Concurrent atomistic-continuum modeling of crystalline materials

Chen, Youping; Shabanov, Sergei; McDowell, David L.

doi:10.1063/1.5099653

Concurrent atomistic-continuum modeling of crystalline materials

Journal Article · Mon Sep 09 00:00:00 EDT 2019 · Journal of Applied Physics

DOI:https://doi.org/10.1063/1.5099653· OSTI ID:1610864

^[1]; Shabanov, Sergei ^[2]; McDowell, David L. ^[3]

Univ. of Florida, Gainesville, FL (United States); DOE/OSTI
Univ. of Florida, Gainesville, FL (United States)
Georgia Inst. of Technology, Atlanta, GA (United States)

In the work reported here, we present a concurrent atomistic-continuum (CAC) method for modeling and simulation of crystalline materials. The CAC formulation extends the Irving-Kirkwood procedure for deriving transport equations and fluxes for homogenized molecular systems to that for polyatomic crystalline materials by employing a concurrent two-level description of the structure and dynamics of crystals. A multiscale representation of conservation laws is formulated, as a direct consequence of Newton's second law, in terms of instantaneous expressions of unit cell-averaged quantities using the mathematical theory of distributions. Finite element (FE) solutions to the conservation equations, as well as fluxes and temperature in the FE representation, are introduced, followed by numerical examples of the atomic-scale structure of interfaces, dynamics of fracture and dislocations, and phonon thermal transport across grain boundaries. In addition to providing a methodology for concurrent multiscale simulation of transport processes under a single theoretical framework, the CAC formulation can also be used to compute fluxes (stress and heat flux) in atomistic and coarse-grained atomistic simulations.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of Florida, Gainesville, FL (United States)

Sponsoring Organization:: National Science Foundation (NSF); USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

Grant/Contract Number:: SC0006539

OSTI ID:: 1610864

Journal Information:: Journal of Applied Physics, Journal Name: Journal of Applied Physics Journal Issue: 10 Vol. 126; ISSN JAPIAU; ISSN 0021-8979

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

References (69)

