Concurrent atomistic-continuum modeling of crystalline materials

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

doi:10.1063/1.5099653

Title: Concurrent atomistic-continuum modeling of crystalline materials

Abstract

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.

Authors:

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

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

Publication Date:: Mon Sep 09 00:00:00 EDT 2019

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

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES); National Science Foundation (NSF)

OSTI Identifier:: 1610864

Grant/Contract Number:: SC0006539; CMMI 1761553; CMMI 1761512

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Applied Physics

Additional Journal Information:: Journal Volume: 126; Journal Issue: 10; Journal ID: ISSN 0021-8979

Publisher:: American Institute of Physics (AIP)

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Physics

Citation Formats


                    Chen, Youping, Shabanov, Sergei, and McDowell, David L. Concurrent atomistic-continuum modeling of crystalline materials.  United States: N. p., 2019. 
Web.  doi:10.1063/1.5099653.

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                    Chen, Youping, Shabanov, Sergei, & McDowell, David L. Concurrent atomistic-continuum modeling of crystalline materials.  United States.  https://doi.org/10.1063/1.5099653

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                    Chen, Youping, Shabanov, Sergei, and McDowell, David L. Mon .  
"Concurrent atomistic-continuum modeling of crystalline materials".  United States.  https://doi.org/10.1063/1.5099653.  https://www.osti.gov/servlets/purl/1610864.

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@article{osti_1610864,

  title        = {Concurrent atomistic-continuum modeling of crystalline materials},

  author       = {Chen, Youping and Shabanov, Sergei and McDowell, David L.},

  abstractNote = {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.},

  doi          = {10.1063/1.5099653},

  journal      = {Journal of Applied Physics},

  number       = 10,

  volume       = 126,

  place        = {United States},

  year         = {Mon Sep 09 00:00:00 EDT 2019},

  month        = {Mon Sep 09 00:00:00 EDT 2019}

}

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Title: Concurrent atomistic-continuum modeling of crystalline materials

Abstract

Citation Formats

A concurrent scheme for passing dislocations from atomistic to continuum domains journal, February 2012

Local stress and heat flux in atomistic systems involving three-body forces journal, February 2006

Heat flux vector in highly inhomogeneous nonequilibrium fluids journal, May 1995

Shear stress- and line length-dependent screw dislocation cross-slip in FCC Ni journal, January 2017

Coarse-grained atomistic simulation of dislocations journal, February 2011

Accurate Interatomic Potentials for Ni, Al and Ni3Al journal, January 1986

Concurrent atomistic and continuum simulation of strontium titanate journal, January 2013

Connecting molecular dynamics to micromorphic theory. (II). Balance laws journal, May 2003

A coherent phonon pulse model for transient phonon thermal transport journal, October 2015

Equations of Mathematical Physics journal, April 1972

A multiscale study of misfit dislocations in PbTe/PbSe(001) heteroepitaxy journal, April 2019

Continuum predictions from molecular dynamics simulations: Shock waves journal, February 2003

Sub-THz Phonon drag on dislocations by coarse-grained atomistic simulations journal, April 2014

Equations of Mathematical Physics journal, December 1971

On the equivalence of the two foundational formulations for atomistic flux in inhomogeneous transport processes journal, March 2019

The Statistical Mechanical Theory of Transport Processes. IV. The Equations of Hydrodynamics journal, June 1950

Local momentum and heat fluxes in transient transport processes and inhomogeneous systems journal, November 2016

Micro-structure in linear elasticity journal, January 1964

Coarse-grained elastodynamics of fast moving dislocations journal, February 2016

Equations of Mathematical Physics journal, November 1968

Pressure tensor for inhomogeneous fluids journal, August 1995

A Coarse-Grained Atomistic Method for 3d Dynamic Fracture Simulation journal, January 2013

Microcontinuum Field Theories book, January 1999

Coarse-grained atomistic simulations of dislocations in Al, Ni and Cu crystals journal, November 2012

Nanoscale Dislocation Patterning in PbTe / PbSe ( 001 ) Lattice-Mismatched Heteroepitaxy journal, December 2001

Atomistic viewpoint of the applicability of microcontinuum theories journal, April 2004

Concurrent atomistic–continuum simulation of polycrystalline strontium titanate journal, August 2015

Effects of phonons on mobility of dislocations and dislocation arrays journal, August 2017

Examining the physical foundation of continuum theories from the viewpoint of phonon dispersion relation journal, January 2003

Asymmetry of the atomic-level stress tensor in homogeneous and inhomogeneous materials journal, September 2018

Imaging phonons journal, December 2014

The fluctuation-dissipation theorem journal, January 1966

Atomistic formulation of a multiscale field theory for nano/micro solids journal, November 2005

