nanoindentation
    J. W. Li, H. B. Lu, Y. S. Ni and J. F. Mei
    Computational Materials Science, 50, 3162–3170 (2011).
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  7. A priori error analysis of two force-based atomistic/continuum models of a periodic chain
    C. Makridakis, C. Ortner and E. Suli
    Numerische Mathematik, 119, 83–121 (2011).
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  8. Position effect of cylindrical indenter on nanoindentation into Cu thin film by multiscale analysis
    H. B. Lu, J. W. Li and Y. Ni
    Computational Materials Science, 50, 2987–2992 (2011).
    Abstract HTML Text
  9. A quasicontinuum methodology for multiscale analyses of discrete microstructural models
    L. A. A. Beex, R. H. J. Peerlings and M. G. D. Geers
    International Journal for Numerical Methods in Engineering, 87, 701–718 (2011).
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  10. A homogenization analysis of the field theoretic approach to the quasi-continuum method
    V. Gavini and L. Liu
    Journal of the Mechanics and Physics of Solids, 59, 1536–1551 (2011).
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  11. A field theoretical approach to the quasi-continuum method
    M. Iyer and V. Gavini
    Journal of the Mechanics and Physics of Solids, 59, 1506–1535 (2011).
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  12. Iterative methods for the force-based quasicontinuum approximation: Analysis of a 1D model problem
    M. Dobson, M. Luskin and C. Ortner
    Computer Methods in Applied Mechanics and Engineering, 200, 2697–2709 (2011).
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  13. Generalized planar fault energy of body-centered cubic Ta and its application to plastic deformation of mode II crack tip
    J. F. Mei, J. W. Li, Y. S. Ni and H. T. Wang
    Acta Phisica Sinica, 60, 066104 (2011).
    Abstract HTML Text
  14. A priori and a posteriori analysis of the quasinonlocal quasicontinuum method in 1D
    C. Ortner
    Mathematics of Computation, 80, 1265–1285 (2011).
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  15. Quasicontinuum simulation of crack propagation in bcc-Fe
    I. R. Vatne, E. Ostby, C. Thaulow and D. Farkas
    Materials Science and Engineering A, 528, 5122–5134 (2011).
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  16. A comparative study of fracture in Al: Quantum mechanical vs. empirical atomistic description
    Q. Peng and G. Lu
    Journal of the Mechanics and Physics of Solids, 59, 775–786 (2011).
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2010