Microcontinuum Field Theories Eringen, A. Cemal https://doi.org/10.1007/978-1-4612-0555-5	book	January 1999
Micro-structure in linear elasticity Mindlin, R. D. Archive for Rational Mechanics and Analysis, Vol. 16, Issue 1 https://doi.org/10.1007/BF00248490	journal	January 1964
Atomistic counterpart of micromorphic theory Chen, Y.; Lee, J. D.; Eskandarian, A. Acta Mechanica, Vol. 161, Issue 1-2 https://doi.org/10.1007/s00707-002-0981-2	journal	March 2003
Comparing EAM Potentials to Model Slip Transfer of Sequential Mixed Character Dislocations Across Two Symmetric Tilt Grain Boundaries in Ni Xu, Shuozhi; Xiong, Liming; Chen, Youping JOM, Vol. 69, Issue 5 https://doi.org/10.1007/s11837-017-2302-1	journal	March 2017
Examining the physical foundation of continuum theories from the viewpoint of phonon dispersion relation Chen, Youping; Lee, James D.; Eskandarian, Azim International Journal of Engineering Science, Vol. 41, Issue 1 https://doi.org/10.1016/S0020-7225(02)00141-6	journal	January 2003
Constitutive relations of micromorphic thermoplasticity Lee, James D.; Chen, Youping International Journal of Engineering Science, Vol. 41, Issue 3-5 https://doi.org/10.1016/S0020-7225(02)00240-9	journal	March 2003
Determining material constants in micromorphic theory through phonon dispersion relations Chen, Youping; Lee, James D. International Journal of Engineering Science, Vol. 41, Issue 8 https://doi.org/10.1016/S0020-7225(02)00321-X	journal	May 2003
Connecting molecular dynamics to micromorphic theory. (I). Instantaneous and averaged mechanical variables Chen, Youping; Lee, James D. Physica A: Statistical Mechanics and its Applications, Vol. 322 https://doi.org/10.1016/S0378-4371(02)01921-0	journal	May 2003
Connecting molecular dynamics to micromorphic theory. (II). Balance laws Chen, Youping; Lee, James D. Physica A: Statistical Mechanics and its Applications, Vol. 322 https://doi.org/10.1016/S0378-4371(02)01922-2	journal	May 2003
Computation of grain boundary stiffness and mobility from boundary fluctuations Foiles, S.; Hoyt, J. Acta Materialia, Vol. 54, Issue 12 https://doi.org/10.1016/j.actamat.2006.03.037	journal	July 2006
A concurrent scheme for passing dislocations from atomistic to continuum domains Xiong, Liming; Deng, Qian; Tucker, Garritt Acta Materialia, Vol. 60, Issue 3 https://doi.org/10.1016/j.actamat.2011.11.002	journal	February 2012
Concurrent atomistic and continuum simulation of strontium titanate Yang, Shengfeng; Xiong, Liming; Deng, Qian Acta Materialia, Vol. 61, Issue 1 https://doi.org/10.1016/j.actamat.2012.09.032	journal	January 2013
Coarse-grained elastodynamics of fast moving dislocations Xiong, Liming; Rigelesaiyin, Ji; Chen, Xiang Acta Materialia, Vol. 104 https://doi.org/10.1016/j.actamat.2015.11.037	journal	February 2016
Shear stress- and line length-dependent screw dislocation cross-slip in FCC Ni Xu, Shuozhi; Xiong, Liming; Chen, Youping Acta Materialia, Vol. 122 https://doi.org/10.1016/j.actamat.2016.10.005	journal	January 2017
Ballistic-diffusive phonon heat transport across grain boundaries Chen, Xiang; Li, Weixuan; Xiong, Liming Acta Materialia, Vol. 136 https://doi.org/10.1016/j.actamat.2017.06.054	journal	September 2017
Phonon spectrum and phonon focusing in coarse-grained atomistic simulations Li, Yang; Li, Weixuan; Chen, Xiang Computational Materials Science, Vol. 162 https://doi.org/10.1016/j.commatsci.2019.02.020	journal	May 2019
A coherent phonon pulse model for transient phonon thermal transport Chen, Xiang; Chernatynskiy, Aleksandr; Xiong, Liming Computer Physics Communications, Vol. 195 https://doi.org/10.1016/j.cpc.2015.05.008	journal	October 2015
