每年出版 6 期
ISSN 打印: 1543-1649
ISSN 在线: 1940-4352
Indexed in
Error Control for Molecular Statics Problems
摘要
In this paper, we present an extension of goal-oriented error estimation and adaptation to the simulation of multiscale problems of molecular statics. Computable error estimates for the quasicontinuum method are developed with respect to specific quantities of interest, and an adaptive strategy based on these estimates is proposed for error control. The theoretical results are illustrated on a nanoindentation problem in which the quantity of interest is the force acting on the indenter. The promising capability of such error estimates and adaptive procedure for the solution of multiscale problems is demonstrated on numerical examples.
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Dobson Matthew, Luskin Mitchell, Ortner Christoph, Stability, Instability, and Error of the Force-based Quasicontinuum Approximation, Archive for Rational Mechanics and Analysis, 197, 1, 2010. Crossref
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Li Junwan, Mei Jifa, Ni Yushan, Lu Huaibao, Jiang Wugui, Two-dimensional quasicontinuum analysis of the strengthening and weakening effect of Cu/Ag interface on nanoindentation, Journal of Applied Physics, 108, 5, 2010. Crossref
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Dobson Matthew, Luskin Mitchell, An Optimal Order Error Analysis of the One-Dimensional Quasicontinuum Approximation, SIAM Journal on Numerical Analysis, 47, 4, 2009. Crossref
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Li Junwan, Ni Yushan, Wang Hongsheng, Mei Jifa, Effects of Crystalline Anisotropy and Indenter Size on Nanoindentation by Multiscale Simulation, Nanoscale Research Letters, 5, 2, 2010. Crossref
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Dobson M., Luskin M., Ortner C., Sharp Stability Estimates for the Force-Based Quasicontinuum Approximation of Homogeneous Tensile Deformation, Multiscale Modeling & Simulation, 8, 3, 2010. Crossref
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Arndt Marcel, Luskin Mitchell, Error Estimation and Atomistic-Continuum Adaptivity for the Quasicontinuum Approximation of a Frenkel–Kontorova Model, Multiscale Modeling & Simulation, 7, 1, 2008. Crossref
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Dobson Matthew, Luskin Mitchell, Iterative Solution of the Quasicontinuum Equilibrium Equations with Continuation, Journal of Scientific Computing, 37, 1, 2008. Crossref
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Bauman Paul T., Dhia Hachmi Ben, Elkhodja Nadia, Oden J. Tinsley, Prudhomme Serge, On the application of the Arlequin method to the coupling of particle and continuum models, Computational Mechanics, 42, 4, 2008. Crossref
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Prudhomme Serge, Chamoin Ludovic, Dhia Hachmi Ben, Bauman Paul T., An adaptive strategy for the control of modeling error in two-dimensional atomic-to-continuum coupling simulations, Computer Methods in Applied Mechanics and Engineering, 198, 21-26, 2009. Crossref
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Miller Ronald E, Tadmor E B, A unified framework and performance benchmark of fourteen multiscale atomistic/continuum coupling methods, Modelling and Simulation in Materials Science and Engineering, 17, 5, 2009. Crossref
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Bauman Paul T., Oden J. Tinsley, Prudhomme Serge, Adaptive multiscale modeling of polymeric materials with Arlequin coupling and Goals algorithms, Computer Methods in Applied Mechanics and Engineering, 198, 5-8, 2009. Crossref
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Larsson Fredrik, Runesson Kenneth, On two-scale adaptive FE analysis of micro-heterogeneous media with seamless scale-bridging, Computer Methods in Applied Mechanics and Engineering, 200, 37-40, 2011. Crossref
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Shapeev Alexander V., Consistent Energy-Based Atomistic/Continuum Coupling for Two-Body Potentials in One and Two Dimensions, Multiscale Modeling & Simulation, 9, 3, 2011. Crossref
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Dobson Matthew, Luskin Mitchell, An analysis of the effect of ghost force oscillation on quasicontinuum error, ESAIM: Mathematical Modelling and Numerical Analysis, 43, 3, 2009. Crossref
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Ben Dhia H., Chamoin Ludovic, Oden J. Tinsley, Prudhomme Serge, A new adaptive modeling strategy based on optimal control for atomic-to-continuum coupling simulations, Computer Methods in Applied Mechanics and Engineering, 200, 37-40, 2011. Crossref
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Arndt Marcel, Luskin Mitchell, Goal-oriented adaptive mesh refinement for the quasicontinuum approximation of a Frenkel-Kontorova model, Computer Methods in Applied Mechanics and Engineering, 197, 49-50, 2008. Crossref
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Dobson M., Luskin M., Ortner C., Iterative methods for the force-based quasicontinuum approximation: Analysis of a 1D model problem, Computer Methods in Applied Mechanics and Engineering, 200, 37-40, 2011. Crossref
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Bělík Pavel, Luskin Mitchell, Analysis of the Quasi-Nonlocal Approximation of Linear and Circular Chains in the Plane, Multiscale Modeling & Simulation, 9, 4, 2011. Crossref
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Van Koten Brian, Luskin Mitchell, Analysis of Energy-Based Blended Quasi-Continuum Approximations, SIAM Journal on Numerical Analysis, 49, 5, 2011. Crossref
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Dobson M., Luskin M., Ortner C., Accuracy of quasicontinuum approximations near instabilities, Journal of the Mechanics and Physics of Solids, 58, 10, 2010. Crossref