  1. Multiscale simulation and Rice-Thomson dislocation model analysis of nanoindentation
    J. W. Li and Y. S. Ni
    Rare Metal Materials and Engineering, 39, 2095–2100 (2010).
    Abstract HTML Text
  2. Initial dislocation topologies of nanoindentation into copper (001) film with a nanocavity
    W. S. Yu and S. P. Shen
    Engineering Fracture Mechanics, 77, 3329–3340 (2010).
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  3. Quasicontinuum simulation of crack propagation in nanocrystalline Ni
    Y. F. Shao and S. Q. Wang
    Acta Physica Sinica, 59, 7258–7265 (2010).
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  4. Accuracy of quasicontinuum approximations near instabilities
    M. Dobson, M. Luskin and C. Ortner
    Journal of the Mechanics and Physics of Solids, 58, 1741–1757 (2010).
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  5. Two-dimensional quasicontinuum analysis of the strengthening and weakening effect of Cu/Ag interface on nanoindentation
    J. W. Li, J. F. Mei, Y. S. Ni, H. B. Lu and W. G. Jiang,
    Journal of Applied Physics, 108, 054309 (2010).
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  6. Quantum mechanical study of solid solution effects on dislocation nucleation during nanoindentation
    Q. Peng, X. Zhang, C. Huang, E. A. Carter and G. Lu
    Modelling and Simulation in Materials Science and Engineering, 18, 075003 (2010).
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  7. Beyond multiscale and multiphysics: Multimaths for model coupling
    X. Blanc, C. Le Bris, F. Legoll and T. Lelievre
    Networks and Heterogeneous Media, 5, 423–460 (2010).
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  8. Multiscale Simulation of the Dislocation Emissions of Single Ni Crystal in Nanoindentation
    J. H. Li, X. Zhao, S. Q. Wang and C. B. Zhang
    Journal of Wuhan University of Technology--Materials Science Edition, 25, 423–428 (2010).
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  9. An adaptive FE-MD model coupling approach
    W. Z. Shan and U. Nackenhorst
    Computational Mechanics, 46, 577–596 (2010).
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  10. A multiscale modelling study of Ni-Cr crack tip initial stage oxidation at different stress intensities
    N. K. Das, I Tirtom and T. Shoji
    Materials Chemistry and Physics, 122, 336–342 (2010).
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  11. Hybrid discrete dislocation models for fatigue crack growth
    W. A. Curtin, V. S. Deshpande, A. Needleman, E. van der Giessen and M. Wallin
    International Journal of Fatigue, 32, 1511–1520 (2010).
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  12. Stability, Instability, and Error of the Force-based Quasicontinuum Approximation
    M. Dobson, M. Luskin and C. Ortner
    Archive for Rational Mechanics and Analysis, 197, 179–202 (2010).
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  13. Multiscale study on the tensile fracture of Al-terminated Cu(111)/\alpha-Al_2O_3(0001) interfaces
    W. Yu and S. Shen
    Computational Materials Science, 48, 228–240 (2010).
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  14. Sharp stability estimates for the force-based quasicontinuum approximation of homogeneous tensile deformation
    M. Dobson and M. Luskin and C. Ortner
    Multiscale Modeling and Simulation, 8, 782–802 (2010).
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  15. A quardature-rule type approximation to the quasi-continuum method
    M. Gunzburger and Y. Z. Zhang
    Multiscale Modeling and Simulation, 8, 571–590 (2010).
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  16. A New Extension of Cauchy-Born Rule for Monolayer Crystal Films
    S. Lu and C. Cho
    Nanoscale Research Letters, 5, 863–867 (2010).
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  17. Multiscale Simulation of Indentation, Retraction and Fracture Processes of Nanocontact
    J .F. Mei and J .W. Li and Y. S. Ni and H. T. Wang
    Nanoscale Research Letters, 5, 692–700 (2010).
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  18. Finite-Temperature Coarse-Graining of One-Dimensional Models: Mathematical Analysis and Computational Approaches
    X. Blanc, C. Le Bris, F. Legoll, C. Patz
    Journal of Nonlinear Science, 20, 241–275 (2010).
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  19. Quasicontinuum study on formation of fivefold deformation twin in nanocrystalline aluminum
    Y. F. Shao and S. Q. Wang
    Scripta Materialia, 62, 419–422 (2010).
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  20. Multi-scale simulation of the nano-metric cutting process
    X. Z. Sun and K. Cheng
    International Journal of Advanced Manufacturing Technology, 47, 891–901 (2010).
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  21. A multiscale cohesive zone model and simulations of fractures
    X. W. Zeng and S. F. Li
    Computer Methods in Applied Mechanics and Engineering, 199, 547–556 (2010).
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  22. Quadrature-rule type approximations to the quasicontinuum method for long-range interatomic interactions
    Y. Z. Zhang and M. Gunzburger
    Computer Methods in Applied Mechanics and Engineering, 199, 648–659 (2010).
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  23. Multiscale computations for carbon nanotubes based on a hybrid QM/QC (quantum mechanical and quasicontinuum) approach
    J. Y. Park, C. H. Park, J. S. Park, K. J. Kong, H. Chang and S. Im
    Journal of the Mechanics and Physics of Solids, 58, 86–102 (2010).
    Abstract HTML Text
  24. An Examination on Atomic-level Stress Calculations by Nanoindentation Simulation via the Quasicontinuum Method
    Y. F. Shao and S. Q. Wang
    Journal of Materials Science & Technology, 26, 56–64 (2010).
    Abstract HTML Text
  25. Quantum mechanical simulations of nanoindentation of Al thin film
    Q. Peng, X. Zhang and G. Lu
    Computational Materials Science, 47, 769–774 (2010).
    Abstract HTML Text
  26. Effects of Crystalline Anisotropy and Indenter Size on Nanoindentation by Multiscale Simulation
    J. W. Li, Y. S. Ni, H. S. Wang and J. F. Mei
    Nanoscale Research Letters, 5, 420–432 (2010).
    Abstract HTML Text
  27. Lattice dynamical finite-element method
    X. H. Liu, J. F. Gu, Y. Shen, J. Li and C. F. Chen
    Acta Materialia, 58, 510–523 (2010).
    Abstract HTML Text
  28. Finite-temperature extension of the quasicontinuum method using Langevin dynamics: entropy losses and analysis of errors
    J. Marian, G. Venturini, B. L. Hansen, J. Knap, M. Ortiz and G. H. Campbell
    Modelling and Simulation in Materials Science and Engineering, 18, 015003 (2010).
    Abstract HTML Text

