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+
+
+
+ 20240926141252-95bdd07cc815870aab5f2ea5067a7c79156f7b23
+ 20240926141252
+
+ JOSS Admin
+ admin@theoj.org
+
+ The Open Journal
+
+
+
+
+ Journal of Open Source Software
+ JOSS
+ 2475-9066
+
+ 10.21105/joss
+ https://joss.theoj.org
+
+
+
+
+ 09
+ 2024
+
+
+ 9
+
+ 101
+
+
+
+ AQCNES: A Quasi-Continuum Non-Equilibrium
+Solver
+
+
+
+ Gerhard
+ Bräunlich
+ https://orcid.org/0009-0003-6052-405X
+
+
+ Shashank
+ Saxena
+ https://orcid.org/0000-0002-5242-9103
+
+
+ Manuel
+ Weberndorfer
+
+
+ Miguel
+ Spinola
+ https://orcid.org/0000-0002-5180-6149
+
+
+ Prateek
+ Gupta
+ https://orcid.org/0000-0003-3666-0257
+
+
+ Dennis M.
+ Kochmann
+ https://orcid.org/0000-0002-9112-6615
+
+
+
+ 09
+ 26
+ 2024
+
+
+ 7068
+
+
+ 10.21105/joss.07068
+
+
+ http://creativecommons.org/licenses/by/4.0/
+ http://creativecommons.org/licenses/by/4.0/
+ http://creativecommons.org/licenses/by/4.0/
+
+
+
+ Software archive
+ 10.5905/ethz-1007-824
+
+
+ GitHub review issue
+ https://github.com/openjournals/joss-reviews/issues/7068
+
+
+
+ 10.21105/joss.07068
+ https://joss.theoj.org/papers/10.21105/joss.07068
+
+
+ https://joss.theoj.org/papers/10.21105/joss.07068.pdf
+
+
+
+
+
+ A fast atomistic approach to
+finite-temperature surface elasticity of crystalline
+solids
+ Saxena
+ Computational Materials
+Science
+ 211
+ 10.1016/j.commatsci.2022.111511
+ 0927-0256
+ 2022
+ Saxena, S., Spinola, M., Gupta, P.,
+& Kochmann, D. M. (2022). A fast atomistic approach to
+finite-temperature surface elasticity of crystalline solids.
+Computational Materials Science, 211, 111511.
+https://doi.org/10.1016/j.commatsci.2022.111511
+
+
+ Nonequilibrium thermomechanics of gaussian
+phase packet crystals: Application to the quasistatic quasicontinuum
+method
+ Gupta
+ Journal of the Mechanics and Physics of
+Solids
+ 153
+ 10.1016/j.jmps.2021.104495
+ 0022-5096
+ 2021
+ Gupta, P., Ortiz, M., & Kochmann,
+D. M. (2021). Nonequilibrium thermomechanics of gaussian phase packet
+crystals: Application to the quasistatic quasicontinuum method. Journal
+of the Mechanics and Physics of Solids, 153, 104495.
+https://doi.org/10.1016/j.jmps.2021.104495
+
+
+ An adaptive quasicontinuum approach for
+modeling fracture in networked materials: Application to modeling of
+polymer networks
+ Ghareeb
+ Journal of the Mechanics and Physics of
+Solids
+ 137
+ 10.1016/j.jmps.2019.103819
+ 0022-5096
+ 2020
+ Ghareeb, A., & Elbanna, A.
+(2020). An adaptive quasicontinuum approach for modeling fracture in
+networked materials: Application to modeling of polymer networks.
+Journal of the Mechanics and Physics of Solids, 137, 103819.
+https://doi.org/10.1016/j.jmps.2019.103819
+
+
+ Quasicontinuum method
+ Miller
+ 2012
+ Miller, & Tadmor, E. B. (2012).
+Quasicontinuum method.
+https://nanohub.org/resources/qcmethod
+
+
+ The quasicontinuum method. Modeling
+microstructure on multiple length scales: A mixed continuum and
+atomistics approach
+ Tadmor
+ 1996
+ Tadmor, E. B. (1996). The
+quasicontinuum method. Modeling microstructure on multiple length
+scales: A mixed continuum and atomistics approach. Brown
+University.