Assessment of atomistic coarse-graining methods Chen, Youping; Zimmerman, Jonathan; Krivtsov, Anton International Journal of Engineering Science, Vol. 49, Issue 12 https://doi.org/10.1016/j.ijengsci.2011.03.018	journal	December 2011
Coarse-graining atomistic dynamics of brittle fracture by finite element method Deng, Qian; Xiong, Liming; Chen, Youping International Journal of Plasticity, Vol. 26, Issue 9 https://doi.org/10.1016/j.ijplas.2010.04.007	journal	September 2010
Coarse-grained atomistic simulations of dislocations in Al, Ni and Cu crystals Xiong, Liming; Deng, Qian; Tucker, Garritt J. International Journal of Plasticity, Vol. 38 https://doi.org/10.1016/j.ijplas.2012.05.002	journal	November 2012
Sub-THz Phonon drag on dislocations by coarse-grained atomistic simulations Xiong, Liming; McDowell, David L.; Chen, Youping International Journal of Plasticity, Vol. 55 https://doi.org/10.1016/j.ijplas.2013.11.004	journal	April 2014
Concurrent atomistic–continuum simulations of dislocation–void interactions in fcc crystals Xiong, Liming; Xu, Shuozhi; McDowell, David L. International Journal of Plasticity, Vol. 65 https://doi.org/10.1016/j.ijplas.2014.08.002	journal	February 2015
Atomistic viewpoint of the applicability of microcontinuum theories Chen, Youping; Lee, James D.; Eskandarian, Azim International Journal of Solids and Structures, Vol. 41, Issue 8 https://doi.org/10.1016/j.ijsolstr.2003.11.030	journal	April 2004
Passing waves from atomistic to continuum Chen, Xiang; Diaz, Adrian; Xiong, Liming Journal of Computational Physics, Vol. 354 https://doi.org/10.1016/j.jcp.2017.10.038	journal	February 2018
Coarse-grained atomistic simulation of dislocations Xiong, Liming; Tucker, Garritt; McDowell, David L. Journal of the Mechanics and Physics of Solids, Vol. 59, Issue 2 https://doi.org/10.1016/j.jmps.2010.11.005	journal	February 2011
An analysis of key characteristics of the Frank-Read source process in FCC metals Xu, Shuozhi; Xiong, Liming; Chen, Youping Journal of the Mechanics and Physics of Solids, Vol. 96 https://doi.org/10.1016/j.jmps.2016.08.002	journal	November 2016
Nucleation and growth of dislocation loops in Cu, Al and Si by a concurrent atomistic-continuum method Xiong, Liming; McDowell, David L.; Chen, Youping Scripta Materialia, Vol. 67, Issue 7-8 https://doi.org/10.1016/j.scriptamat.2012.07.026	journal	October 2012
Edge dislocations bowing out from a row of collinear obstacles in Al Xu, Shuozhi; Xiong, Liming; Chen, Youping Scripta Materialia, Vol. 123 https://doi.org/10.1016/j.scriptamat.2016.06.018	journal	October 2016
Effects of phonons on mobility of dislocations and dislocation arrays Chen, Xiang; Xiong, Liming; McDowell, David L. Scripta Materialia, Vol. 137 https://doi.org/10.1016/j.scriptamat.2017.04.033	journal	August 2017
Statistical Mechanics of Nonequilibrium Liquids Evans, Denis J.; Morriss, Gary https://doi.org/10.1017/CBO9780511535307	book	January 2008
Imaging Phonons Wolfe, James P. https://doi.org/10.1017/CBO9780511665424	book	January 1998
Imaging phonons Nicoletti, Olivia Nature Materials, Vol. 14, Issue 1 https://doi.org/10.1038/nmat4187	journal	December 2014
Sequential slip transfer of mixed-character dislocations across Σ3 coherent twin boundary in FCC metals: a concurrent atomistic-continuum study Xu, Shuozhi; Xiong, Liming; Chen, Youping npj Computational Materials, Vol. 2, Issue 1 https://doi.org/10.1038/npjcompumats.2015.16	journal	January 2016
Continuum predictions from molecular dynamics simulations: Shock waves Root, Seth; Hardy, Robert J.; Swanson, David R. The Journal of Chemical Physics, Vol. 118, Issue 7 https://doi.org/10.1063/1.1537243	journal	February 2003