The Statistical Mechanical Theory of Transport Processes. III. The Coefficients of Shear and Bulk Viscosity of Liquids journal, October 1949

Coarse-graining atomistic dynamics of brittle fracture by finite element method journal, September 2010

Reformulation of microscopic balance equations for multiscale materials modeling journal, April 2009

Imaging Phonons book, January 1998

Statistical Mechanics of Nonequilibrium Liquids book, January 2008

Connecting molecular dynamics to micromorphic theory. (I). Instantaneous and averaged mechanical variables journal, May 2003

Comparing EAM Potentials to Model Slip Transfer of Sequential Mixed Character Dislocations Across Two Symmetric Tilt Grain Boundaries in Ni journal, March 2017

The Statistical Mechanical Theory of Transport Processes I. General Theory journal, March 1946

Physical foundation and consistent formulation of atomic-level fluxes in transport processes journal, November 2018

Determining material constants in micromorphic theory through phonon dispersion relations journal, May 2003

The origin of the distinction between microscopic formulas for stress and Cauchy stress journal, November 2016

PyCAC: The concurrent atomistic-continuum simulation environment journal, January 2018

An analysis of key characteristics of the Frank-Read source process in FCC metals journal, November 2016

Nucleation and growth of dislocation loops in Cu, Al and Si by a concurrent atomistic-continuum method journal, October 2012

N processes, the relaxation-time approximation, and lattice thermal conductivity journal, September 1985

Equations of Mathematical Physics journal, October 1971

Misfit-energy-increasing dislocations in vapor-deposited CoFe/NiFe multilayers journal, April 2004

Validation of the Concurrent Atomistic-Continuum Method on Screw Dislocation/Stacking Fault Interactions journal, April 2017

Concurrent atomistic–continuum simulations of dislocation–void interactions in fcc crystals journal, February 2015

Ballistic-diffusive phonon heat transport across grain boundaries journal, September 2017

Assessment of atomistic coarse-graining methods journal, December 2011

Defect energetics in SrTiO 3 symmetric tilt grain boundaries journal, March 2011

Interatomic potentials for monoatomic metals from experimental data and ab initio calculations journal, February 1999

Edge dislocations bowing out from a row of collinear obstacles in Al journal, October 2016

Phonon spectrum and phonon focusing in coarse-grained atomistic simulations journal, May 2019

Coarse-grained simulations of single-crystal silicon journal, February 2009

Atomistic counterpart of micromorphic theory journal, March 2003

Sequential slip transfer of mixed-character dislocations across Σ3 coherent twin boundary in FCC metals: a concurrent atomistic-continuum study journal, January 2016

Concurrent atomistic and continuum simulation of bi-crystal strontium titanate with tilt grain boundary journal, March 2015

Constitutive relations of micromorphic thermoplasticity journal, March 2003

Passing waves from atomistic to continuum journal, February 2018

Assessing the applicability of quantum corrections to classical thermal conductivity predictions journal, June 2009

Trapping of hydrogen to lattice defects in nickel journal, May 1995

Computation of grain boundary stiffness and mobility from boundary fluctuations journal, July 2006

Control-volume representation of molecular dynamics journal, May 2012

A concurrent scheme for passing dislocations from atomistic to continuum domains
journal, February 2012

Local stress and heat flux in atomistic systems involving three-body forces
journal, February 2006

Heat flux vector in highly inhomogeneous nonequilibrium fluids
journal, May 1995

Shear stress- and line length-dependent screw dislocation cross-slip in FCC Ni
journal, January 2017

Coarse-grained atomistic simulation of dislocations
journal, February 2011

Accurate Interatomic Potentials for Ni, Al and Ni3Al
journal, January 1986

Concurrent atomistic and continuum simulation of strontium titanate
journal, January 2013

Connecting molecular dynamics to micromorphic theory. (II). Balance laws
journal, May 2003

A coherent phonon pulse model for transient phonon thermal transport
journal, October 2015

Equations of Mathematical Physics
journal, April 1972

A multiscale study of misfit dislocations in PbTe/PbSe(001) heteroepitaxy
journal, April 2019

Continuum predictions from molecular dynamics simulations: Shock waves
journal, February 2003

Sub-THz Phonon drag on dislocations by coarse-grained atomistic simulations
journal, April 2014

Equations of Mathematical Physics
journal, December 1971

On the equivalence of the two foundational formulations for atomistic flux in inhomogeneous transport processes
journal, March 2019

The Statistical Mechanical Theory of Transport Processes. IV. The Equations of Hydrodynamics
journal, June 1950