2009

  1. Analysis of a one-dimensional nonlocal quasi-continuum method
    P. B. Ming and J. Z. Yang
    Multiscale Modeling & Simulation, 7, 1838–1875 (2009).
    Abstract HTML Text
  2. An analysis of the effect of ghost force oscillation on quasicontinuum error
    M. Dobson and M. Luskin
    ESAIM-Mathematical Modelling and Numerical Analysis, 43, 591–604 (2009).
    Abstract HTML Text
  3. Coupling atomistic accuracy with continuum effectivity for predictive simulations in materials research - the Quasicontinuum Method
    B. Eidel
    International Journal of Materials Research, 100, 1503–1512 (2009).
    Abstract HTML Text
  4. Effects of small indenter size and its position on incipient yield loading during nanoindentation
    W. S. Yu and S. P. Shen
    Materials Science and Engineering A, 526, 211–218 (2009).
    Abstract HTML Text
  5. An analysis of node-based cluster summation rules in the quasicontinuum method
    M. Luskin and C. Ortner
    SIAM Journal of Numerical Analysis, 47, 3070–3086 (2009).
    Abstract HTML Text
  6. Multiscale analysis of the effects of nanocavity on nanoindentation
    W. S. Yu and S. P. Shen
    Computational Materials Science, 46, 425–430 (2009).
    Abstract HTML Text
  7. An optimal order error analysis of the one-dimensional quasicontinuum approximation
    M. Dobson and M. Luskin
    SIAM Journal of Numerical Analysis, 47, 2455–2475 (2009).
    Abstract HTML Text
  8. A unified framework and performance benchmark of fourteen multiscale atomistic/continuum coupling methods
    R. E. Miller and E. B. Tadmor
    Modelling and Simulation in Materials Science and Engineering, 17, 053001 (2009).
    Abstract HTML Text
  9. An efficient three-dimensional adaptive quasicontinuum method using variable-node elements
    S. Kwon, Y. Lee, J. Y. Park, D. Sohn, J. H. Lim and S. Im
    Journal of Computational Physics, 228, 4789–4810 (2009).
    Abstract HTML Text
  10. Efficient algorithms for discrete lattice calculations
    M. Arndt, V. Sorkin and E. B. Tadmor
    Journal of Computational Physics, 228, 4858–4880 (2009).
    Abstract HTML Text
  11. Quasicontinuum simulation of single crystal nano-plate with a mixed-mode crack
    T. Zhou, X. H. Yang and C. Y. Chen
    International Journal of Solids and Structures, 46, 1975–1980 (2009).
    Abstract HTML Text
  12. Multiscale simulation of nanoindentation on Al thin film
    J. W. Li, Y. S. Ni, Y. H. Lin, C. Luo and W. G. Jiang
    Acta Metallurgica Sinica, 45, 129–136 (2009).
    Abstract HTML Text
  13. Hybrid atomistic simulation methods for materials systems
    N. Bernstein, J. R. Kermode and G. Csanyi
    Reports on Progress in Physics, 72, 026501 (2009).
    Abstract HTML Text
  14. A note on the regularity of reduced models obtained by nonlocal quasi-continuum-like approaches
    M. Anitescu, D. Negrut, P. Zapol and A. El-Azab
    Mathematical Programming, 118, 207–236 (2009).
    Abstract HTML Text
  15. A variational formulation of the quasicontinuum method based on energy sampling in clusters
    B. Eidel and A. Stukowski
    Journal of Mechanics and Physics of Solids, 57, 87–108 (2009).
    Abstract HTML Text

2008

  1. Computational Study on Misfit Dislocation in Ni-Based Superalloys by Quasicontinuum Method
    J. R. P. Djuansjah, K. Yashiro and Y. Tomita
    Materials Transactions, 49, 2507–2514 (2008).
    Abstract HTML Text
  2. Quasicontinuum study of incipient plasticity under nanoscale contact in nanocrystalline aluminum
    V. Dupont and F. Sansoz
    Acta Materialia, 56, 6013–6026 (2008).
    Abstract HTML Text
  3. Quasicontinuum simulation of indentation on FCC metals
    H. T. Wang, Z. D. Qin, Y. S. Ni and W. Zhang
    Transactions of Nonferrous Metals Society of China, 18, 1164–1171 (2008).
    Abstract HTML Text
  4. Multiscale simulation of onset plasticity during nanoindentation of Al (001) surface
    J. Jin, S. A. Shevlin and Z. X. Guo
    Acta Materialia, 56, 4358–4368 (2008).
    Abstract HTML Text
  5. Error estimate of force-based quasicontinuum method
    P. B. Ming
    Communications in Mathematical Sciences, 6, 1087–1095 (2008).
    Abstract HTML Text
  6. Quasicontinuum method simulation of the initial plastic deformation of single crystal Cu in nanoindentation
    X. Zhao, J. H. Li, S. Q. Wang and C. B. Zhang
    Acta Metallurgica Sinica, 44, 1455–1460 (2008).
    Abstract HTML Text
  7. Nanocontact between BCC tungsten and FCC nickel using the quasicontinuum method
    P. Chen and Y. P. Shen
    International Journal of Solids and Structures`, 45, 6001–6017 (2008).
    Abstract HTML Text
  8. Effect of surface roughness on nanoindentation test of thin films
    W. G. Jiang, J. J. Su and X. Q. Feng
    Engineering Fracture Mechanics, 75, 4965–4972 (2008).
    Abstract HTML Text
  9. Quasicontinuum-Like Reduction of Density Functional Theory Calculations of Nanostructures
    D. Negrut, M. Anitescu, A. El-Azab and P. Zapol
    Journal of Nanoscience and Nanotechnology, 8, 3729–3740 (2008).
    Abstract HTML Text
  10. Goal-oriented adaptive mesh refinement for the quasicontinuum approximation of a Frenkel-Kontorova model
    M. Arndt and M. Luskin
    Computer Methods in Applied Mechanics and Engineering, 197, 4298–4306 (2008).
    Abstract HTML Text
  11. Multiscale simulation of onset plasticity during nanoindentation of Al (001) surface
    J. Jin, S. A. Shivlin and Z. X. Guo
    Acta Materialia, 56, 4358–4368 (2008).
    Abstract HTML Text
  12. Iterative solution of the quasicontinuum equilibrium equations with continuation
    M. Dobson and M. Luskin
    Journal of Scientific Computing, 37, 19–41 (2008).
    Abstract HTML Text
  13. Quantum simulation of materials at micron scales and beyond
    Q. Peng, X. Zhang, L. Hung, E. A. Carter and G. Lu
    Physical Review B, 78, 054118 (2008).
    Abstract HTML Text
  14. Multiscale mechanical analysis of silicon nanostructures by combined finite temperature models
    Z. Tang and N. R. Aluru
    Computational Methods in Applied Mechanics and Engineering, 197, 3215–3224 (2008).
    Abstract HTML Text
  15. A finite temperature continuum theory based on interatomic potential in crystalline solids
    A. C. To, W. K. Liu and A. Kopacz
    Computational Mechanics, 42, 531–541 (2008).
    Abstract HTML Text
  16. A cohesive finite element for quasi-continua
    X. H. Liu, S. F. Li and N. Sheng
    Computational Mechanics, 42, 543–553 (2008).
    Abstract HTML Text
  17. Adaptive nonlocal quasicontinuum for deformations of curved crystalline structures
    J. Y. Parks and S. Im
    Physical Review B, 77, 184109 (2008).
    Abstract HTML Text
  18. A Quasicontinuum study of nanovoid collapse under uniaxial loading in Ta
    J. Marian, J. Knap and G. H. Campbell
    Acta Materialia, 56, 2389–2399 (2008).
    Abstract HTML Text
  19. Error estimation and atomistic-continuum adaptivity for the quasicontinuum approximation of a Frenkel-Kontorova model
    M. Arndt and M. Luskin
    Multiscale Modeling and Simulation, 7, 147–170 (2008).
    Abstract HTML Text
  20. A variational approach to coarse graining of equilibrium and non-equilibrium atomistic description at finite temperature
    Y. Kulkarni, J. Knap and M. Ortiz
    Journal of the Mechanics and Physics of Solids, 56, 1417–1449 (2008).
    Abstract HTML Text
  21. Analysis of a force-based quasicontinuum approximation
    M. Luskin and M. Dobson
    ESAIM-Mathematical Modelling and Numerical Analysis,, 42, 113–139 (2008).
    Abstract HTML Text
  22. Multiscale modeling of polymers - The Pseudo Amorphous Cell
    V. B. Tan, X. S. Zeng, M. Deng, K. M. Lim and T. E. Tay
    Computer Methods in Applied Mechanics and Engineering, 197, 536–554 (2008).
    Abstract HTML Text
  23. Breakdown of self-similar hardening Behavior in Au nanopillar microplasticity
    J. Marian and J. Knap
    International Journal for Multiscale Computational Engneering, 5, 287–294 (2008).
    Abstract HTML Text
  24. Towards a taxonomy for multiscale methods in computational mechanics: building blocks of existing methods
    V. Gravemeier, S. Lenz and W. A. Wall
    Computational Mechanics, 41, 279–291 (2008).
    Abstract HTML Text
  25. A variational approach to coarse graining of equilibrium and non-equilibrium atomistic description at finite temperature
    Y. Kulkarni, J. Knap and M. Ortiz
    Journal of the Mechanics and Physics of Solids, 56, 1417–1449 (2008).
    Abstract HTML Text
  26. Analysis of a quasicontinuum method in one dimension
    C. Ortner and E. Suli
    ESAIM-Mathematical Modelling and Numerical Analysis, 42, 57–91 (2008).
    Abstract HTML Text

