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Acta Materialia, ISSN 1359-6454, 2005, Volume 53, Issue 7, pp. 1931 - 1944
Molecular simulations using the quasicontinuum method are performed to understand the mechanical response at the nanoscale of grain boundaries (GBs) under... 
Quasicontinuum method | Simulation | Nanocrystalline materials | Grain boundary structure | Grain boundary cohesion
Journal Article
Multiscale Modeling and Simulation, ISSN 1540-3459, 2013, Volume 11, Issue 3, pp. 766 - 794
  We present a [Gamma]-convergence analysis of the quasicontinuum method focused on the behavior of the approximate energy functionals in the continuum limit... 
Quasicontinuum method | Atomistic-To-continuum modelsł | Convergence
Journal Article
by Knap, J and Ortiz, M
Journal of the Mechanics and Physics of Solids, ISSN 0022-5096, 2001, Volume 49, Issue 9, pp. 1899 - 1923
Journal Article
Physica D: Nonlinear Phenomena, ISSN 0167-2789, 02/2019, Volume 389, pp. 24 - 50
We consider a monatomic nonlinear mass–spring chain with first and second-neighbor interactions and show that there is a parameter range where solitary waves... 
Nonlinear lattice | Quasicontinuum model | Modulation equation | Solitary waves | Second-neighbor interactions | MATHEMATICS, APPLIED | ENVELOPE SOLITONS | PHYSICS, MULTIDISCIPLINARY | APPROXIMATIONS | PHASE-TRANSITIONS | BREATHER | MODEL | PHYSICS, MATHEMATICAL | MOTION | DISCRETE | CHAINS
Journal Article
Engineering Fracture Mechanics, ISSN 0013-7944, 2008, Volume 75, Issue 17, pp. 4965 - 4972
By using the two-dimensional quasicontinuum method, the nanoindentation process on a single crystal copper thin film with surface roughness is simulated to... 
Quasicontinuum method | Nanohardness | Thin films | Surface roughness | Nanoindentation | QUASI-CONTINUUM METHOD | NANO-INDENTATION | SIZE | SIMULATION | DEFORMATION | MULTILAYERS | MECHANICS | SOLIDS | ELASTIC-MODULUS | HARDNESS
Journal Article
Computational Materials Science, ISSN 0927-0256, 09/2017, Volume 137, pp. 162 - 170
Using quasicontinuum method (QCM), we study GB migration in the dissociated edge dislocation interacting with a symmetrical tilt grain boundary (STGB) upon the... 
Quasicontinuum method | Edge dislocation | Interaction | Migration | Grain boundary
Journal Article
by Liao, MJ and Lin, P and Zhang, L
COMMUNICATIONS IN COMPUTATIONAL PHYSICS, ISSN 1815-2406, 01/2020, Volume 27, Issue 1, pp. 198 - 226
In this paper, we develop the residual based a posteriori error estimates and the corresponding adaptive mesh refinement algorithm for atomistic/continuum... 
2-BODY POTENTIALS | DERIVATION | coarse graining | quasicontinuum method | a posteriori error estimate | DEFECTS | MODELS | Atomistic models | QUASI-CONTINUUM APPROXIMATION | CONVERGENCE | PHYSICS, MATHEMATICAL | atomistic-to-continuum coupling
Journal Article
Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 09/2014, Volume 279, pp. 29 - 45
We present a practical implementation of an energy-based atomistic-to-continuum (a/c) coupling scheme without ghost forces, and numerical tests evaluating its... 
Quasi-nonlocal | Error analysis | Quasicontinuum | Atomistic/continuum coupling | 2-BODY POTENTIALS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | Ghosts | Accuracy | Joining | Mathematical models | Computer simulation | Mathematics - Numerical Analysis
Journal Article
Journal of the Mechanics and Physics of Solids, ISSN 0022-5096, 03/2014, Volume 64, Issue 1, pp. 154 - 169
Lattice models and discrete networks naturally describe mechanical phenomena at the mesoscale of fibrous materials. A disadvantage of lattice models is their... 
Quasicontinuum method | Virtual power | Multiscale | Lattice model | Dissipation | PHYSICS, CONDENSED MATTER | MATERIALS SCIENCE, MULTIDISCIPLINARY | FABRICS | VARIATIONAL FORMULATION | SIMULATION | FAILURE | CONCRETE | DAMAGE | FIBER NETWORKS | MECHANICS | LARGE-DEFORMATION | SOLIDS | Networks | Crystal defects | Mathematical analysis | Lattices | Quality control | Mathematical models | Computational efficiency
Journal Article
Journal of the Mechanics and Physics of Solids, ISSN 0022-5096, 2008, Volume 56, Issue 4, pp. 1417 - 1449
The aim of this paper is the development of equilibrium and non-equilibrium extensions of the quasicontinuum (QC) method. We first use variational mean-field... 
Variational calculus | Maximum entropy principle | Quasicontinuum | Finite-elements | Nanoindentation | PHYSICS, CONDENSED MATTER | maximum entropy principle | DEFECTS | variational calculus | quasicontinuum | finite-elements | THERMAL-EXPANSION | MATERIALS SCIENCE, MULTIDISCIPLINARY | nanoindentation | ARGON | MECHANICS | METALS | SOLIDS | NUCLEATION
Journal Article
Journal of the Mechanics and Physics of Solids, ISSN 0022-5096, 09/2015, Volume 82, Issue C, pp. 378 - 413
Journal Article
Journal of the Mechanics and Physics of Solids, ISSN 0022-5096, 10/2014, Volume 70, Issue 1, pp. 242 - 261
The quasicontinuum (QC) method [Tadmor, E.B., Phillips, R., Ortiz, M., 1996. Mixed atomistics and continuum models of deformation in solids. Langmuir 12,... 
