Characterization of the material behavior and identification of effective elastic moduli based on molecular dynamics simulations of coarse-grained silica: dataset

Abstract:
(from [1])

The addition of fillers can significantly improve the mechanical behavior of polymers. The responsible mechanisms at the molecular level can be well assessed
by particle-based simulation techniques, such as molecular dynamics. However, the high computational cost of these simulations prevents the study of macroscopic
samples. Continuum-based approaches, particularly micromechanics, offer a more efficient alternative but require precise constitutive models for all
constituents, which are usually unavailable at these small length scales. In this contribution, we derive a molecular-dynamics-informed constitutive law by
employing a characterization strategy introduced in a previous publication. We choose silicon dioxide (silica) as an exemplary filler material used in polymer
composites and perform uniaxial and shear deformation tests with molecular dynamics. The material exhibits elastoplastic behavior with a pronounced anisotropy.
Based on the pseudo-experimental data, we calibrate an anisotropic elastic constitutive law and reproduce the material response for small strains accurately.  
The study validates the characterization strategy that facilitates the calibration of constitutive laws from molecular dynamics simulations. Furthermore, the
obtained material model for coarse-grained silica forms the basis for future continuum-based investigations of polymer nanocomposites. In general, the presented
transition from a fine-scale particle model to a coarse and  computationally efficient continuum description adds to the body of knowledge of molecular science
as well as the engineering community.
 

Contact:
Maximilian Ries
Institute of Applied Mechanics
Friedrich-Alexander-Universität Erlangen-Nürnberg
Egerlandstr. 5
91058 Erlangen

Software:
All simulations were performed with LAMMPS [3], version: 29 Oct 2020 / 20201029
Compiled with
Compiler: GNU C++ 4.8.5 20150623 (Red Hat 4.8.5-39) with OpenMP not enabled
C++ standard: C++11
Active compile time flags:
-DLAMMPS_GZIP
-DLAMMPS_SMALLBIG

Installed packages:
CLASS2, KSPACE, MANYBODY, MC, MOLECULE, MPIIO, OPT, VORONOI, USER-INTEL, USER-MISC, USER-MOLFILE, USER-NETCD

License:
Creative Commons Attribution 4.0 International
 
Context:
Data set supplementing  journal paper:
[1] Ries, M.; Bauer, C.; Weber, F.; Steinmann, P. & Pfaller, S., "Characterization of the material behavior and identification of effective elastic moduli based on molecular dynamics simulations of coarse-grained silica", Mathematics and Mechanics of Solids, 2022, 108128652211080.

This dataset contains the results presented in [1] and the necessary data to obtain those.

Content:
The files to reproduce our simulations and their results are structured as follows:

• 01_potentials
  tabulated potentials calibrated via iterative Boltzmann inversion in [2] kindly provided by the Müller-Plathe group at Technische Universität Darmstadt
  • Angle_table
    angular interactions
  • Bond_table
    bond interactions
  • Nonbond_table
    pair interactions
• 02_sample
  Lammps data file (molecular style) of the investigated silica sample
• 03_simulations
  The condensed simulation directories with the naming convention given below are organized in the following subfolders:
  • 01_time-proportional
    time-proportional simulation data
  • 02_time-periodic
    time-periodic simulation data

Each simulation directory contains:

• lammps input file (*.in) of the specific simulation
• input.prm: input parameters of the specific simulation (read by the input file)
• meta.info: meta data of the specific simulation run
• LAMMPS_out:
  simulation results (lammps thermo_out) in tabulated form, an overview of columns is given below
  • thermo_out.Dat: raw output
  • thermo_out_SG.Dat: smoothed output (Savitzky-Golay filter)
  • thermo_out_STD.Dat: standard deviation of raw output

Naming convention:
Silica-[deformation]-[direction]_[deformation function]-[deformation magnitude]_[deformation rate]
●    [deformation]: uniaxial tension (UT), simple shear (SS)
●    [direction]: deformation carried out in X/Y/Z (UT) or XY/XZ/YZ (SS)
●    [deformation function]: time-proportional (strain), time-periodic (strain_ampl)
●    [deformation magnitude]: maximum strain (time-proportional), strain amplitude (time-periodic); unitless
●    [deformation rate]: rate-[strain rate] (only time-proportional): 0.001/ns-0.1/ns