+
+
+ A unified framework and performance benchmark
+of fourteen multiscale atomistic/continuum coupling
+methods
+ Miller
+ Modelling and Simulation in Materials Science
+and Engineering
+ 5
+ 17
+ 10.1088/0965-0393/17/5/053001
+ 2009
+ Miller, & Tadmor, E. B. (2009). A
+unified framework and performance benchmark of fourteen multiscale
+atomistic/continuum coupling methods. Modelling and Simulation in
+Materials Science and Engineering, 17(5), 053001.
+https://doi.org/10.1088/0965-0393/17/5/053001
+
+
+ Coupling atomistics and continuum in solids:
+Status, prospects, and challenges
+ Wernik
+ International Journal of Mechanics and
+Materials in Design
+ 5
+ 10.1007/s10999-008-9087-x
+ 2009
+ Wernik, J., & Meguid, S. A.
+(2009). Coupling atomistics and continuum in solids: Status, prospects,
+and challenges. International Journal of Mechanics and Materials in
+Design, 5, 79–110.
+https://doi.org/10.1007/s10999-008-9087-x
+
+
+ Automatic adaptivity in the fully nonlocal
+quasicontinuum method for coarse-grained atomistic
+simulations
+ Tembhekar
+ International Journal for Numerical Methods
+in Engineering
+ 9
+ 110
+ 10.1002/nme.5438
+ 2017
+ Tembhekar, I., Amelang, J. S., Munk,
+L., & Kochmann, D. M. (2017). Automatic adaptivity in the fully
+nonlocal quasicontinuum method for coarse-grained atomistic simulations.
+International Journal for Numerical Methods in Engineering, 110(9),
+878–900. https://doi.org/10.1002/nme.5438
+
+
+ MXE: A package for simulating long-term
+diffusive mass transport phenomena in nanoscale systems
+ Mendez
+ Computer Physics
+Communications
+ 260
+ 10.1016/j.cpc.2020.107315
+ 0010-4655
+ 2021
+ Mendez, J. P., & Ponga, M.
+(2021). MXE: A package for simulating long-term diffusive mass transport
+phenomena in nanoscale systems. Computer Physics Communications, 260,
+107315.
+https://doi.org/10.1016/j.cpc.2020.107315
+
+
+ Structural relaxation made
+simple
+ Bitzek
+ Physical review letters
+ 17
+ 97
+ 10.1103/PhysRevLett.97.170201
+ 2006
+ Bitzek, E., Koskinen, P., Gähler, F.,
+Moseler, M., & Gumbsch, P. (2006). Structural relaxation made
+simple. Physical Review Letters, 97(17), 170201.
+https://doi.org/10.1103/PhysRevLett.97.170201
+
+
+ The quasicontinuum method: Overview,
+applications and current directions
+ Miller
+ Journal of Computer-Aided Materials
+Design
+ 3
+ 9
+ 10.1023/A:1026098010127
+ 2002
+ Miller, & Tadmor, E. B. (2002).
+The quasicontinuum method: Overview, applications and current
+directions. Journal of Computer-Aided Materials Design, 9(3), 203–239.
+https://doi.org/10.1023/A:1026098010127
+
+
+ Nonequilibrium free-energy calculation of
+solids using LAMMPS
+ Freitas
+ Computational Materials
+Science
+ 112
+ 10.1016/j.commatsci.2015.10.050
+ 2016
+ Freitas, R., Asta, M., & De
+Koning, M. (2016). Nonequilibrium free-energy calculation of solids
+using LAMMPS. Computational Materials Science, 112, 333–341.
+https://doi.org/10.1016/j.commatsci.2015.10.050
+
+
+ Atomistic calculations of elastic properties
+of metallic fcc crystal surfaces
+ Shenoy
+ Physical Review B
+ 9
+ 71
+ 10.1103/PhysRevB.71.094104
+ 2005
+ Shenoy, V. B. (2005). Atomistic
+calculations of elastic properties of metallic fcc crystal surfaces.
+Physical Review B, 71(9), 094104.
