Approaching and overcoming the limitations of the multiscale Capriccio method for simulating the mechanical behavior of amorphous materials – data set

readme_dataSet1dAnd3d.txt

## Description ##

This readme describes the folder and file structure of the data sets published along contribution [1] via "DataSet1dAnd3d.zip".

## Context ##

[1] L. Laubert, F. Weber, F. Detrez, and S. Pfaller, "Approaching and overcoming the limitations of the multiscale Capriccio method for simulating the mechanical behavior of amorphous materials", International Journal of Engineering Science, vol. 217, p. 104317, 2025. https://doi.org/10.1016/j.ijengsci.2025.104317
[2] L. Laubert, "One-dimensional framework imitating the Capriccio method for coupling the finite element method with particle-based techniques", Software, Zenodo, 2024. https://doi.org/10.5281/zenodo.14796809
[3] L. Laubert, "Framework for projecting displacements of particles and nodes resulting from Capriccio method coupled deformation simulations to a one-dimensional representation", Software, Zenodo, 2025. https://doi.org/10.5281/zenodo.14796824
[4] S. Pfaller, M. Ries, W. Zhao, C. Bauer , F. Weber, L. Laubert, "CAPRICCIO - Tool to run concurrent Finite Element-Molecular Dynamics Simulations", Software, Zenodo, 2025. https://doi.org/10.5281/zenodo.12606758
[5] L. Laubert, "Establishing a framework for conducting comparative one- and multidimensional studies on the coupling of the finite element method with particle-based techniques", Project Thesis, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), 2023. https://doi.org/10.5281/zenodo.7924368
[6] W. Felix, M. Vassaux, L. Laubert, and S. Pfaller, "Measuring the fracture properties of brittle materials using molecular simulations: Application to mode I and mode III in silica glass", in preparation, 2025.

## Abstract (from [1]) ##
The Capriccio method is a computational technique for coupling finite element (FE) and molecular dynamics (MD) domains to bridge their length scales and to provide boundary conditions typically employed in large-scale engineering applications. Earlier studies showed that strain inconsistencies between the coupled domains are caused by the coupling region’s (bridging domain, BD) resistance to spatial motion. Thus, this work examines influences of coupling parameters on strain convergence in Capriccio-coupled setups to study the mechanical behavior of solid amorphous materials. To this end, we employ a linear elastic 1D setup, imitating essential features of the Capriccio method, including force-transmitting anchor points (AP), which couple the domains via linear elastic springs. To assess the effect of more complex interactions in 3D models versus 1D results, we use an interdimensional mapping scheme, allowing qualitative and quantitative comparisons. For validation, we employ both an inelastic polystyrene MD model and a predominantly elastic silica glass MD model, each coupled to a corresponding FE material description. Our 1D results demonstrate that decreasing the conventionally high AP stiffness, along with other less significant measures, diminishes this motion resistance, revealing an optimal ratio between the material stiffness of the coupled domains and the cumulative AP stiffness. The 3D silica setup confirms that these measures ensure decent domain adherence and sufficiently low strain incompatibilities to study the mechanical behavior of elastic models. However, these measures turn out limited and may not ensure sufficient accuracy for studying the deformation and fracture behavior of Capriccio-coupled inelastic models. To overcome this, we employ a modified coupling approach, revising the Capriccio method’s AP concept by introducing a much lower so-called molecular statics stiffness during the FE calculation and a higher AP stiffness during only the MD calculation. Initial results on the 1D setup indicate that essential coupling limitations can be overcome, albeit with the risk of oscillatory strain amplifications depending on the BD’s design. This novel approach may enable a more accurate analysis of the mechanical behavior of coupled inelastic amorphous materials. We recommend evaluating its performance in 3D alongside additional methodological extensions. Overall, our results outline the current limitations of the Capriccio method and lay the groundwork for its targeted extension to study the mechanical behavior and, in particular, fracture phenomena in inelastic amorphous materials.

## Contact ##

Lukas Laubert
Institute of Applied Mechanics
Friedrich-Alexander-Universiät Erlangen-Nürnberg
Egerlandstraße 5
91058 Erlangen