The Statistical Mechanical Theory of Transport Processes I. General Theory Kirkwood, John G. The Journal of Chemical Physics, Vol. 14, Issue 3 https://doi.org/10.1063/1.1724117	journal	March 1946
The Statistical Mechanical Theory of Transport Processes. III. The Coefficients of Shear and Bulk Viscosity of Liquids Kirkwood, John G.; Buff, Frank P.; Green, Melvin S. The Journal of Chemical Physics, Vol. 17, Issue 10 https://doi.org/10.1063/1.1747099	journal	October 1949
The Statistical Mechanical Theory of Transport Processes. IV. The Equations of Hydrodynamics Irving, J. H.; Kirkwood, John G. The Journal of Chemical Physics, Vol. 18, Issue 6 https://doi.org/10.1063/1.1747782	journal	June 1950
Local stress and heat flux in atomistic systems involving three-body forces Chen, Youping The Journal of Chemical Physics, Vol. 124, Issue 5 https://doi.org/10.1063/1.2166387	journal	February 2006
Equations of Mathematical Physics Vladimirov, V. S.; Streit, Ludwig Physics Today, Vol. 24, Issue 10 https://doi.org/10.1063/1.3022385	journal	October 1971
Equations of Mathematical Physics Polozhiy, G. N.; Weiss, George Physics Today, Vol. 21, Issue 11 https://doi.org/10.1063/1.3034622	journal	November 1968
Reformulation of microscopic balance equations for multiscale materials modeling Chen, Youping The Journal of Chemical Physics, Vol. 130, Issue 13 https://doi.org/10.1063/1.3103887	journal	April 2009
Atomistic formulation of a multiscale field theory for nano/micro solids Chen, Y.; Lee, J. Philosophical Magazine, Vol. 85, Issue 33-35 https://doi.org/10.1080/14786430500362595	journal	November 2005
Concurrent atomistic–continuum simulation of polycrystalline strontium titanate Yang, Shengfeng; Zhang, Ning; Chen, Youping Philosophical Magazine, Vol. 95, Issue 24 https://doi.org/10.1080/14786435.2015.1076178	journal	August 2015
The fluctuation-dissipation theorem Kubo, R. Reports on Progress in Physics, Vol. 29, Issue 1 https://doi.org/10.1088/0034-4885/29/1/306	journal	January 1966
Coarse-grained simulations of single-crystal silicon Xiong, Liming; Chen, Youping Modelling and Simulation in Materials Science and Engineering, Vol. 17, Issue 3 https://doi.org/10.1088/0965-0393/17/3/035002	journal	February 2009
Trapping of hydrogen to lattice defects in nickel Angelo, J. E.; Moody, N. R.; Baskes, M. I. Modelling and Simulation in Materials Science and Engineering, Vol. 3, Issue 3 https://doi.org/10.1088/0965-0393/3/3/001	journal	May 1995
Concurrent atomistic and continuum simulation of bi-crystal strontium titanate with tilt grain boundary Yang, Shengfeng; Chen, Youping Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 471, Issue 2175 https://doi.org/10.1098/rspa.2014.0758	journal	March 2015
Asymmetry of the atomic-level stress tensor in homogeneous and inhomogeneous materials Rigelesaiyin, Ji; Diaz, Adrian; Li, Weixuan Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 474, Issue 2217 https://doi.org/10.1098/rspa.2018.0155	journal	September 2018
On the equivalence of the two foundational formulations for atomistic flux in inhomogeneous transport processes Diaz, Adrian; Davydov, Denis; Chen, Youping Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 475, Issue 2223 https://doi.org/10.1098/rspa.2018.0688	journal	March 2019
N processes, the relaxation-time approximation, and lattice thermal conductivity Armstrong, Baxter H. Physical Review B, Vol. 32, Issue 6 https://doi.org/10.1103/PhysRevB.32.3381	journal	September 1985
Interatomic potentials for monoatomic metals from experimental data and ab initio calculations Mishin, Y.; Farkas, D.; Mehl, M. J. Physical Review B, Vol. 59, Issue 5 https://doi.org/10.1103/PhysRevB.59.3393	journal	February 1999