+https://doi.org/10.1103/PhysRevB.71.094104
+
+
+ Examination of computed aluminum grain
+boundary structures and energies that span the 5D space of
+crystallographic character
+ Homer
+ Acta Materialia
+ 234
+ 10.1016/j.actamat.2022.118006
+ 2022
+ Homer, E. R., Hart, G. L., Owens, C.
+B., Hensley, D. M., Spendlove, J. C., & Serafin, L. H. (2022).
+Examination of computed aluminum grain boundary structures and energies
+that span the 5D space of crystallographic character. Acta Materialia,
+234, 118006.
+https://doi.org/10.1016/j.actamat.2022.118006
+
+
+ Finite-temperature grain boundary properties
+from quasistatic atomistics
+ Spínola
+ Computational Materials
+Science
+ 244
+ 10.1016/j.commatsci.2024.113270
+ 0927-0256
+ 2024
+ Spínola, M., Saxena, S., Gupta, P.,
+Runnels, B., & Kochmann, D. M. (2024). Finite-temperature grain
+boundary properties from quasistatic atomistics. Computational Materials
+Science, 244, 113270.
+https://doi.org/10.1016/j.commatsci.2024.113270
+
+
+ New monte carlo method to compute the free
+energy of arbitrary solids. Application to the fcc and hcp phases of
+hard spheres
+ Frenkel
+ The Journal of chemical
+physics
+ 7
+ 81
+ 10.1063/1.448024
+ 1984
+ Frenkel, D., & Ladd, A. J.
+(1984). New monte carlo method to compute the free energy of arbitrary
+solids. Application to the fcc and hcp phases of hard spheres. The
+Journal of Chemical Physics, 81(7), 3188–3193.
+https://doi.org/10.1063/1.448024
+
+
+ Thermomechanical properties dependence on
+chain length in bulk polyethylene: Coarse-grained molecular dynamics
+simulations
+ Zhao
+ Journal of materials research
+ 25
+ 10.1557/JMR.2010.0061
+ 2010
+ Zhao, J., Nagao, S., & Zhang, Z.
+(2010). Thermomechanical properties dependence on chain length in bulk
+polyethylene: Coarse-grained molecular dynamics simulations. Journal of
+Materials Research, 25, 537–544.
+https://doi.org/10.1557/JMR.2010.0061
+
+
+ Stochastic predictions of bulk properties of
+amorphous polyethylene based on molecular dynamics
+simulations
+ Vu-Bac
+ Mechanics of Materials
+ 68
+ 10.1016/j.mechmat.2013.07.021
+ 2014
+ Vu-Bac, N., Lahmer, T., Keitel, H.,
+Zhao, J., Zhuang, X., & Rabczuk, T. (2014). Stochastic predictions
+of bulk properties of amorphous polyethylene based on molecular dynamics
+simulations. Mechanics of Materials, 68, 70–84.
+https://doi.org/10.1016/j.mechmat.2013.07.021
+
+
+ Summation rules for a fully nonlocal
+energy-based quasicontinuum method
+ Amelang
+ Journal of the Mechanics and Physics of
+Solids
+ 82
+ 10.1016/j.jmps.2015.03.007
+ 2015
+ Amelang, J. S., Venturini, G. N.,
+& Kochmann, D. M. (2015). Summation rules for a fully nonlocal
+energy-based quasicontinuum method. Journal of the Mechanics and Physics
+of Solids, 82, 378–413.
+https://doi.org/10.1016/j.jmps.2015.03.007
+
+
+ Thermal surface free energy and stress of
+iron
+ Schönecker
+ Scientific reports
+ 1
+ 5
+ 10.1038/srep14860
+ 2015
+ Schönecker, S., Li, X., Johansson,
+B., Kwon, S. K., & Vitos, L. (2015). Thermal surface free energy and
+stress of iron. Scientific Reports, 5(1), 1–7.
+https://doi.org/10.1038/srep14860
+
+
+ Embedded-atom potential for fe and its
+application to self-diffusion on fe (1 0 0)
+ Chamati
+ Surface Science
+ 9
+ 600
+ 10.1016/j.susc.2006.02.010
+ 2006
+ Chamati, H., Papanicolaou, N.,
+Mishin, Y., & Papaconstantopoulos, D. (2006). Embedded-atom
+potential for fe and its application to self-diffusion on fe (1 0 0).
