Investigating fracture mechanisms of thermoplastics at the micrometre scale using large-scale MD simulations: supplementary information and dataset

Abstract (from [1]): 
Fracture in thermoplastics is fundamentally a multiscale process, where nanometre-scale polymer chain movement drives micrometre-scale mechanics. Because neither traditional experiments nor conventional simulation methods can access these dimensions simultaneously, it remains an enigma how these fracture processes are linked across the scales. 

In the end, a critical challenge remains: Bridging the atomic (nanometre) and microscopic length scales to fully connect molecular architecture to global failure properties. While numerous multiscale simulation techniques are being developed to reduce or even close this gap, their validation is hindered by a severe lack of suitable, high-fidelity benchmark data spanning both the nano- and micro-regimes. To provide this crucial data, we developed a novel framework that successfully upscales an established coarse-grained molecular dynamics (MD) model of a generic thermoplastic. This approach enables simulations covering multiple micrometres of material using up to 30 million coarse-grained superatoms, significantly exceeding previous MD limits. We systematically investigate the influence of boundary conditions, pre-crack length, and key chain properties (chain length, chain entanglement and bending stiffness) on crack propagation.

Our analysis reveals two major findings essential for multiscale modelling: first, crack propagation in thermoplastics is not governed by a minimal pre-crack length, but is primarily sensitive to the interplay between boundary conditions and simulation domain size. Second, we can identify and characterise an inactive zone - an obstacle region - that forms immediately between the crack tip and the developing polymer fibrils. This zone, whose existence was previously only hinted at, must be overcome for sustained crack growth, representing a key nanoscale mechanism.

These micrometre scale MD simulations offer multiscale insights into failure of thermoplastics and provide the robust, high-resolution benchmark data necessary for the confident development and validation of next-generation multiscale modelling techniques for thermoplastics.

Contact: 
Eva Maria Richter
Institute of Applied Mechanics 
Friedrich-Alexander-Universität Erlangen-Nürnberg
Paul-Gordan-Straße 3
91052 Erlangen

Software: 
All simulations were performed with LAMMPS  [2-6] (version 2 August 2023 and 22 July 2025)
Compiler: GNU C++ 8.5.0 20210514 (Red Hat 8.5.0-28) with OpenMP not enabled
C++ standard: C++11
Embedded fmt library version: 10.2.0
Embedded JSON class version: 3.12.0

Active compile time flags:
-DLAMMPS_GZIP
-DLAMMPS_SMALLBIG
sizeof(smallint): 32-bit
sizeof(imageint): 32-bit
sizeof(tagint):   32-bit
sizeof(bigint):   64-bit

Installed packages: MOLECULE KSPACE 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-COMMAND EXTRA-COMPUTE EXTRA-DUMP EXTRA-FIX EXTRA-MOLECULE EXTRA-PAIR FEP GRANULAR INTEL INTERLAYER MANIFOLD MANYBODY MC MEAM MESONT MGPT MISC ML-RANN ML-SNAP ML-UF3 MOFFF OPENMP OPT ORIENT PERI PLUGIN PTM QEQ QTB REACTION REAXFF REPLICA RIGID SHOCK SMTBQ SPH SPIN SRD TALLY UEF YAFF DIELECTRIC PHONON

For the analysis of results, OVITO Pro was used [7] (version 3.11.2). 

License:
Creative Commons Attribution 4.0 International

Context: 
This dataset contains the necessary data to obtain the results presented in [1]. We perfom uniaxial tensile tests of a generic theromplastic polymer (GTP) [8] while varying the crack length, material parameters, crack shape and boundary conditions.

Content: 
Throughout this dataset, LAMMPS lj units are used. Names of the folders correspond to the numbering presented in Figure 3 in [1]. In every folder, there are two LAMMPS input scripts:
- crack.in
- input.prm

To run a sample, an additional data file of the GTP is necessary. The equilibrated data file is not included in this repository due to size but can be generated using the procedure in [1,9]. Further information about this data file is provided below under the section describing the lammps_data_file variable.