2007

  1. Atomic mechanism of shear localization during indentation of a nanostructured metal
    F. Sansoz and V. Dupont
    Materials Science & Engineering C, 27, 1509–1513 (2007).
    Abstract HTML Text
  2. Continuum constitutive models from analytical free energies
    C. J. Kimmer and R. E. Jones
    Journal of Condensed Physics--Condensed Matter, 19, 326207 (2007).
    Abstract HTML Text
  3. Predictions of nanohardness and elastic modulus of thin film material with the quasicontinuum method
    J. W. Li and W. G. Jiang
    Acta Metallurgica Sinica, 43, 851–856 (2007).
    Abstract HTML Text
  4. Interaction mechanism between edge dislocations and asymmetrical tilt grain boundaries investigated via quasicontinuum simulations
    T. Shimokawa, T. Kinari and S. Shintaku
    Physical Review B, 75, 144108 (2007).
    Abstract HTML Text
  5. A multilattice quasicontinuum for phase transforming materials: Cascading Cauchy Born kinematics
    M. Dobson, R. S. Elliott, M. Luskin and E. B. Tadmor
    Journal of Computer-Aided Materials Design, 14 (supplement 1), 219–237 (2007).
    Abstract HTML Text
  6. Numerical studies of a coarse-grained approximation for dynamics of an atomic chain
    P. Lin and P. Plechac
    International Journal for Multiscale Computational Engineering, 5, 351–367 (2007).
    Abstract HTML Text
  7. Goal-oriented atomistic-continuum adaptivity for the quasicontinuum approximation
    M. Arndt and M. Luskin
    International Journal for Multiscale Computational Engineering, 5, 407–415 (2007).
    Abstract HTML Text
  8. Hybrid continuum mechanics and atomistic methods for simulating materials deformation and failure
    R. E. Miller and E. B. Tadmor
    MRS Bulletin, 32, 920–926 (2007).
    Abstract HTML Text
  9. A contact mechanics model for quasi-continua
    R. A. Sauer and S. F. Li
    International Journal for Numerical Methods in Engineering, 71, 931–962 (2007).
    Abstract HTML Text
  10. Atomistic to continuum limits for computational materials science
    X. Blanc, C. Le Bris, P. L. Lions
    ESAIM-Mathematical Modelling and Numerical Analysis, 41, 391–426 (2007).
    Abstract HTML Text
  11. A temperature-related homogenization technique and its implementation in the meshfree particle method for nanoscale simulations
    S. P. Xiao and W. X. Yang
    International Journal for Numerical Methods in Engineering, 69, 2099–2125 (2007).
    Abstract HTML Text
  12. Size and microstructure effects on the mechanical behavior of FCC bicrystals by quasicontinuum method
    F. Sansoz and J. F. Molinari
    Thin Solid Films, 515, 3158–3163 (2007).
    Abstract HTML Text
  13. Quasi-continuum orbital-free density-functional theory: A route to multi-million atom non-periodic DFT calculation.
    V. Gavini, K. Bhattacharya and M. Ortiz.
    Journal of the Mechanics and Physics of Solids, 55, 697–718 (2007).
    Abstract HTML Text
  14. Convergence analysis of a quasi-continuum approximation for a two-dimensional material without defects
    P. Lin
    SIAM Journal on Numerical Analysis, 45, 313–332 (2007).
    Abstract HTML Text