+Surface Science, 600(9), 1793–1803.
+https://doi.org/10.1016/j.susc.2006.02.010
+
+
+ Structural stability and lattice defects in
+copper: Ab initio, tight-binding, and embedded-atom
+calculations
+ Mishin
+ Physical Review B
+ 22
+ 63
+ 10.1103/PhysRevB.63.224106
+ 2001
+ Mishin, Y., Mehl, M.,
+Papaconstantopoulos, D., Voter, A., & Kress, J. (2001). Structural
+stability and lattice defects in copper: Ab initio, tight-binding, and
+embedded-atom calculations. Physical Review B, 63(22), 224106.
+https://doi.org/10.1103/PhysRevB.63.224106
+
+
+
+
+
+
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@@ -0,0 +1,1054 @@
+
+
+
+
+
+
+
+Journal of Open Source Software
+JOSS
+
+2475-9066
+
+Open Journals
+
+
+
+7068
+10.21105/joss.07068
+
+AQCNES: A Quasi-Continuum Non-Equilibrium
+Solver
+
+
+
+https://orcid.org/0009-0003-6052-405X
+
+Bräunlich
+Gerhard
+
+
+
+
+https://orcid.org/0000-0002-5242-9103
+
+Saxena
+Shashank
+
+
+
+
+
+Weberndorfer
+Manuel
+
+
+
+
+https://orcid.org/0000-0002-5180-6149
+
+Spinola
+Miguel
+
+
+
+
+https://orcid.org/0000-0003-3666-0257
+
+Gupta
+Prateek
+
+
+
+
+https://orcid.org/0000-0002-9112-6615
+
+Kochmann
+Dennis M.
+
+
+
+
+
+Mechanics & Materials Laboratory, ETH Zürich,
+Switzerland
+
+
+
+
+Department of Applied Mechanics, Indian Institute of
+Technology Delhi, India
+
+
+
+
+Scientific IT Services, ETH Zürich,
+Switzerland
+
+
+
+
+4
+5
+2024
+
+9
+101
+7068
+
+Authors of papers retain copyright and release the
+work under a Creative Commons Attribution 4.0 International License (CC
+BY 4.0)
+2022
+The article authors
+
+Authors of papers retain copyright and release the work under
+a Creative Commons Attribution 4.0 International License (CC BY
+4.0)
+
+
+
+C++
+atomistics
+statistical mechanics
+quasi continuum
+finite temperature
+
+
+
+
+
+ Summary
+
The behavior of macroscopic structures is determined by fast atomic
+ interactions at the nanoscales. Current atomic simulation techniques,
+ such as molecular dynamics (MD), are limited to a millions of atoms
+ and hence a few micrometers of domain length. Moreover,
+ finite-temperature vibrational frequencies of around tens of terahertz
+ restrict the time step of MD to femtoseconds, precluding the
+ simulation of problems of engineering interest. Consequently, there
+ has been a significant focus in recent decades on developing
+ multiscale modeling techniques to extend atomistic accuracy to larger
+ length scales and longer time frames. Existing techniques, such as the
+ quasicontinuum (QC) method, are restricted to spatial upscaling at
+ zero temperature, while temporal upscaling methods like the maximum
+ entropy (max-ent) approach are constrained to fully resolved atomistic
+ simulations at finite temperature.
+
The software introduced here, AQCNES, is a
+ C++-based framework that integrates the spatial-upscaling technique of
+ the quasicontinuum method with the statistical-mechanics-based
+ temporal upscaling technique known as Gaussian phase packets. Message
+ Passing Interface (MPI) is employed to enable massive parallelism,
+ which enhances the scalability of the software. This enables
+ computationally efficient and robust simulations of large atomistic
+ ensembles at finite temperature.