While the main file, crack.in undergos only minor changes throughout all samples (for instance for varying the crack shape and boundary conditions), respective parameters are varied in the input.prm file. Placeholders in the input file, marked with XXX have to be replaced with respective paths when reproducing the results. Four parameters are most important in this context:
- lammps_data_file: This is the name of the GTP input data file. This data file is produced in two steps beforehand: We apply a random walker algorithm [9] with the respective values for chain length and chain dispersity, as described in [1]. Furthermore, the initial box size is set. For highly entangled samples, XXX more space is needed (as the sample shrinks) during equilibration. For samples with a low entanglement, XXX percent more space is granted. After the sample was generated, it is equilibrated, as described in [1]. The lammps_data_file describes in the input.prm files therefore should be an already equilibrated sample [1].
- bending_stiffness: This variable describes the bending stiffness K (energy) within the cosine/delta potential. The stiffness is only varied in sample F (compared to the reference configuration D)
- half_crack_size: This variable is used to describe the length of the pre-crack. In particular half of it. The radii of the crack tips are not considered. If we aim for a total initial pre-crack size of 1086 \sigma - if we measure from one crack tip to thte other, we have to subtract 6 \sigma (for both crack radii) and divide the results in half, leading to a value of 540 \sigma which then has to be entered for the half_crack_size variable. 

References:
[1] E. M. Richter, F. Weber, M. Ries, S. Pfaller, Investigating fracture mechanisms of thermoplastics at the micrometre scale using large-scale MD simulations, 2026, under revision.
[2] Molecular dynamics software lammps: Website, Website, https://www.lammps.org/, last visited: 06th February
2026
[3] S. J. Plimpton, A. Kohlmeyer, A. P. Thompson, S. G. Moore, and R. Berger, Lammps: Large-scale
atomic/molecular massively parallel simulator, en, 2023.
[4] D. Surblys, H. Matsubara, G. Kikugawa, and T. Ohara, “Application of atomic stress to compute heat flux via
molecular dynamics for systems with many-body interactions,” Physical Review E, vol. 99, no. 5, p. 051 301,
2019.
[5] D. Surblys, H. Matsubara, G. Kikugawa, and T. Ohara, “Methodology and meaning of computing heat flux via
atomic stress in systems with constraint dynamics,” Journal of Applied Physics, vol. 130, no. 21, 2021.
[6] A. P. Thompson, H. M. Aktulga, R. Berger, et al., “Lammps - a flexible simulation tool for particle-based
materials modeling at the atomic, meso, and continuum scales,” Computer Physics Communications, vol. 271,
p. 108 171, 2022.
[7] A. Stukowski, “Visualization and analysis of atomistic simulation data with ovito–the open visualization tool,”
Modelling and Simulation in Materials Science and Engineering, vol. 18, no. 1, p. 015 012, 2009
[8] F. Weber, V. Dötschel, P. Steinmann, S. Pfaller, and M. Ries, “Evaluating the impact of filler size and filler
content on the stiffness, strength, and toughness of polymer nanocomposites using coarse-grained molecular
dynamics,” Engineering Fracture Mechanics, vol. 307, p. 110 270, 2024
[9] J. Roksvaag and M. Ries, “An efficient self-avoiding random walk algorithm to generate large-scale olymer and
polymer nanocomposite samplesat molecular resolution,” Manuscript under revision.

Funding: 
The authors gratefully acknowledge funding by various sources: the overall research (Eva Maria Richter, Felix Weber, Maximilian Ries, Sebastian Pfaller) was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), Germany – 377472739/GRK 2423/2-2023. Sebastian Pfaller is funded by the DFG, Germany – 505866713 and the Agence nationale de la recherché (ANR, French Research Agency), France – ANR-22-CE92-0049. 
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, Germany project 440719683.