The Capriccio method as a versatile tool for quantifying the fracture properties of glassy materials under complex loading conditions with chemical specificity – dataset

Abstract (from [1]): Molecular dynamics (MD) simulations are widely used to provide insights into fracture mechanisms while maintaining chemical specificity. However, particle-based techniques such as MD are limited in terms of accessible length scales and applicable boundary conditions, which restricts the investigation of fracture phenomena in typical engineering settings. In an attempt to overcome these limitations, we apply the partitioned-domain Capriccio method to couple atomistic MD samples representing silica glass with the finite element (FE) method. With this approach, we perform mode I (rectangular panel under tension, three-, and four-point bending), mode II as well as mode III (rectangular panel under in-plane or out-of-plane shear) simulations. Thereby, we investigate multiple criteria to identify the onset of crack propagation based on the virial stress, the number of pair interactions, the kinetic energy/temperature, the crack velocity, and the crack opening displacement. The approach presented provides quantitatively plausible results for the critical stress intensity factors KIc, KIIc, and KIIIc. This contribution shows that the Capriccio method is a flexible means of performing fracture simulations that take into account boundary conditions typical of experimental test setups with atomistic specificity near the crack tip. While also pointing out the current limitations of the Capriccio method, we demonstrate its potential to integrate atomistic insights into FE models with significantly larger overall dimensions. Contact: Felix Weber Institute of Applied Mechanics Friedrich-Alexander-Universität Erlangen-Nürnberg Egerlandstr. 5 91058 Erlangen Germany Software: All simulations were performed with LAMMPS [2,3] (version 2 Aug 2023, stable_2Aug2023_update2) Compiler: GNU C++ 11.2.0 with OpenMP not enabled C++ standard: C++11 Active compile time flags: -DLAMMPS_GZIP -DLAMMPS_SMALLBIG Installed packages: AMOEBA ASPHERE BOCS BODY BPM BROWNIAN CG-DNA CG-SPICA CLASS2 COLLOID CORESHELL DIFFRACTION DIPOLE DPD-BASIC DPD-MESO DPD-REACT DPD-SMOOTH DRUDE EFF EXTRA-COMPUTE EXTRA-DUMP EXTRA-FIX EXTRA-MOLECULE EXTRA-PAIR FEP GRANULAR INTEL INTERLAYER KSPACE MANIFOLD MANYBODY MC MEAM MESONT MGPT MISC ML-RANN ML-SNAP MOFFF MOLECULE OPENMP OPT ORIENT PERI PLUGIN PTM QEQ QTB REACTION REAXFF REPLICA RIGID SHOCK SMTBQ SPH SPIN SRD TALLY UEF VORONOI YAFF ATC DIELECTRIC ML-IAP PHONON License: Creative Commons Attribution 4.0 International Context: This dataset contains the results presented in [1] and the necessary data to obtain those. Content: Throughout this dataset, LAMMPS [2,3] metal units are used. We apply the SHIK potential [4,5] in the molecular dynamics simulations. In part of the simulations, we apply the Capriccio code (version 2.0.1) [6], which couples LAMMPS and Matlab (version R2022a) [7]. The finite element meshes were generated in Abaqus/CAE (version 2021.HF7) [8]. The files to reproduce the simulations and their results are structured as follows: LAMMPS_scripts: capriccio_MD_main.in: LAMMPS input script for the Capriccio code cracktip_quantities.in: LAMMPS input script get_forces.in: LAMMPS input script to evaluate per-atom forces rerun_RDF.in: LAMMPS input script to evaluate radial and angle distribution functions SHIK.silica.lmpmod: Parameters of the SHIK potential as used in the pure MD simulations. Note that this file must be located at the same level as the Lammps script. However, to avoid redundancy, it is only provided once here. potentials.lmpmod: SHIK potential and interactions in the dissipative particle dynamics region, including the anchor point potential, as used in the Capriccio simulations. Note that this file must be located at the same level as the input_files folders. However, to avoid redundancy, it is only provided once here. - Simulations: Mechanical loading simulations FEMD: Coupled finite element-molecular dynamics simulations using the Capriccio code SPP: Stochastic boundary conditions in x-direction, periodic boundary conditions in y- and z-direction tension: Uniaxial tension [Lx]x[Ly]x[Lz]_k[anchor stiffness]_fr[friction