+
+
+ Statement of need
+
Commonly used atomic simulation techniques describe the entire
+ ensemble as a collection of particles, each having a position and
+ velocity in three-dimensional space. This fully refined spatial
+ representation in state space restricts the possible dimensions of the
+ ensemble to microscopic scales. Moreover, case studies of material
+ defects using atomistic simulations are often limited to Molecular
+ Statics (MS) or use unrealistically high loading rates
+ (Homer
+ et al., 2022;
+ Shenoy,
+ 2005). This is unavoidable because finite-temperature MD
+ simulations need long equilibration times and expensive
+ post-processing techniques
+ (Frenkel
+ & Ladd, 1984) to extract relevant thermodynamic
+ information. However, physically relevant material behavior is
+ observed at finite temperature. Therefore, research in the past
+ decades has focused on multiscale modeling techniques to advance
+ atomistic simulations to larger length scales and longer time scales
+ (Miller
+ & Tadmor, 2009;
+ Wernik
+ & Meguid, 2009).
+
Most research groups working in the broad field of upscaling
+ atomistic simulations have their proprietary codes. Two available
+ open-source codes are QuasiContinuum
+ (Miller
+ & Tadmor, 2012) based on the quasicontinuum (QC) method and
+ MultiBench
+ (Miller
+ & Tadmor, 2009), which is an implementation of fourteen
+ popular spatial upscaling methods. However, both are limited to
+ zero-temperature simulations for crystalline solids in two dimensions.
+ The MXE package in
+ LAMMPS
+ (Mendez
+ & Ponga, 2021) is an implementation of the temporal
+ upscaling technique max-ent for a fully
+ resolved atomic ensemble with no spatial coarse-graining. To the best
+ of the authors’ knowledge, there is no such open-source atomistic
+ simulation software that combines the aforementioned spatial and
+ temporal upscaling techniques.
+
AQCNES is a software that can predict
+ long-term behavior of large atomic ensembles using the spatio-temporal
+ upscaling of classical atomistic calculations. It enables the
+ calculation of material properties at finite (non-zero) temperature
+ from atomic scales, offering promising applications in solid-state
+ material science across scales. In the present implementation, full
+ atomistic resolution is needed for regions of local disorder as well
+ as for amorphous materials, although extension of the QC for amorphous
+ systems have been proposed
+ (Ghareeb
+ & Elbanna, 2020) and can be considered as a possible
+ extension. Hence, AQCNES is capable of
+ simulating both crystalline and amorphous materials in a temporally
+ upscaled fashion at zero and non-zero temperature, while the spatial
+ upscaling capability is limited to crystalline systems. It can also
+ simulate large atomic rearrangements induced by severe deformations in
+ multi-resolution domains by using an updated Lagrangian formulation
+ (Gupta
+ et al., 2021). This formulation uses the relaxed state after
+ every load step as the new reference configuration. An adaptive
+ neighborhood calculation strategy (similar to Tembhekar et al.
+ (2017))
+ is adopted, where the neighborhoods are regenerated if the maximum
+ relative displacement of a neighbor with respect to a sampling atom
+ exceeds a given buffer radius. This unique combination of features
+ positions AQCNES as a versatile and powerful
+ tool in the realm of atomistic simulations.
+
+
+ Functionality
+
A technique known as Gaussian Phase Packets (GPP)
+ (Gupta
+ et al., 2021) is used to upscale in time. Instead of the
+ instantaneous phase-space coordinates (position
+
+ and momentum
+
+ ), statistical averages
+
+ and variances
+
+ of these coordinates are tracked for the entire ensemble in GPP, thus
+ separating the slow mean atomic motion from fast atomic vibrations.
+ The covariance matrices represented above are fully populated for the
+ most general case. However, in order to make the system of equations
+ more tractable, interatomic correlations are assumed to be zero.
+ Further, intra-atomic covariance matrices are assumed to be spherical
+ Gaussian clouds. This leads to
+
+ where subscript
+
+ i
+ runs over all atoms in the ensemble and
+
+ 𝐈
+ is an identity matrix in 3D space. Hence, the set of variables
+
+ is solved for every atomic site. It can be shown that in the
+ quasistatic limit, mean momenta
+
+ and thermal momenta
+
+ βi
+ vanish for every atom. The mean positions
+
+ and position variances
+
+ {Σi:i=1,…,N}
+ are obtained using the following equilibrium conditions
+ (Gupta
+ et al., 2021):
+
+
where
+
+ denotes the net force acting on atom
+
+ i
+ having mass
+
+ mi.