2006

  1. Hybrid atomistic-coarse-grained treatment of multiscale processes in heterogeneous materials: A self-consistent-field approach
    D. J. Diestler, H. Zhou, R. Feng and X. C. Zeng
    Journal of Chemical Physics, 125, 064705 (2006).
    Abstract HTML Text
  2. Error control for molecular statics problems
    S. Prudhomme, P. T. Bauman and J. T. Oden
    International Journal for Multiscale Computational Engineering, 4, 647–662 (2006).
    Abstract HTML Text
  3. Grain growth behavior at absolute zero during nanocrystalline metal indentation
    F. Sansoz and V. Dupont
    Applied Physics Letters, 89, Art. No. 111901 (2006).
    Abstract HTML Text
  4. Quasicontinuum simulation of nanoindentation of nickel film
    F. L. Zeng and Y. Sun
    Acta Mechanica Solida Sinica, 19, 283–288 (2006).
    Abstract HTML Text
  5. Temperature-related Cauchy-Born rule for multiscale modeling of crystalline solids
    S. P. Xiao and W. X. Yang
    Computational Materials Science, 37, 374–379 (2006).
    Abstract HTML Text
  6. Multiscale modeling of physical phenomena: Adaptive control of models
    J. T. Oden, S. Prudhomme, A. Romkes and P. T. Bauman
    SIAM Journal on Scientific Computing, 28, 2359–2389 (2006).
    Abstract HTML Text
  7. A concurrent multiscale method based on the meshfree method and molecular dynamics analysis
    Y. T. Gu and L. C. Zhang
    Multiscale Modeling & Simulation, 5, 1128–1155 (2006).
    Abstract HTML Text
  8. Uniform accuracy of the quasicontinuum method
    W. E, J. F. Lu and J. Z. Yang
    Physical Review B, 74, Art. No. 214115 (2006).
    Abstract HTML Text
  9. Multiscale simulation on nanometric cutting of single crystal copper
    X. Z. Sun, S. J. Chen, K. Cheng, D. H. Hu and W. J. Chu
    Proceedings of the Institution of Mechanical Engineers Part B-Journal of Enginee, 220, 1217–1222 (2006).
    Abstract HTML Text
  10. Finite-temperature quasicontinuum method for multiscale analysis of silicon nanostructures
    Z. Tang, H. Zhao, G. Li and N. R. Aluru
    Physical Review B, 74, Art. No. 064110 (2006).
    Abstract HTML Text
  11. Two-grain nanoindentation using the quasicontinuum method: Two-dimensional model approach
    R. A. Iglesias and E. P. M. Leiva
    Acta Materialia, 54, 2655–2664 (2006).
    Abstract HTML Text
  12. Prediction of dislocation nucleation during nanoindentation of Al3Mg by the orbital-free density functional theory local quasicontinuum method
    R. L. Hayes, G. Ho, M. Ortiz M and E. A. Carter
    Philosophical Magazine, 86, 2343–2358 (2006).
    Abstract HTML Text
  13. Rapid thermal equilibration in coarse-grained molecular dynamics
    S. P. A. Gill, Z. Jia, B. Leimkuhler and A. C. F. Cocks
    Physical Review B, 73, Art. No. 184304 (2006).
    Abstract HTML Text
  14. A quasicontinuum method for deformations of carbon nanotubes
    J. Y. Park, Y. S. Cho, S. Y. Kim, S. Jun and S. Im
    Computer Modeling in Engineering & Sciences, 11, 61–72 (2006).
    Abstract HTML Text
  15. From electrons to finite elements: A concurrent multiscale approach for metals
    G. Lu, E. B. Tadmor and E. Kaxiras
    Physical Review B, 73, Art. No. 024108 (2006).
    Abstract HTML Text
  16. Atomistic based continuum investigation of plastic deformation in nanocrystalline copper
    D. H. Warner, F. Sansoz and J. F. Molinari
    International Journal of Plasticity, 22, 754–774 (2006).
    Abstract HTML Text

