DOI: 10.5281/zenodo.5557076
title: Characterization of the material behavior and identification of effective elastic moduli based on molecular dynamics simulations of coarse-grained silica: dataset

description: <strong>Abstract</strong>:<br> (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<br> by particle-based simulation techniques, such as molecular dynamics. However, the high computational cost of these simulations prevents the study of macroscopic<br> samples. Continuum-based approaches, particularly micromechanics, offer a more efficient alternative but require precise constitutive models for all<br> constituents, which are usually unavailable at these small length scales. In this contribution, we derive a molecular-dynamics-informed constitutive law by<br> employing a characterization strategy introduced in a previous publication. We choose silicon dioxide (silica) as an exemplary filler material used in polymer<br> composites and perform uniaxial and shear deformation tests with molecular dynamics. The material exhibits elastoplastic behavior with a pronounced anisotropy.<br> Based on the pseudo-experimental data, we calibrate an anisotropic elastic constitutive law and reproduce the material response for small strains accurately. <br> The study validates the characterization strategy that facilitates the calibration of constitutive laws from molecular dynamics simulations. Furthermore, the<br> obtained material model for coarse-grained silica forms the basis for future continuum-based investigations of polymer nanocomposites. In general, the presented<br> transition from a fine-scale particle model to a coarse and computationally efficient continuum description adds to the body of knowledge of molecular science<br> as well as the engineering community.<br> <br> <strong>Contact</strong>:<br> Maximilian Ries<br> Institute of Applied Mechanics<br> Friedrich-Alexander-Universität Erlangen-Nürnberg<br> Egerlandstr. 5<br> 91058 Erlangen <br> <strong>Software</strong>:<br> All simulations were performed with LAMMPS [3], version: 29 Oct 2020 / 20201029<br> Compiled with<br> Compiler: GNU C++ 4.8.5 20150623 (Red Hat 4.8.5-39) with OpenMP not enabled<br> C++ standard: C++11<br> Active compile time flags:<br> -DLAMMPS_GZIP<br> -DLAMMPS_SMALLBIG <strong>Installed packages:</strong><br> CLASS2, KSPACE, MANYBODY, MC, MOLECULE, MPIIO, OPT, VORONOI, USER-INTEL, USER-MISC, USER-MOLFILE, USER-NETCD <br> <strong>License:</strong><br> Creative Commons Attribution 4.0 International<br> <br> <strong>Context</strong>:<br> Data set supplementing journal paper:<br> [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. <br> This dataset contains the results presented in [1] and the necessary data to obtain those. <br> <strong>Content</strong>:<br> The files to reproduce our simulations and their results are structured as follows: 01_potentials<br> tabulated potentials calibrated via iterative Boltzmann inversion in [2] kindly provided by the Müller-Plathe group at Technische Universität Darmstadt Angle_table<br> angular interactions Bond_table<br> bond interactions Nonbond_table<br> pair interactions 02_sample<br> Lammps data file (molecular style) of the investigated silica sample 03_simulations<br> The condensed simulation directories with the naming convention given below are organized in the following subfolders: 01_time-proportional<br> time-proportional simulation data 02_time-periodic<br> 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:<br> 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 <br> <strong>Naming convention</strong>:<br> Silica-[deformation]-[direction]_[deformation function]-[deformation magnitude]_[deformation rate]<br> ● [deformation]: uniaxial tension (UT), simple shear (SS)<br> ● [direction]: deformation carried out in X/Y/Z (UT) or XY/XZ/YZ (SS)<br> ● [deformation function]: time-proportional (strain), time-periodic (strain_ampl)<br> ● [deformation magnitude]: maximum strain (time-proportional), strain amplitude (time-periodic); unitless<br> ● [deformation rate]: rate-[strain rate] (only time-proportional): 0.001/ns-0.1/ns <br> <strong>Output quantities</strong> (columns of *.Dat files):<br> ● Step: time step<br> ● Time: time in fs<br> ● TotEng: total energy in kcal/mol<br> ● PotEng: potential energy in kcal/mol<br> ● KinEng: kinetic energy in kcal/mol<br> ● E_pair: pair energy in kcal/mol<br> ● E_bond: bond energy in kcal/mol<br> ● E_angle: angle energy in kcal/mol<br> ● E_dihed: dihedral energy in kcal/mol<br> ● Temp: temperature in K<br> ● Press: hydrostatic pressure in atm<br> ● Pxx: xx component of pressure tensor in atm<br> ● Pyy: yy component of pressure tensor in atm<br> ● Pzz: zz component of pressure tensor in atm<br> ● Pxy: xy component of pressure tensor in atm<br> ● Pxz: xz component of pressure tensor in atm<br> ● Pyz: yz component of pressure tensor in atm<br> ● Volume: volume of simulation box in (Angstroms)^3<br> ● Lx: box length in x direction in Angstroms<br> ● Ly: box length in y direction in Angstroms<br> ● Lz: box length in z direction in Angstroms<br> ● Density: density in g/(cm^3)<br> ● c_RG: radius of gyration in Angstroms<br> ● c_RG[1]: squared radius of gyration tensor (xx component) in (Angstroms)^2<br> ● c_RG[2]: squared radius of gyration tensor (yy component) in (Angstroms)^2<br> ● c_RG[3]: squared radius of gyration tensor (zz component) in (Angstroms)^2<br> ● c_RG[4]: squared radius of gyration tensor (xy component) in (Angstroms)^2<br> ● c_RG[5]: squared radius of gyration tensor (xz component) in (Angstroms)^2<br> ● c_RG[6]: squared radius of gyration tensor (yz component) in (Angstroms)^2<br> ● c_bondave[1]: bond energy averaged over all atoms in kcal/mol<br> ● c_bondave[2]: bond distance averaged over all atoms in Angstroms<br> ● c_bondave[3]: squared bond distance averaged over all atoms in (Angstroms)^2<br> ● c_angleave[1]: angle energy averaged over all atoms in kcal/mol<br> ● c_angleave[2]: angle averaged over all atoms degree<br> ● c_angleave[3]: cosine of angle (unitless)<br> ● c_angleave[4]: squared cosine of angle (unitless)<br> ● c_MSD[1]: mean squared displacement x-direction in (Angstroms)^2<br> ● c_MSD[2]: mean squared displacement y-direction in (Angstroms)^2<br> ● c_MSD[3]: mean squared displacement z-direction in (Angstroms)^2<br> ● c_MSD[4]: total mean squared displacement in (Angstroms)^2<br> ● c_COM[1]: x coordinate of center of mass in Angstroms<br> ● c_COM[2]: y coordinate of center of mass in Angstroms<br> ● c_COM[3]: z coordinate of center of mass in Angstroms<br> ● v_strain_xx: xx component of engineering strain tensor (unitless) <br> ● v_strain_yy: yy component of engineering strain tensor (unitless) <br> ● v_strain_zz: zz component of engineering strain tensor (unitless) <br> ● v_vMisesequivstress: von Mises equivalent stress in MPa<br> ● v_Cauchy_xx: xx component of stress tensor in MPa <br> ● v_Cauchy_yy: yy component of stress tensor in MPa<br> ● v_Cauchy_zz: zz component of stress tensor in MPa<br> ● v_Cauchy_xy: xy component of stress tensor in MPa<br> ● v_Cauchy_xz: xz component of stress tensor in MPa<br> ● v_Cauchy_yz: yz component of stress tensor in MPa<br> ● v_strain_xy: xy component of engineering strain tensor (unitless) <br> ● v_strain_xz: xz component of engineering strain tensor (unitless) <br> ● v_strain_yz: yz component of engineering strain tensor (unitless) <strong>References</strong>:<br> [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.<br> [2] Ghanbari, A.; Ndoro, T. V. M.; Leroy, F.; Rahimi, M.; Böhm, M. C. & Müller-Plathe, F., “Interphase Structure in Silica-Polystyrene<br> Nanocomposites: A Coarse-Grained Molecular Dynamics Study”, Macromolecules, 2012, 45, 572-584.<br> [3] Plimpton, S., “Fast parallel algorithms for short-range molecular dynamics,” Journal of computational physics, 1995, 117, 1-19.
description: Sebastian Pfaller is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - 396414850 (Individual Research Grant 'Identifikation von Interphaseneigenschaften in Nanokompositen'). Maximilian Ries, Christof Bauer, {Felix Weber}, Paul Steinmann, and Sebastian Pfaller are funded by the DFG - 377472739 (Research Training Group GRK 2423 'Fracture across Scales - FRASCAL').