Quasicontinuum method | Summation rule | Atomistic model | Summation | Multiscale | PHYSICS, CONDENSED MATTER | MECHANICS | MODELS | MATERIALS SCIENCE, MULTIDISCIPLINARY | Interpolation | Computer simulation | Quality control | Nuclear power generation | Mathematical models | Computational efficiency | Sampling | Three dimensional
Journal Article
by Yu, WS and Wang, ZQ and Shen, SP
COMPUTATIONAL MATERIALS SCIENCE, ISSN 0927-0256, 09/2017, Volume 137, pp. 162 - 170
Using quasicontinuum method (QCM), we study GB migration in the dissociated edge dislocation interacting with a Sigma 11 symmetrical tilt grain boundary (STGB)... 
Quasicontinuum method | Interaction | Migration | MATERIALS SCIENCE, MULTIDISCIPLINARY | FCC METALS | Edge dislocation | COHERENT TWIN BOUNDARIES | SCREW DISLOCATIONS | DEFORMATION | CENTERED-CUBIC METALS | SLIP TRANSFER MECHANISMS | ATOMISTIC SIMULATION | TILT BOUNDARY | Grain boundary | LATTICE DISLOCATIONS | INTERATOMIC POTENTIALS
Journal Article
International Journal for Numerical Methods in Engineering, ISSN 0029-5981, 03/2019, Volume 117, Issue 10, pp. 1059 - 1078
Journal Article
Computers and Structures, ISSN 0045-7949, 11/2017, Volume 192, pp. 50 - 70
The quasicontinuum (QC) method, originally proposed by Tadmor, Ortiz and Phillips in 1996, is a computational technique that can efficiently handle regular... 
Finite elements | Multiscale modelling | Quasicontinuum | Elastic-brittle material | Lattice model | MECHANICS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, CIVIL | BOND FAILURE | FRACTURE MODEL
Journal Article
Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 01/2013, Volume 253, pp. 160 - 168
► Accurately couple a point-based atomistic region to a volume-based continuum region. ► Theoretical optimization of the blending function and mesh refinement.... 
Quasicontinuum method | Atomistic-to-continuum coupling | Coarse graining | Atomistic models | APPROXIMATION | PARTICLE | ARLEQUIN METHOD | POTENTIALS | FRACTURE | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | METALS | SOLIDS | FRENKEL-KONTOROVA MODEL | ERROR
Journal Article
Journal of the Mechanics and Physics of Solids, ISSN 0022-5096, 2010, Volume 58, Issue 2, pp. 86 - 102
An effective multiscale computing scheme based on QM/QC (quantum mechanics/quasicontinuum) is applied for simulation of Carbon nanotubes (CNTS) mechanics.... 
D. Multiscale computing | A. Fracture | B. Carbon nanotubes | C. Quasicontinuum | ROOM-TEMPERATURE | PHYSICS, CONDENSED MATTER | DEFECTS | HYDROCARBONS | Multiscale computing | DIAMOND | MATERIALS SCIENCE, MULTIDISCIPLINARY | Carbon nanotubes | Fracture | STRENGTH | POTENTIALS | Quasicontinuum | DEFORMATION | SINGLE-WALL | MECHANICS | SYSTEMS
Journal Article
IMA Journal of Numerical Analysis, ISSN 0272-4979, 04/2012, Volume 32, Issue 2, pp. 373 - 393
The accurate and efficient computation of the deformation of crystalline solids requires the coupling of atomistic models near lattice defects such as cracks... 
Finite-range interaction | Hybrid method | Coupling | Quasicontinuum | Quasinonlocal | Atomistic-to-continuum | coupling | MATHEMATICS, APPLIED | hybrid method | quasicontinuum | APPROXIMATION | ERROR | finite-range interaction | quasinonlocal | atomistic-to-continuum
Journal Article
ESAIM: Mathematical Modelling and Numerical Analysis, ISSN 0764-583X, 11/2017, Volume 51, Issue 6, pp. 2263 - 2288
We formulate a patch test consistent atomistic-to-continuum coupling (a/c) scheme that employs a second-order (potentially higher-order) finite element method... 
Quasicontinuum method | Atomistic-to-continuum coupling | Error analysis | Coarse graining | Atomistic models | MATHEMATICS, APPLIED | coarse graining | quasicontinuum method | error analysis | atomistic-to-continuum coupling | Finite element method | Nonlinear programming | Coupling | Continuum modeling | Patch tests
Journal Article
ESAIM: Mathematical Modelling and Numerical Analysis, ISSN 0764-583X, 5/2009, Volume 43, Issue 3, pp. 591 - 604
The atomistic to continuum interface for quasicontinuum energies exhibits nonzero forces under uniform strain that have been called ghost forces. In this... 
Ghost force | Atomistic to continuum | Quasicontinuum | atomistic to continuum | MATHEMATICS, APPLIED | MECHANICS | DEFECTS | APPROXIMATION | ghost force | ADAPTIVITY | FRENKEL-KONTOROVA MODEL
Journal Article