coefficient]_ls[load step]_[specifier]_[sample] SSP: Coupling with stochastic boundary conditions in x- and y-direction, periodic boundary conditions in z-direction 3PB: Three-point bending simulations [Lx]x[Ly]x[Lz]_k[anchor stiffness]_ls[load step]_eq[equilibration steps]_[supports]_[specifier]_[sample] 4PB: Four-point bending simulations [Lx]x[Ly]x[Lz]_k[anchor stiffness]_ls[load step]_eq[equilibration steps]_[supports]_[specifier]_[sample] shear: In-plane shear simulations (mode II) [Lx]x[Ly]x[Lz]_k[anchor stiffness]_ls[load step]_eq[equilibration steps]_rate[loading rate]_crate[cooling rate]_[specifier]_[sample] tension: Tensile simulations on notched systems (mode I) [Lx]x[Ly]x[Lz]_k[anchor stiffness]_ls[load step]_eq[equilibration steps]_rate[loading rate]_crate[cooling rate]_[specifier]_[sample]_[specifier] tension_uncracked: Tensile simulations on unnotched systems [Lx]x[Ly]x[Lz]_k[anchor stiffness]_ls[load step]_eq[equilibration steps]_rate[loading rate]_crate[cooling rate]_[specifier]_[sample] SSS: Stochastic boundary conditions in all spatial directions shear: Out-of-plane shear simulations (mode III) [Lx]x[Ly]x[Lz]_k[anchor stiffness]_ls[load step]_eq[equilibration steps]_rate[loading rate]_crate[cooling rate]_[specifier]_[sample] MD: Pure molecular dynamics simulations silica_cyclic: Cyclic loading free_lateral: Free lateral deformation at zero pressure cooling_rate_[cooling rate] [Lx]x[Ly]x[Lz]_rate[strain rate]_ampl[strain amplitude]_[sample] silica_sshear: Simple shear fix_lateral: Fixed lateral system dimensions cooling_rate_[cooling rate] [Lx]x[Ly]x[Lz]_rate[strain rate]_[sample] silica_ut: Uniaxial tension fix_lateral: Fixed lateral system dimensions cooling_rate_[cooling rate] [Lx]x[Ly]x[Lz]_rate[strain rate]_[sample] free_lateral: Free lateral deformation at zero pressure cooling_rate_[cooling rate] [Lx]x[Ly]x[Lz]_rate[strain rate]_[sample] Systems: Generation and equilibration of pure molecular dynamics systems cooling_rate_[cooling rate] [Lx]x[Ly]x[Lz]_[sample] Parameters used above: anchor stiffness: Anchor point spring stiffness in eV / Å^2 cooling rate: Quenching rate in K / ps equilibration steps: Number of molecular dynamics time steps applied for the equilibration of the systems at zero load friction coefficient: Dissipative particle dynamics friction coefficient in load step: Surface traction size in eV*ps / Å^2 loading rate: Surface traction rate in GPa / ns Lx: Initial length of the molecular dynamics domain in x-direction in Å Ly: Initial length of the molecular dynamics domain in y-direction in Å Lz: Initial length of the molecular dynamics domain in z-direction in Å sample: Sample ID specifier: Optional specifier crack: Notch length in the molecular dynamics domain in Å dsplxntr1: Application of the compensative surface shift dsplxntr2: Application of twice the compensative surface shift FEgs5.625: Global seed of the finite element mesh of 5.625 Å, two finite element layers in each pure finite element domain and bridging domain FEgs5.625el3: Global seed of the finite element mesh of 5.625 Å, three finite element layers in each pure finite element domain and bridging domain fixx: Loaded faces of the finite element domain fixed in x-direction free: Free contraction in Capriccio-coupled lateral directions fromls: Load applied to the finite element domain constant from a certain load step LxFE: Initial length of the finite element domain in x-direction LxyFE: Initial length of the finite element domain in x- and y-direction noBDaddFE: Bridging domain not enlarged by 1.0 Å at its boundary with the finite element domain noBDaddFEMD: Bridging domain enlarged by 1.0 Å at its boundaries with the finite element and the molecular dynamics domain noBDaddMD: Bridging domain not enlarged by 1.0 Å at its boundary with the molecular dynamics domain norefl: Simulations without applying reflective walls in the molecular dynamics simulations pacman_t: Force-controlled K-test simulations pacman_u: Displacement-controlled K-test simulations strain amplitude: Strain amplitude of the cyclic deformation simulations strain rate: Strain rate in 1 / ns supports: Supports modeled by d: Dirichlet boundary conditions n: Neumann boundary conditions Each simulation directory contains: FEMD: input_files: silica.ac: Initial anchor point coordinates silica.cae: Abaqus .cae file of the finite element domain silica.data: Initial LAMMPS data file silica.inp: Abaqus .inp file of the finite element domain input_parameters: Capriccio.prm: Input parameters MD_data: cracktip_quantities_[obsreg]A: Evaluation of crack tip quantities in an observation region of obsreg Å; dynobs: dynamic allocation of atoms to a stationary observation region cracktip_quantities.table: LAMMPS thermo output in tabulated form lammps_log.table: LAMMPS thermo output in tabulated form meta.info: Meta data of the simulation run structs_current.mat: Current Matlab structs output by Capriccio code MD: *.in: LAMMPS input script of the simulation input.prm: Input parameters of the simulation (read by the input script) LAMMPS_out: Simulation results *.data: Resulting LAMMPS data file lammps_log.table: LAMMPS thermo output in tabulated form meta.info: Meta data of the simulation run Exemplary trajectory outputs (FE_data/structs/*.mat and MD_data/lammpstrj/silica.lammpstrj) as generated by the Capriccio code are provided for the following simulations: FEMD/SSP/tension/100x100x50_k1.0_ls1e-5_eq1e5_rate20.0_crate0.26_1: Strip under mode I FEMD/SSP/shear/100x100x50_k1.0_ls1e-5_eq1e5_rate20.0_crate0.26_1: Strip under mode II FEMD/SSS/shear/100x100x50_k1.0_ls1e-5_eq1e5_rate20.0_crate0.26_fixx_1: Strip under mode III In [1], Ovito [9] was applied for the visualization of the samples. For the contour plots of the von Mises stress in the molecular dynamics domain given in [1], the von Mises stress in each evaluation bin is derived from the mean virial stress tensor calculated in this bin. This is based on the notion that, in continuum mechanics, a material point inherits its properties as the average of various underlying atoms [9]. References: [1] F. Weber, M. Vassaux, L. Laubert, S. Pfaller, "The Capriccio method as a versatile tool for quantifying the fracture properties of glassy materials under complex loading conditions with chemical specificity", Engineering Fracture Mechanics, vol. 333, p. 111841, 2026. [2] S. Plimpton, "Fast parallel algorithms for short-range molecular dynamics", Journal of computational physics, vol. 117, no. 1, pp. 1-19, 1995. [3] 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, vol. 271, p. 108171, 2022. [4] S. Sundararaman, L. Huang, S. Ispas, and W. Kob, "New optimization scheme to obtain interaction potentials for oxide glasses", The Journal of Chemical Physics, vol. 148, no. 19, 2018. [5] S. Sundararaman, L. Huang, S. Ispas, and W. Kob, "New interaction potentials for alkali and alkaline-earth aluminosilicate glasses", The Journal of Chemical Physics, vol. 150, no. 15, 2019. [6] S. Pfaller, M. Ries, W. Zhao, C. Bauer, F. Weber, and L. Laubert, "CAPRICCIO - Tool to run concurrent Finite Element-Molecular Dynamics Simulations (2.0.1)", Zenodo, https://doi.org/10.5281/zenodo.12606758. [7] The MathWorks, Inc., "Matlab. the language of technical computing", https://de.mathworks.com/help/matlab/. [8] Dassault Systèmes. "Abaqus documentation", https://abaqus-docs.mit.edu/2017/English/SIMACAEEXCRefMap/simaexc-c-docproc.htm. [9] E. B. Tadmor and R. E. Miller, "Modeling materials: continuum, atomistic and multiscale techniques", Cambridge University Press, 2011. Funding: The authors gratefully acknowledge funding by various sources: The overall research was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – 377472739/GRK 2423/2-2023. Lukas Laubert and Sebastian Pfaller are funded by the DFG – 505866713 and the Agence nationale de la recherché (ANR, French Research Agency) – ANR-22-CE92-0049. Sebastian Pfaller is furthermore funded by the DFG – 396414850 (Individual Research Grant ‘Identifikation von Interphaseneigenschaften in Nanokompositen’). The international collaboration has been funded by an International Emerging Action (IEA) grant from Centre National de la Rercherche Scientifique (CNRS). In addition, scientific support and HPC resources have been provided by the Erlangen National High Performance Computing Center (NHR@FAU) of the Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU) under the NHR project b136dc. NHR funding is provided by federal and Bavarian state authorities. NHR@FAU hardware is partially funded by the DFG project 440719683.