+ Infomation about momentum variances
+
+ {Ωi:i=1,…,N}
+ is obtained from the thermodynamic process which brings the system to
+ equilibrium. The governing equations
+ (1) of these
+ statistical parameters can be shown to yield configurations which
+ minimize a thermalized Helmholtz free-energy at the temperature of
+ interest. The reader is referred to Gupta et al.
+ (2021) for
+ further details. AQCNES uses FIRE
+ (Bitzek
+ et al., 2006) to relax the system of equations
+ (1) and thus obtain
+ a thermodynamically relaxed structure of the ensemble after a
+ quasi-static minimization. This approach is more robust and
+ computationally efficient
+ (Saxena
+ et al., 2022) than tracking individual atomic trajectories.
+ Moreover, it makes the simulation of realistic and quasistatic loading
+ scenarios possible, in contrast to the unrealistically high strain
+ rates accessible by MD simulations
+ (Vu-Bac
+ et al., 2014;
+ Zhao
+ et al., 2010).
+
For spatial coarse-graining, AQCNES uses QC
+ (Miller
+ & Tadmor, 2002;
+ Tadmor,
+ 1996). QC exploits the long-range order in crystalline
+ materials to explicitly model
+
+ Nh≪N
+ representative(rep-) atoms in the domain and uses
+ techniques from continuum-level finite-element modeling to obtain all
+ other atomic degrees of freedom as a function of those of the
+ representative atoms. Fully atomistic resolution is retained in the
+ vicinity of material defects, where the long-range order is broken.
+ The mean position
+
+ and position variance
+
+ Σi
+ of an atom
+
+ i
+ are obtained by the following interpolation:
+
+
where
+
+ is the shape function for repatom
+
+ a
+ evaluated at the position of atom
+
+ i
+ in the reference configuration. This reduces the number of degrees of
+ freedom to solve from
+
+ 4N
+ to
+
+ 4Nh
+ for finite-temperature simulations. For energy and force calculation
+ in every minimisation iteration, a set of
+
+
+ Ns≪N
+ sampling atoms is selected. The approximate Hamiltonian of the entire
+ system can then be written as:
+
+ ℋ≈∑α=1Nswαℋα,
+
where
+
+ wα
+ are the sampling atom weights and
+
+ ℋα
+ is the energy of the
+
+ αth
+ sampling atom. A detailed explanation of optimally choosing sampling
+ atom locations and weights can be found in Amelang et al.
+ (2015).
+
+
+ Example applications
+
The following gives a summary of the mechanics and material science
+ applications where AQCNES has already been
+ used:
+
+
+
Surface Elasticity: Surfaces in solids are the
+ simplest extended defects and contribute to excess energy, leading
+ to an inherent stress associated with them. Their presence also
+ changes the elastic moduli of the solid as compared to those of
+ the bulk solid. AQCNES was used by Saxena
+ et al.
+ (2022)
+ to perform a detailed case study of three differently
+ crystallographically oriented surfaces for FCC and BCC metals as a
+ function of temperature. The results were also compared against
+ those obtained from state-of-the-art thermodynamic integration
+ techniques
+ (Freitas
+ et al., 2016), showing convincing accuracy. The comparison
+ of computational times taken by MD and
+ AQCNES (see
+ [table:sim_times])
+ shows that there is an approximately fifty-fold computational
+ speedup and a significant reduction in the computational resources
+ needed for computing the excess surface free energy for an
+ ensemble at finite temperature.
+ [fig:surfaces]
+ shows the surface free energy, stresses, and elastic constants for
+ the (001), (011), and (111) surfaces in BCC iron computed using
+ AQCNES and their comparison with MD
+ simulations and ab-initio results by Schönecker
+ et al.
+ (2015).
+ The embedded atom method (EAM) potential developed by Chamati et
+ al.
+ (2006)
+ was used for AQCNES and MD simulations.