Local momentum and heat fluxes in transient transport processes and inhomogeneous systems
journal, November 2016

Micro-structure in linear elasticity
journal, January 1964

Coarse-grained elastodynamics of fast moving dislocations
journal, February 2016

Equations of Mathematical Physics
journal, November 1968

Pressure tensor for inhomogeneous fluids
journal, August 1995

A Coarse-Grained Atomistic Method for 3d Dynamic Fracture Simulation
journal, January 2013

Microcontinuum Field Theories
book, January 1999

Coarse-grained atomistic simulations of dislocations in Al, Ni and Cu crystals
journal, November 2012

Nanoscale Dislocation Patterning in $PbTe / PbSe (001)$ Lattice-Mismatched Heteroepitaxy
journal, December 2001

Atomistic viewpoint of the applicability of microcontinuum theories
journal, April 2004

Concurrent atomistic–continuum simulation of polycrystalline strontium titanate
journal, August 2015

Effects of phonons on mobility of dislocations and dislocation arrays
journal, August 2017

Examining the physical foundation of continuum theories from the viewpoint of phonon dispersion relation
journal, January 2003

Asymmetry of the atomic-level stress tensor in homogeneous and inhomogeneous materials
journal, September 2018

Imaging phonons
journal, December 2014

The fluctuation-dissipation theorem
journal, January 1966

Atomistic formulation of a multiscale field theory for nano/micro solids
journal, November 2005

The Statistical Mechanical Theory of Transport Processes. III. The Coefficients of Shear and Bulk Viscosity of Liquids
journal, October 1949

Coarse-graining atomistic dynamics of brittle fracture by finite element method
journal, September 2010

Reformulation of microscopic balance equations for multiscale materials modeling
journal, April 2009

Imaging Phonons
book, January 1998

Statistical Mechanics of Nonequilibrium Liquids
book, January 2008

Connecting molecular dynamics to micromorphic theory. (I). Instantaneous and averaged mechanical variables
journal, May 2003

Comparing EAM Potentials to Model Slip Transfer of Sequential Mixed Character Dislocations Across Two Symmetric Tilt Grain Boundaries in Ni
journal, March 2017

The Statistical Mechanical Theory of Transport Processes I. General Theory
journal, March 1946

Physical foundation and consistent formulation of atomic-level fluxes in transport processes
journal, November 2018

Determining material constants in micromorphic theory through phonon dispersion relations
journal, May 2003

The origin of the distinction between microscopic formulas for stress and Cauchy stress
journal, November 2016

PyCAC: The concurrent atomistic-continuum simulation environment
journal, January 2018

An analysis of key characteristics of the Frank-Read source process in FCC metals
journal, November 2016

Nucleation and growth of dislocation loops in Cu, Al and Si by a concurrent atomistic-continuum method
journal, October 2012

N processes, the relaxation-time approximation, and lattice thermal conductivity
journal, September 1985

Equations of Mathematical Physics
journal, October 1971

Misfit-energy-increasing dislocations in vapor-deposited CoFe/NiFe multilayers
journal, April 2004

Validation of the Concurrent Atomistic-Continuum Method on Screw Dislocation/Stacking Fault Interactions
journal, April 2017

Concurrent atomistic–continuum simulations of dislocation–void interactions in fcc crystals
journal, February 2015

Ballistic-diffusive phonon heat transport across grain boundaries
journal, September 2017

Assessment of atomistic coarse-graining methods
journal, December 2011

Defect energetics in SrTiO $_{3}$ symmetric tilt grain boundaries
journal, March 2011

Interatomic potentials for monoatomic metals from experimental data and ab initio calculations
journal, February 1999

Edge dislocations bowing out from a row of collinear obstacles in Al
journal, October 2016

Phonon spectrum and phonon focusing in coarse-grained atomistic simulations
journal, May 2019

Coarse-grained simulations of single-crystal silicon
journal, February 2009

Atomistic counterpart of micromorphic theory
journal, March 2003

Sequential slip transfer of mixed-character dislocations across Σ3 coherent twin boundary in FCC metals: a concurrent atomistic-continuum study
journal, January 2016

Concurrent atomistic and continuum simulation of bi-crystal strontium titanate with tilt grain boundary
journal, March 2015

Constitutive relations of micromorphic thermoplasticity
journal, March 2003

Passing waves from atomistic to continuum
journal, February 2018

Assessing the applicability of quantum corrections to classical thermal conductivity predictions
journal, June 2009

Trapping of hydrogen to lattice defects in nickel
journal, May 1995

Computation of grain boundary stiffness and mobility from boundary fluctuations
journal, July 2006

Control-volume representation of molecular dynamics
journal, May 2012