2005

  1. Coarse-grained molecular dynamics: Nonlinear finite elements and finite temperature
    R. E. Rudd and J. Q. Broughton
    Physical Review B, 72, 144104 (2005).
    Abstract HTML Text
  2. Coarse-grained free-energy-functional treatment of quasistatic multiscale processes in heterogeneous materials
    H. Zhou, R. Feng, D. J. Diestler and X. C. Zeng
    Journal of Chemical Physics, 123, 164109 (2005).
    Abstract HTML Text
  3. Multiscale enrichment based on partition of unity
    J. Fish and Z. Yuan
    International Journal for Numerical Methods in Engineering, 62, 1341–1359 (2005).
    Abstract HTML Text
  4. Continuum mechanics modeling and simulation of carbon nanotubes
    M. Arroyo and T. Belytschko
    Meccanica, 40, 455–469 (2005).
    Abstract HTML Text
  5. Inhomogeneous multiscale dynamics in harmonic lattices
    D. Cubero and S. N. Yaliraki
    Journal of Chemical Physics, 122, 034108 (2005).
    Abstract HTML Text
  6. A finite-temperature dynamic coupled atomistic/discrete dislocation method
    S. Qu, V. Shastry, W. A. Curtin and R. E. Miller
    Modelling and Simulation in Materials Science and Engineering, 13, 1101–1118 (2005).
    Abstract HTML Text
  7. Multiscale simulation of surface step effects on nanoindentation
    D. B. Shan, L. Yuan and B. Guo
    Materials Science and Engineering A-Structural Materials Properties Microstructu, 412, 264–270 (2005).
    Abstract HTML Text
  8. Analysis of a prototypical multiscale method coupling atomistic and continuum mechanics
    X. Blanc, C. Le Bris and F. Legoll
    ESAIM-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et, 39, 797–826 (2005).
    Abstract HTML Text
  9. Prediction of dislocation nucleation during nanoindentation by the orbital-free density functional theory local quasi-continuum method
    R. L. Hayes, M. Fago, M. Ortiz M and E. A. Carter
    Multiscale Modeling & Simulation, 4, 359–389 (2005).
    Abstract HTML Text
  10. Derivation of higher order gradient continuum models from atomistic models for crystalline solids
    M. Arndt and M. Griebel
    Multiscale Modeling & Simulation, 4, 531–562 (2005).
    Abstract HTML Text
  11. Finite-temperature quasicontinuum: Molecular dynamics without all the atoms
    L. M. Dupuy, E. B. Tadmor, R. E. Miller and R. Phillips
    Physical Review Letters, 95, Art. No. 060202 (2005).
    Abstract HTML Text
  12. Nanovoid deformation in aluminum under simple shear
    J. Marian, J. Knap and M. Ortiz
    Acta Materialia, 53, 2893–2900 (2005).
    Abstract HTML Text
  13. A new quasi-continuum constitutive model for crack growth in an isotropic solid
    Z. N. Zhang and X. R. Ge
    European Journal of Mechanics A-Solids, 24, 243–252 (2005).
    Abstract HTML Text
  14. Quasicontinuum analysis of Cu/Al2O3 interface via quasicontinuum analysis
    Y. Hangai, N. Yoshikawa, S. V. Dmitriev, M. Kohyama and S. Tanaka
    Journal of the Japan Institute of Metals, 69, 194–197 (2005).
    Abstract HTML Text
  15. Mechanical behavior of Sigma tilt grain boundaries in nanoscale Cu and Al: A quasicontinuum study
    F. Sansoz and J. F. Molinari
    Acta Materialia, 53, 1931–1944 (2005).
    Abstract HTML Text
  16. Large scale atomistic simulation of Cu/Al2O3 interface via quasicontinuum analysis
    Y. Hangai, N. Yoshikawa, S. V. Dmitriev, M. Kohyama and S. Tanaka
    Journal of the Japan Institute of Metals, 69, 90–95 (2005).
    Abstract HTML Text

2004

  1. Incidence of atomic shuffling on the shear and decohesion behavior of a symmetric tilt grain boundary in copper
    F. Sansoz and J. F. Molinari
    Scripta Materialia, 50, 1283–1288 (2004).
    Abstract HTML Text
  2. An extension of the quasicontinuum treatment of multiscale solid systems to nonzero temperature
    D. J. Diestler, Z. B. Wu and X. C. Zeng
    Journal of Chemical Physics, 121, 9279–9282 (2004).
    Abstract HTML Text
  3. Density-functional-theory-based local quasicontinuum method: Prediction of dislocation nucleation
    M. Fago, R. L. Hayes, E. A. Carter and M. Ortiz
    Physical Review B, 70, Art. No. 100102 (2004).
    Abstract HTML Text
  4. Matching conditions in the quasicontinuum method: Removal of the error introduced at the interface between the coarse-grained and fully atomistic region
    T. Shimokawa, J. J. Mortensen, J. Schiotz J and K. W. Jacobsen
    Physical Review B, 69, Art. No. 214104 (2004).
    Abstract HTML Text
  5. Quasicontinuum models for interface multiscale model
    Y. Hangai and N. Yoshikawa
    Key Engineering Materials, 261-263, 729–734 Part 1 and 2 (2004).
    Abstract HTML Text
  6. Multiscale plasticity modeling: coupled atomistics and discrete dislocation mechanics
    L. E. Shilkrot, R. E. Miller and W. A. Curtin
    Journal of the Mechanics and Physics of Solids, 52, 755–787 (2004).
    Abstract HTML Text
  7. Analysis of multiscale methods
    W. E and P. B. Ming
    Journal of Computational Mathematics, 22, 210–219 (2004).
    Abstract HTML Text
  8. Predictive modeling of nanoindentation-induced homogeneous dislocation nucleation in copper
    T. Zhu, J. Li, K. J. Van Vliet, S. Ogata, S. Yip and S. Suresh
    Journal of the Mechanics and Physics of Solids, 52, 691–724 (2004).
    Abstract HTML Text
  9. Finite element implementation of virtual internal bond model for simulating crack behavior
    G. Thiagarajan, K. J. Hsia and Y. Huang
    Engineering Fracture Mechanics, 71, 401–423 (2004).
    Abstract HTML Text