+
+
+
+
+
+
Simulation times for a surface free energy computation for
+ the (001) surface in Fe at 300 K with AQCNES and thermodynamic
+ integration in LAMMPS (adapted from Saxena et al. (2022)).
+
+
+
+
+
+
No. of atoms
+
No. of procs.
+
No. of iterations
+
Simulation time (min)
+
+
+
+
+
AQCNES
+
2624
+
25
+
767
+
9.79
+
+
+
LAMMPS
+
16400
+
128
+
+
+ 4.8⋅107
+
422
+
+
+
+
+
+
+
(a) Surface free energy density
+
+
+ (ξ)
+ and average surface stress
+
+ (τavg)
+ vs. temperature
+
+ (T)
+ and (b) polar compliance plots (in Å
+
+ 2/eV)
+ for the (001), (011), and (111) surfaces in BCC iron (adapted from
+ Saxena et al.
+ (2022)).
+
+
+
+
+
+
Grain Boundaries: Grain boundaries (GBs) are
+ regions of crystallographic mismatch between two differently
+ oriented grains. They significantly influence the mechanical and
+ thermal properties of polycrystalline materials. Hence,
+ investigating GB properties via atomic simulations is of
+ scientific interest in the material science community.
+ AQCNES has been used to find relaxed
+ energies of
+
+ [001]
+ and
+
+ [011]
+ symmetric-tilt GBs in copper as a function of temperature for a
+ range of tilt angles
+ (Spínola
+ et al., 2024). Different metastable states have been
+ explored for each temperature and tilt angle. In addition, the
+ lowest-energy metastable state was subjected to a quasistatic
+ displacement-driven shear to obtain the shear coupling factor of
+ all grain boundaries. AQCNES could also
+ identify the Helmholtz free energy of bicrystals, for which the
+ standard thermodynamic integration techniques failed due to hops
+ of the system from one metastable state to another.
+ [fig:grain_boundaries]
+ summarizes the excess grain boundary free energy density and the
+ shear coupling factors for the lowest energy metastable state of
+
+
+ [001]
+ tilt axis grain boundaries in copper. The EAM potential developed
+ by Mishin et al.
+ (2001)
+ was used for these simulations.
+
+
+
(a) Excess grain boundary free energy density
+
+
+ (γgb)
+ and (b) shear coupling factor
+
+ (β)
+ vs. tilt angle for the
+
+ [001]
+ symmetric tilt grain boundaries in copper at different
+ temperatures (adapted from Spínola et al.
+ (2024)).
+
+
+
+
+
+
+
+
+
Nanoindentation:
+ Nanoindentation is a widely used technique to probe the mechanical
+ properties of materials and nanostructures.
+ AQCNES has been used to simulate the
+ three-dimensional thermo-mechanically-coupled nanoindentation of
+ copper
+ (Gupta
+ et al., 2021). Two layers of spatial coarse graining were
+ used to simulate a cube of side length
+
+
+ 0.077µm
+ with
+
+ 0.2
+ million representative atoms. The complicated microstructure of
+ prismatic dislocation loops below the nanoindenter could be
+ observed in the finite-temperature simulations at
+
+
+ 300
+ and
+
+ 600K.
+ The temperature dependence of the critical indenter force before
+ dislocation nucleation could also be captured.
+ [fig:nanoindentation]
+ shows the microstructure below the indenter and the indenter force
+ for different temperatures.
+
+
+
(a) Dislocation loops generated as a result of
+ nanoindentation beneath the spherical indenter at a depth of 1
+ nm. (b) Indenter force vs. depth for isothermal
+ nanoindentation at different temperatures (adapted from Gupta
+ et al.
+ (2021)).
+
+
+
+
+
+
+
+ Dependencies and API documentation
+
The project uses
+ CMake
+ as its build system generator. The following third party libraries are
+ required and located using CMake’s
+ find_package.
