On equilibrating non-periodic molecular dynamics samples for coupled particle-continuum simulations of amorphous polymers: dataset

Abstract:
(from [1])
In the context of fracture simulations of polymers, the molecular mechanisms in the vicinity of the
crack tip are of particular interest. Nevertheless, to keep the computational cost to a minimum, a
coarser resolution must be used in the remaining regions of the numerical sample. For the specific
case of amorphous polymers, the Capriccio method bridges the gap between the length and time scales
involved at the different levels of resolution by concurrently coupling molecular dynamics (MD) with
the finite element method (FEM). Within the scope of the Capriccio approach, the coupling to the
molecular MD region introduces non-periodic, so-called stochastic boundary conditions (SBC). In
similarity to typical simulations under periodic boundary conditions (PBC), the SBC MD simulations
must reach an equilibrium state before mechanical loads are exerted on the coupled systems. In this
contribution, we hence extensively study the equilibration properties of non-periodic MD samples
using the Capriccio method. We demonstrate that the relaxation behavior of an MD-FE coupled
MD domain utilizing non-periodic boundary conditions is rather insensitive to the specific coupling
parameters of the method chosen to implement the boundary conditions. The behavior of an exemplary
system equilibrated with the parameter set considered as optimal is further studied under uniaxial
tension and we observe some peculiarities in view of creep and relaxation phenomena. This raises
important questions to be addressed in the further development of the Capriccio method.

Contact:
Felix Weber
Institute of Applied Mechanics
Friedrich-Alexander-Universität Erlangen-Nürnberg
Egerlandstr. 5
91058 Erlangen
Germany

Context:
This dataset contains the results presented in [1] and related data.

Content:
Throughout this data set, Lammps [2] real units are used. The following folders contain the results obtained under periodic boundary conditions:
- biax_PBC: biaxial loading 
- equil_PBC: equilibration
- ut_PBC: uniaxial tension
Each simulation directory contains:
- input.prm: input parameters of the specific simulation (read by the input file)
- job.out: simulation log file
- meta.info: meta data of the specific simulation run
- Lammps input file (*.in) of the specific simulation
- Lammps data file (*.data, molecular style) of the investigated sample
- LAMMPS_out: resulting Lammps data and restart (*.rst) files and simulation results (Lammps thermo_out) in 
tabulated form, an overview of the columns is given in the respective folders

The following folders contain the results obtained under stochastic boundary conditions using the Capriccio method [3]:
- best: equilibration with the parameter set considered to be most suitable for the MD-FE coupled equilibration
- biax: biaxial loading
- bridging: equilibration with different adaptivity levels of the bridging domain
- descr_obs: equilibration with a Lagrangian frame for the description of the observation region
- dpd: equilibration with different thicknesses of the dissipative particle dynamics (DPD) region
- friccoeff: equilibration with different friction coefficients applied in the dissipative particle dynamics region
- fur: equilibration with different numbers of fur beads 
- gausspoints: equilibration with different numbers of quadrature points per direction 
- min: equilibration applying an initial, static energy minimization
- nodes: equilibration with a higher number of finite element nodes
- shifted: equilibration with particle systems obtained at different positions and points in time within the periodic master system
- smdcub: equilibration with different remaining stiffness ratios for the cubic modified weighting factor
- smdlin: equilibration with different remaining stiffness ratios for the linear modified weighting factor
- timestepsize: equilibration with different molecular dynamics time step sizes
- ut: uniaxial tension
- ut_friccoeff: uniaxial tension with different friction coefficients applied in the dissipative particle dynamics region
- weighting: equilibration with different energy weighting functions
- youngsmod: equilibration with different Young's moduli
Each simulation directory contains:
- input_files: Abaqus [4] input file (*.inp) and Lammps data file (*.data, molecular style) of the investigated sample
- MD_data: Results evaluated in the molecular dynamics region. MD_data contains the following subfolders: 
anchorforces (dumped force components on the anchor points (AP) in kcal/mol, files anchorforce_[load step]_[MD-FE iteration].AF), 
data (resulting Lammps data files *.[load step].[MD-FE iteration].data), Density (dumped mass density in the observation region in kg/m^3), 
Energy (dumped total (kinetic + potential), angle, bond, and pair energies in kcal/(mol*Angstrom)), Strain (integral strains in the
observation region in x-, y-, and z-direction calculated by means of the Matlab [5] script calc_OBSstrain.m),
Stress (stresses in the observation region in MPa), and Temperature (temperature in the observation region in K)
- job.out: simulation log file
- meta.info: meta data of the specific Lammps simulation
Information on the subfolders is given in the respective folders.

References:
[1] F. Weber, M. Ries, C. Bauer, C. R. Wick, S. Pfaller, "On equilibrating non-periodic molecular dynamics samples for coupled
particle-continuum simulations of amorphous polymers", Forces in Mechanics, 2023, 10, 100159.
[2] A. P. Thompson, H. M. Aktulga, R. Berger, D. S. Bolintineanu, W. M. Brown, P. S. Crozier, P. J. in 't Veld, A. Kohlmeyer, 
S. G. Moore, T. D. Nguyen, R. Shan, M. J. Stevens, J. Tranchida, C. Trott, S. J. Plimpton, "LAMMPS - a flexible simulation tool 
for particle-based materials modeling at the atomic, meso, and continuum scales", Computer Physics Communications, 2022, 271, 108171.
[3] S. Pfaller, M. Rahimi, G. Possart, P. Steinmann, F. Müller-Plathe, M. C. Böhm, "An Arlequin-based method to couple molecular dynamics 
and finite element simulations of amorphous polymers and nanocomposites", Computer Methods in Applied Mechanics and Engineering, 
2013, 260, 109-129. 
[4] Dassault Systèmes, "Abaqus documentation", URL: https://abaqus-docs.mit.edu/2017/English/SIMACAEEXCRefMap/simaexc-c-docproc.htm.
[5] The MathWorks, Inc, "MATLAB. The Language of Technical Computing", URL: https://de.mathworks.com/help/matlab/.

Funding:
This research was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) -
377472739/GRK 2423/1-2019. The authors are very grateful for this support. Sebastian Pfaller is furthermore
funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - 396414850 (Individual
Research Grant ’Identifikation von Interphaseneigenschaften in Nanokompositen’).