DOI: 10.5281/zenodo.13644830
title: The Capriccio method as a versatile tool for quantifying the fracture properties of glassy materials under complex loading conditions with chemical specificity – dataset

description: 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: Parameters of the SHIK potential + dissipative particle dynamics region + anchor points 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: Initial 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 bin is calculated from the mean virial stress tensor acting in that bin.

 

 

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", accepted for publication in Engineering Fracture Mechanics.

[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.

 

 

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.