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Miller Ronald E., Tadmor Ellad B., Hybrid Continuum Mechanics and Atomistic Methods for Simulating Materials Deformation and Failure, MRS Bulletin, 32, 11, 2007. Crossref
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Dobson Matthew, Luskin Mitchell, Analysis of a force-based quasicontinuum approximation, ESAIM: Mathematical Modelling and Numerical Analysis, 42, 1, 2008. Crossref
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Oden J. Tinsley, Prudhomme Serge, Control of modeling error in calibration and validation processes for predictive stochastic models, International Journal for Numerical Methods in Engineering, 87, 1-5, 2011. Crossref
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Prudhomme S., Ben Dhia H., Bauman P.T., Elkhodja N., Oden J.T., Computational analysis of modeling error for the coupling of particle and continuum models by the Arlequin method, Computer Methods in Applied Mechanics and Engineering, 197, 41-42, 2008. Crossref
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Luskin M., Ortner C., Van Koten B., Formulation and optimization of the energy-based blended quasicontinuum method, Computer Methods in Applied Mechanics and Engineering, 253, 2013. Crossref
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Chamoin Ludovic, Desvillettes Laurent, Control of modeling errors in the coupling of linear transport and diffusion models, Computer Methods in Applied Mechanics and Engineering, 261-262, 2013. Crossref
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Chen Jingrun, García-Cervera Carlos J., Li Xiantao, An Atomistic/Continuum Coupling Method Using Enriched Bases, Multiscale Modeling & Simulation, 13, 3, 2015. Crossref
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Amelang J.S., Venturini G.N., Kochmann D.M., Summation rules for a fully nonlocal energy-based quasicontinuum method, Journal of the Mechanics and Physics of Solids, 82, 2015. Crossref
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Memarnahavandi Arash, Larsson Fredrik, Runesson Kenneth, A goal-oriented adaptive procedure for the quasi-continuum method with cluster approximation, Computational Mechanics, 55, 4, 2015. Crossref
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Tembhekar I., Amelang J. S., Munk L., Kochmann D. M., Automatic adaptivity in the fully nonlocal quasicontinuum method for coarse‐grained atomistic simulations, International Journal for Numerical Methods in Engineering, 110, 9, 2017. Crossref
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Rokoš O., Peerlings R. H. J., Zeman J., Beex L. A. A., An adaptive variational Quasicontinuum methodology for lattice networks with localized damage, International Journal for Numerical Methods in Engineering, 112, 2, 2017. Crossref
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Wu Xiaojie, Li Xiantao, Simulations of micron-scale fracture using atomistic-based boundary element method, Modelling and Simulation in Materials Science and Engineering, 25, 8, 2017. Crossref
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Chen Jingrun, García-Cervera Carlos J., An efficient multigrid strategy for large-scale molecular mechanics optimization, Journal of Computational Physics, 342, 2017. Crossref
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Bauman Paul T., Adowski Timothy R., Modeling Laser Attenuation in Reacting Flows Using Adaptive Finite Elements, 55th AIAA Aerospace Sciences Meeting, 2017. Crossref
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Wang Hao, Yang Siyao, Analysis of the Residual-Type and the Gradient Recovery-Type a Posteriori Error Estimators for a Consistent Atomistic-to-Continuum Coupling Method in One-Dimension, Multiscale Modeling & Simulation, 16, 2, 2018. Crossref
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Wang Hao, Liao Mingjie, Lin Ping, Zhang Lei, A Posteriori Error Estimation and Adaptive Algorithm for Atomistic/Continuum Coupling in Two Dimensions, SIAM Journal on Scientific Computing, 40, 4, 2018. Crossref
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Wang Hong Sheng, Ni Yu Shan, Lu Huai Bao, Quasicontinuum Analysis of Dislocation Propagation during Nanocontact, Advanced Materials Research, 941-944, 2014. Crossref
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Chen Huajie, Liao Mingjie, Wang Hao, Wang Yangshuai, Zhang Lei, Adaptive QM/MM coupling for crystalline defects, Computer Methods in Applied Mechanics and Engineering, 354, 2019. Crossref
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Luskin Mitchell, Ortner Christoph, Atomistic-to-continuum coupling, Acta Numerica, 22, 2013. Crossref
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Voyiadjis George Z., Faghihi Danial, Overview of Enhanced Continuum Theories for Thermal and Mechanical Responses of the Microsystems in the Fast-Transient Process, Journal of Engineering Materials and Technology, 136, 4, 2014. Crossref
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Voyiadjis George Z., Song Yooseob, Open issues in strain gradient continuum plasticity and other approaches to address size effects, in Gradient-Enhanced Continuum Plasticity, 2020. Crossref
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Li Junwan, Lu Huaibao, Ni Yushan, Mei Jifa, Quasicontinuum study the influence of misfit dislocation interactions on nanoindentation, Computational Materials Science, 50, 11, 2011. Crossref
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Wang Yangshuai, Chen Huajie, Liao Mingjie, Ortner Christoph, Wang Hao, Zhang Lei, A Posteriori Error Estimates for Adaptive QM/MM Coupling Methods, SIAM Journal on Scientific Computing, 43, 4, 2021. Crossref
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Rokoš O., Peerlings R.H.J., Zeman J., eXtended variational quasicontinuum methodology for lattice networks with damage and crack propagation, Computer Methods in Applied Mechanics and Engineering, 320, 2017. Crossref