2003

  1. Nonlinear mechanical response and rippling of thick multiwalled carbon nanotubes
    M. Arroyo and T. Belytschko
    Physical Review Letters, 45, 215505 (2003).
    Abstract HTML Text
  2. A constrained sequential-lamination algorithm for the simulation of sub-grid microstructure in martensitic materials
    S. Aubry, M. Fago and M. Ortiz
    Computer Methods in Applied Mechanics and Engineering, 192, 2823–2843 (2003).
    Abstract HTML Text
  3. On higher gradients in continuum-atomistic modelling
    R. Sunyk and P. Steinmann
    International Journal of Solids and Structures, 40, 6877–6896 (2003).
    Abstract HTML Text
  4. Modeling fracture in nanomaterials via a virtual internal bond method
    H. J. Gao and B. H. Ji
    Engineering Fracture Mechanics, 70, 1777–1791 (2003).
    Abstract HTML Text
  5. Atomistic/continuum coupling in computational materials science
    W. A. Curtin and R. E. Miller
    Modelling and Simulation in Materials Science and Engineering, 11, R33–R68 (2003).
    Abstract HTML Text
  6. Theoretical and numerical analysis for the quasi-continuum approximation of a material particle model
    P. Lin
    Mathematics of Computation, 72, 657–675 (2003).
    Abstract HTML Text
  7. Multi-scale modeling strategies in materials science - The quasicontinuum method
    V. B. Shenoy
    Bulletin of Materials Science, 26, 53–62 (2003).
    Abstract HTML Text
  8. Coarse-graining description of solid systems at nonzero temperature
    Z. B. Wu, D. J. Diestler, R. Feng and X. C. Zeng
    Journal of Chemical Physics, 119, 8013–8023 (2003).
    Abstract HTML Text
  9. Effect of indenter-radius size on Au(001) nanoindentation
    J. Knap and M. Ortiz
    Physical Review Letters, 90, 226102 (2003).
    Abstract HTML Text
  10. A peierls criterion for the onset of deformation twinning at a crack tip
    E. B. Tadmor and S. Hai
    Journal of the Mechanics and Physics of Solids, 51, 765–793 (2003).
    Abstract HTML Text
  11. Deformation twinning at aluminum crack tips
    S. Hai and E. B. Tadmor
    Acta Materialia, 51, 117–131 (2003).
    Abstract HTML Text
  12. Mixed atomistic/continuum methods: static and dynamic quasicontinuum methods
    Eds A. Finel, D. Maziere, M. Veron
    Proceedings of the NATO Conference "Thermodynamics, Microstructures and Plasticity", (Kluwer, Dortrecht, 2003), (2003).
    Abstract HTML Text

2002

  1. A coupled atomistic/continuum model of defects in solids
    L. E. Shilkrot and W. A. Curtin and R. E. Miller
    Journal of the Mechanics and Physics of Solids, 50, 2085–2106 (2002).
    Abstract HTML Text
  2. Modeling the full monty: baring the nature of surfaces across time and space
    F. Starrost and E. A. Carter
    Surface Science, 500, 323–346 (2002).
    Abstract HTML Text
  3. Polarization switching in PbTiO3: An ab initio finite element simulation
    E. B. Tadmor, U. V. Waghmare, G. S. Smith and E. Kaxiras
    Acta Materialia, 50, 2989–3002 (2002).
    Abstract HTML Text
  4. Coarse-grained descriptions of multiple scale processes in solid systems
    D. J. Diestler
    Physical Review B, 66, 184104 (2002).
    Abstract HTML Text
  5. The quasicontinuum method revisited
    J. J. Mortensen, J. Schiotz and K. W. Jacobsen
    Challenges in Molecular Simulations, 4, 119 (2002).
    Abstract HTML Text
  6. An atomistic-based finite deformation membrane for single layer crystalline films
    M. Arroyo and T. Belytschko
    Journal of the Mechanics and Physics of Solids, 50, 1941–1977 (2002).
    Abstract HTML Text
  7. Quasicontinuum representations of atomic-scale mechanics: From proteins to dislocations
    R. Phillips, M. Dittrich and K.Schulten
    Annual Review of Materials Research, 32, 219–233 (2002).
    Abstract HTML Text
  8. The quasicontinuum method: Overview, applications and current directions
    R. E. Miller and E. B. Tadmor
    Journal of Computer-Aided Materials Design, 9, 203–239 (2002).
    Abstract HTML Text
  9. The elastic modulus of single-wall carbon nanotubes: a continuum analysis incorporating interatomic potentials
    P. Zhang, Y. Huang, P. H. Geubelle, P. A. Klein and K. C. Hwang
    International Journal of Solids and Structures, 39, 3893–3906 (2002).
    Abstract HTML Text
  10. Fracture nucleation in single-wall carbon nanotubes under tension: A continuum analysis incorporating interatomic potentials
    P. Zhang, Y. Huang, H. Gao and K. C. Hwang
    Journal of Applied Mechanics, 69, 454–458 (2002).
    Abstract HTML Text
  11. Numerical simulation of cohesive fracture by the virtual-internal-bond model
    P. Zhang, P. A. Klein, Y. Huang, H. Gao and P. D. Wu
    Computer Modeling in Engineering and Sciences, 3, 263–289 (2002).
    Abstract HTML Text