Output quantities (columns of *.Dat files):
●    Step: time step
●    Time: time in fs
●    TotEng: total energy in kcal/mol
●    PotEng: potential energy in kcal/mol
●    KinEng: kinetic energy in kcal/mol
●    E_pair: pair energy in kcal/mol
●    E_bond: bond energy in kcal/mol
●    E_angle: angle energy in kcal/mol
●    E_dihed: dihedral energy in kcal/mol
●    Temp: temperature in K
●    Press: hydrostatic pressure in atm
●    Pxx: xx component of pressure tensor in atm
●    Pyy: yy component of pressure tensor in atm
●    Pzz: zz component of pressure tensor in atm
●    Pxy: xy component of pressure tensor in atm
●    Pxz: xz component of pressure tensor in atm
●    Pyz: yz component of pressure tensor in atm
●    Volume: volume of simulation box in (Angstroms)^3
●    Lx: box length in x direction in Angstroms
●    Ly: box length in y direction in Angstroms
●    Lz: box length in z direction in Angstroms
●    Density: density in g/(cm^3)
●    c_RG: radius of gyration in Angstroms
●    c_RG[1]: squared radius of gyration tensor (xx component) in (Angstroms)^2
●    c_RG[2]: squared radius of gyration tensor (yy component) in (Angstroms)^2
●    c_RG[3]: squared radius of gyration tensor (zz component) in (Angstroms)^2
●    c_RG[4]: squared radius of gyration tensor (xy component) in (Angstroms)^2
●    c_RG[5]: squared radius of gyration tensor (xz component) in (Angstroms)^2
●    c_RG[6]: squared radius of gyration tensor (yz component) in (Angstroms)^2
●    c_bondave[1]: bond energy averaged over all atoms in kcal/mol
●    c_bondave[2]: bond distance averaged over all atoms in  Angstroms
●    c_bondave[3]: squared bond distance averaged over all atoms in (Angstroms)^2
●    c_angleave[1]: angle energy averaged over all atoms in kcal/mol
●    c_angleave[2]: angle averaged over all atoms degree
●    c_angleave[3]: cosine of angle (unitless)
●    c_angleave[4]: squared cosine of angle (unitless)
●    c_MSD[1]: mean squared displacement x-direction in (Angstroms)^2
●    c_MSD[2]: mean squared displacement y-direction in (Angstroms)^2
●    c_MSD[3]: mean squared displacement z-direction in (Angstroms)^2
●    c_MSD[4]: total mean squared displacement in (Angstroms)^2
●    c_COM[1]: x coordinate of center of mass in Angstroms
●    c_COM[2]: y coordinate of center of mass in Angstroms
●    c_COM[3]: z coordinate of center of mass in Angstroms
●    v_strain_xx: xx component of engineering strain tensor (unitless)  
●    v_strain_yy: yy component of engineering strain tensor (unitless)   
●    v_strain_zz: zz component of engineering strain tensor (unitless)   
●    v_vMisesequivstress: von Mises equivalent stress in MPa
●    v_Cauchy_xx: xx component of stress tensor in MPa  
●    v_Cauchy_yy: yy component of stress tensor in MPa
●    v_Cauchy_zz: zz component of stress tensor in MPa
●    v_Cauchy_xy: xy component of stress tensor in MPa
●    v_Cauchy_xz: xz component of stress tensor in MPa
●    v_Cauchy_yz: yz component of stress tensor in MPa
●    v_strain_xy: xy component of engineering strain tensor (unitless)  
●    v_strain_xz: xz component of engineering strain tensor (unitless)  
●    v_strain_yz: yz component of engineering strain tensor (unitless)  

References:
[1] Ries, M.; Bauer, C.; Weber, F.; Steinmann, P. & Pfaller, S., "Characterization of the material behavior and identification of effective elastic moduli based on molecular dynamics simulations of coarse-grained silica", Mathematics and Mechanics of Solids, 2022, 108128652211080.
[2] Ghanbari, A.; Ndoro, T. V. M.; Leroy, F.; Rahimi, M.; Böhm, M. C. & Müller-Plathe, F., “Interphase Structure in Silica-Polystyrene
Nanocomposites: A Coarse-Grained Molecular Dynamics Study”, Macromolecules, 2012, 45, 572-584.
[3] Plimpton, S., “Fast parallel algorithms for short-range molecular dynamics,” Journal of computational physics, 1995, 117, 1-19.