Misfit-energy-increasing dislocations in vapor-deposited CoFe/NiFe multilayers Zhou, X. W.; Johnson, R. A.; Wadley, H. N. G. Physical Review B, Vol. 69, Issue 14 https://doi.org/10.1103/PhysRevB.69.144113	journal	April 2004
Assessing the applicability of quantum corrections to classical thermal conductivity predictions Turney, J. E.; McGaughey, A. J. H.; Amon, C. H. Physical Review B, Vol. 79, Issue 22 https://doi.org/10.1103/PhysRevB.79.224305	journal	June 2009
Defect energetics in SrTiO 3 symmetric tilt grain boundaries Lee, H. -S.; Mizoguchi, T.; Mistui, J. Physical Review B, Vol. 83, Issue 10 https://doi.org/10.1103/PhysRevB.83.104110	journal	March 2011
Heat flux vector in highly inhomogeneous nonequilibrium fluids Todd, B. D.; Daivis, Peter J.; Evans, Denis J. Physical Review E, Vol. 51, Issue 5 https://doi.org/10.1103/PhysRevE.51.4362	journal	May 1995
Pressure tensor for inhomogeneous fluids Todd, B. D.; Evans, Denis J.; Daivis, Peter J. Physical Review E, Vol. 52, Issue 2 https://doi.org/10.1103/PhysRevE.52.1627	journal	August 1995
Control-volume representation of molecular dynamics Smith, E. R.; Heyes, D. M.; Dini, D. Physical Review E, Vol. 85, Issue 5 https://doi.org/10.1103/PhysRevE.85.056705	journal	May 2012
Local momentum and heat fluxes in transient transport processes and inhomogeneous systems Chen, Youping; Diaz, Adrian Physical Review E, Vol. 94, Issue 5 https://doi.org/10.1103/PhysRevE.94.053309	journal	November 2016
Physical foundation and consistent formulation of atomic-level fluxes in transport processes Chen, Youping; Diaz, Adrian Physical Review E, Vol. 98, Issue 5 https://doi.org/10.1103/PhysRevE.98.052113	journal	November 2018
Nanoscale Dislocation Patterning in PbTe / PbSe ( 001 ) Lattice-Mismatched Heteroepitaxy Springholz, G.; Wiesauer, K. Physical Review Letters, Vol. 88, Issue 1 https://doi.org/10.1103/PhysRevLett.88.015507	journal	December 2001
Equations of Mathematical Physics Vladimirov, V. S.; Schroeck, Franklin E. American Journal of Physics, Vol. 39, Issue 12 https://doi.org/10.1119/1.1976723	journal	December 1971
The origin of the distinction between microscopic formulas for stress and Cauchy stress Chen, Youping EPL (Europhysics Letters), Vol. 116, Issue 3 https://doi.org/10.1209/0295-5075/116/34003	journal	November 2016
Accurate Interatomic Potentials for Ni, Al and Ni3Al Voter, Arthur F.; Chen, Shao Ping MRS Proceedings, Vol. 82 https://doi.org/10.1557/PROC-82-175	journal	January 1986
PyCAC: The concurrent atomistic-continuum simulation environment Xu, Shuozhi; Payne, Thomas G.; Chen, Hao Journal of Materials Research, Vol. 33, Issue 7 https://doi.org/10.1557/jmr.2018.8	journal	January 2018
A multiscale study of misfit dislocations in PbTe/PbSe(001) heteroepitaxy Li, Yang; Fan, Zhaochuan; Li, Weixuan Journal of Materials Research, Vol. 34, Issue 13 https://doi.org/10.1557/jmr.2019.69	journal	April 2019
A Coarse-Grained Atomistic Method for 3d Dynamic Fracture Simulation Deng, Qian; Chen, Youping International Journal for Multiscale Computational Engineering, Vol. 11, Issue 3 https://doi.org/10.1615/IntJMultCompEng.2013005442	journal	January 2013
Statistical Mechanics of Nonequilibrium Liquids Evans, Denis J.; Morriss, Gary P. ANU Press https://doi.org/10.22459/smnl.08.2007	book	January 2007
Equations of Mathematical Physics Thomee, Vidar; Vladimirov, V. S. Mathematics of Computation, Vol. 26, Issue 118 https://doi.org/10.2307/2005193	journal	April 1972
Validation of the Concurrent Atomistic-Continuum Method on Screw Dislocation/Stacking Fault Interactions Xu, Shuozhi; Xiong, Liming; Chen, Youping Crystals, Vol. 7, Issue 5 https://doi.org/10.3390/cryst7050120	journal	April 2017

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