2001

  1. Crack behavior at bi-crystal interfaces: A mixed atomistic and continuum approach
    A. R. Pillai and R. E. Miller
    Materials Research Society Symposium Proceedings, 653, Z2.9.1–Z2.9.7 (2001).
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  2. Multiscale simulations of silicon nanoindentation
    G. S. Smith, E. B. Tadmor, N. Bernstein and E. Kaxiras
    Acta Materialia, 49, 4089–4101 (2001).
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  3. An analysis of the quasicontinuum method
    J. Knap J and M. Ortiz
    Journal of the Mechanics and Physics of Solids, 49, 1899–1923 (2001).
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  4. Reconciliation of atomic-level and continuum notions concerning the interaction of dislocations and obstacles
    K. Hardikar, Vivek Shenoy and R. Phillips
    Journal of the Mechanics and Physics of Solids, 49, 1951–1967 (2001).
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  5. Formation and strength of dislocation junctions in FCC metals: A study by dislocation dynamics and atomistic simulations
    C. S. Shin, M. C. Fivel, D. Rodney, R. Phillips, V. B. Shenoy and L. Dupuy
    Journal de Physique IV, 11, 19–26 (2001).
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  6. Mixed atomistic continuum models of material behavior: The art of transcending atomistics and informing continua
    M. Ortiz, A. M. Cuitino, J. Knap and M. Koslowski
    MRS Bulletin, 26, 216–221 (2001).
    (no abstract)

2000

  1. Atomistic-continuum simulation of nano-indentation in molybdenum
    R. C. Picu
    Journal of Computer-Aided Materials Design, 7, 77–87 (2000).
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  2. Nucleation of dislocations beneath a plane strain indenter
    Vivek Shenoy, R. Phillips and E. B. Tadmor
    Journal of the Mechanics and Physics of Solids, 48, 649–673 (2000).
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  3. Multiscale simulation of loading and electrical resistance in silicon nanoindentation
    G. S. Smith, E. B. Tadmor and E. Kaxiras
    Physical Review Letters, 84, 1260–1263 (2000).
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1999

  1. Electronic structure boundary value problems without all of the atoms
    H. T. Johnson, R. Phillips and L. B. Freund
    Materials Research Society Symposium Proceedings, 538, 479–484 (1999).
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  2. Finite temperature quasicontinuum methods
    Vijay Shenoy, Vivek Shenoy and R. Phillips
    Materials Research Society Symposium Proceedings, 538, 465–471 (1999).
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  3. Hierarchical models of plasticity: dislocation nucleation and interaction
    R. Phillips, D. Rodney, Vivek Shenoy, E. B. Tadmor and M. Ortiz
    Modelling and Simulation in Materials Science and Engineering, 7, 769–780 (1999).
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  4. Nanoindentation and incipient plasticity
    E. B. Tadmor, R. Miller, R. Phillips and M. Ortiz
    Journal of Materials Research, 14, 2233–2250 (1999).
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  5. An adaptive finite element approach to atomic-scale mechanics — the quasicontinuum method
    V. B. Shenoy, R. Miller, E. B. Tadmor, D. Rodney, R. Phillips and M. Ortiz
    Journal of the Mechanics and Physics of Solids, 47, 611–642 (1999).
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  6. Structure and strength of dislocation junctions: An atomic level analysis
    D. Rodney and R. Phillips
    Physical Review Letters, 82, 1704–1707 (1999).
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  7. Mixed finite element and atomistic formulation for complex crystals
    E. B. Tadmor, G. S. Smith, N. Bernstein and E. Kaxiras
    Physical Review B, 59, 235–245 (1999).
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  8. Nanomechanics of defects in solids
    M. Ortiz and R. Phillips
    Advances in Applied Mechanics, 36, 1–79 (1999).
    (no abstract)

1998

  1. Quasicontinuum models of fracture and plasticity
    R. Miller, M. Ortiz, R. Phillips, V. B. Shenoy and E. B. Tadmor
    Engineering Fracture Mechanics, 61, 427–444 (1998).
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  2. Crack nucleation and growth as strain localization in a virtual-bond continuum
    P. Klein and H. Gao
    Engineering Fracture Mechanics, 61, 21–48 (1998).
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  3. Quasicontinuum simulation of fracture at the atomic scale
    R. Miller, E. B. Tadmor, R. Phillips and M. Ortiz
    Modelling and Simulation in Materials Science and Engineering, 6, 607–638 (1998).
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  4. Numerical simulation of crack growth in an isotropic solid with randomized internal cohesive bonds
    H. Gao and P. Klein
    Journal of the Mechanics and Physics of Solids, 46, 187–218 (1998).
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  5. Quasicontinuum models of interfacial structure and deformation
    V. B. Shenoy, R. Miller, E. B. Tadmor, R. Phillips and M. Ortiz
    Physical Review Letters, 80, 742–745 (1998).
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1996

  1. Mixed Atomistic and Continuum Models of Deformation in Solids
    E. B. Tadmor, R. Phillips and M. Ortiz
    Langmuir, 12, 4529–4534 (1996).
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  2. Quasicontinuum analysis of defects in solids
    E. B. Tadmor, M. Ortiz and R. Phillips
    Philosophical Magazine A, 73, 1529–1563 (1996).
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