+
+
+
Boost
+ (components: program_options, mpi, serialization): version
+ 1.67
+
+
+
Eigen:
+ version 3.4
+
+
+
MPI:
+ version 3.1
+
+
+
PETSc:
+ version 3.15
+
+
+
CGAL:
+ version 5.4
+
+
+
PnetCDF:
+ Version 1.12
+
+
+
nlohmannjson:
+ Version 3.10
+
+
+
Scotch/ParMETIS
+
+
+
qcmesh:
+ Version 1.0
+
+
+
VTK:
+ Version 9.3
+
+
+
The dependency versions mentioned above are not strictly the
+ minimum versions required, but the ones which have been tested to work
+ well. The code quality of the project is analyzed in a CI pipeline
+ which runs inside the development docker
+ container
+ and on the ETH HPC cluster
+ Euler.
+ The pipeline covers the following checks:
+
+
+
Building the docker container and publishing it to
+ registry.gitlab.ethz.ch.
+
+
+
Building documentation and publishing it to
+ qc.mm.ethz.ch.
+
+
+
Code compilation and running unit/integration tests.
+
+
+
Presence of a license header for each source file.
+
+
+
Consistency of code formatting using
+ clang-format
+ for C++ and
+ ruff
+ for Python.
+
+
+
Static code analysis (linter) using
+ clang-tidy
+ for C++ and
+ ruff
+ for Python.
+
+
+
Detailed documentation of the API can be found on the
+ AQCNES
+ website,
+ and simple examples to get started can be found
+ here.
+ Importantly, the use of AQCNES is not limited
+ to these examples and the ones listed in this contribution.
+
+
+ Acknowledgements
+
The support from the European Research Council (ERC) under the
+ European Union’s Horizon 2020 research and innovation program (grant
+ agreement no. 770754) is gratefully acknowledged. We also acknowledge
+ contributions to the code from Stefan Zimmerman and Anny Wang.
+
+
+
+
+
+
+
+
+ SaxenaShashank
+ SpinolaMiguel
+ GuptaPrateek
+ KochmannDennis M.
+
+ A fast atomistic approach to finite-temperature surface elasticity of crystalline solids
+ Computational Materials Science
+ 2022
+ 211
+ 0927-0256
+ https://www.sciencedirect.com/science/article/pii/S092702562200266X
+ 10.1016/j.commatsci.2022.111511
+ 111511
+
+
+
+
+
+
+ GuptaPrateek
+ OrtizMichael
+ KochmannDennis M.
+
+ Nonequilibrium thermomechanics of gaussian phase packet crystals: Application to the quasistatic quasicontinuum method
+ Journal of the Mechanics and Physics of Solids
+ 2021
+ 153
+ 0022-5096
+ https://www.sciencedirect.com/science/article/pii/S0022509621001630
+ 10.1016/j.jmps.2021.104495
+ 104495
+
+
+
+
+
+
+ GhareebAhmed
+ ElbannaAhmed
+
+ An adaptive quasicontinuum approach for modeling fracture in networked materials: Application to modeling of polymer networks
+ Journal of the Mechanics and Physics of Solids
+ 2020
+ 137
+ 0022-5096
+ https://www.sciencedirect.com/science/article/pii/S0022509619304405
+ 10.1016/j.jmps.2019.103819
+ 103819
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+
+ Miller
+ TadmorEllad B
+
+ Quasicontinuum method
+ 201205
+ https://nanohub.org/resources/qcmethod
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+
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+
+ The quasicontinuum method. Modeling microstructure on multiple length scales: A mixed continuum and atomistics approach
+ Brown University
+ 1996
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+
+
+ Miller
+ TadmorE B
+
+ A unified framework and performance benchmark of fourteen multiscale atomistic/continuum coupling methods
+ Modelling and Simulation in Materials Science and Engineering
+ 200905
+ 17
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+ https://dx.doi.org/10.1088/0965-0393/17/5/053001
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+ WernikJM
+ MeguidShaker A
+
+ Coupling atomistics and continuum in solids: Status, prospects, and challenges
+ International Journal of Mechanics and Materials in Design
+ Springer
+ 2009
+ 5
+ 10.1007/s10999-008-9087-x
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+ KochmannDennis M
+
+ Automatic adaptivity in the fully nonlocal quasicontinuum method for coarse-grained atomistic simulations
+ International Journal for Numerical Methods in Engineering
+ Wiley Online Library
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