## License ##

Creative Commons Attribution Non Commercial 4.0 International

## Folder structure, files, and notation ##

The data sets in "DataSet1dAnd3d" are split across two main folders:
    a) "1dDataSet" contains all simulation and postprocessing data as well as a documentation of all studies conducted using the one-dimensional framework [2]:
        - The spreadsheet "Documentation_data1d-OverCapLimit.xlsx" comprises the system and parameter settings for all conducted 1D simulations and resulting error values; it relates the folder and file names of related simulations as well as postprocessing data using the identifiers and structure from [1] with indication of the associated tables and figures.
        - The folders comprise visualizations for all studies documented in "Documentation_data1d-OverCapLimit.xlsx", also covering all simulations referred to in [1]:
            [file types]
            * "*.mat" files contain the full simulation data, which can be used to reconstruct every diagram.
            * ".fig" files contain visualizations of data that can be handled interactively using MATLAB.
            * ".pdf" files are PDF exports of the ".fig" files that can be opened using any PDF reader.
            * ".mp4" files are compressed video files, also indicated through "vid" after the second underscore, that contain videos of displacement of or position plots:
                ' "position" indicates a video showing all system parts their current position.
                ' "displacement" indicates a video showing the current displacement of all system parts over their initial position before the first load step.
            * ".txt" files contain text output from the simulation or postprocessing, including error values, as also indicated by "output" in the file names.
            * ".m" files contain text that were used for system definitions in [2]
            [file notation]
            * The abbreviation in the beginning of each file name before the first underscore, e.g., "com1BD", refers to the substudy name, which is listed in "Documentation_data1d-OverCapLimit.xlsx".
            * "disp_over_initPos" refers to a "displacement over initial position" diagram
            * "energy_over_LS" refers to a "total system energy over load step number" diagram
            * "energy_over_strain" refers to a "total system energy over target strain" diagram
            * "energy_over_totIS" refers to a "total system energy over the total number of iteration steps" diagram
            * "ls_over_currPos" shows the system state of all system parts at certain load step numbers by their current position along the deformation axis
            * "pos_zero" shows a system in its inital state by the spatial positions of all system parts
            * "srain_over_LS" refers to a "actual strain over load step number" diagram
            * "srain_over_strain" refers to a "actual strain over target strain" diagram
            * "srain_over_totIS" refers to a "actual strain over the total number of iteration steps" diagram
            * "forces" indicates a video or diagram that contains the resulting nodal (blue), particle (red), and anchor point (green) forces as well as the Lagrange Multiplier values (yellow); more information is provided in [5]
            * "monolithic" refers to monolithically solved load setups
            * "staggered" refers to staggered solved load setups
    b) "3dDataSet" contains 3D simulation and preparational data using [4] and a documentation:
        - The spreadsheet "Documentation_data3d_OverCapLimit.xlsx" comprises the system and parameter settings for all conducted 3D simulations, parameter values and procedure settings from the system preparation, as well as resulting error values; also stating corresponding information and results from 1D imitations; it relates the folder and file names of related simulations as well as postprocessing data using the identifiers and structure from [1] with indication of the associated tables and figures.
        - "3dSandwich_PS_sysPrepData" contains input, output, and postprocessing files from the 3D system setups related to system data from before and after the equilibration process for the polystyrene MD model, split across the folders "beforeEquilibration" and "afterEquilibration", respectively. The (folder) names assigned to the respective preparational setups used in this study can be found in “Documentation_data3d-OverCapLimit.xlsx”.
            * the respective folders contain files similar to those defined under [simulation input files] above, which are related to the system state before or after the equilibration, respectively
            * "Capriccio.prm" contains Parameter values used for the simulation in LAMMPS and the FEM package from [4]
            * "bounds.dat" states the x, y, and z dimensions of the MD setups
        - "3dSandwich_PS_resultData" (inlcuding subpath "ACK_lenBD") comprises results from three-dimensional Capriccio-based coupled simulations using the polystyrene (PS) MD model as specified in "Documentation_data3d-OverCapLimit.xlsx":
            * "input_files" contains the simulation input files and potential tables:
                [potential tables]
                ' "Angle_table_NANO" – bending interactions between two consecutive bonds
                ' "Bond_table_NANO" – pair-wise bonded interactions between two particles
                ' "Nonbond_table_NANO" – non-bonded interactions using a cut-off radius of 1.5 nm
                [simulation input files]
                ' "PS_CG_SBC.ac" – initial anchor Point IDs and positions
                ' "PS_CG_SBC.cae" – Abaqus file containing the FE mesh setup and the specified boundary conditions (only for reference; not used during the simulations)
                ' "PS_CG_SBC.data" – initial atoms IDs, molecule IDs, atom types, atom positions, and image flags
                ' "PS_CG_SBC.inp" – FE Input file containing the FE mesh setup and the specified boundary conditions
            * "input_parameters" contains parameter files for the simulation parameters in LAMMPS and the FEM package from [4]
            * The remaining are results files following the same notation as in [file types] above from a) "1dDataSet" with the following exceptions and additions:
                ' The abbreviation in the beginning of each file name before the first underscore, e.g., "06a", refers to the substudy name, which is listed in "Documentation_data3d-OverCapLimit.xlsx".
                ' ".mat", ".mp4", ".fig", and ".pdf" files result from the postprocessing using [3], applying the box slicing and averaging process described in [1]
                ' "strain_strain" refers to "actual strain over target strain" diagrams using the quantities resulting from the box slicing procedures described in [1]
                ' "lammps_log.txt" are logs of complete LAMMPS runs, comprising output information about, e.g., total energy, temperature, pressure, etc. from the total MD System
        - "3dSandwich_silica_resultData+sysPrep" comprises results from three-dimensional Capriccio-based coupled simulations using the silica MD model:
            * "dirichlet" both contain subfolders containing the respective simulation-related data and illustrations related to the studies listed in "Documentation_data1d-OverCapLimit.xlsx". Here, the same file types as defined for the PS simulations are available. Furthermore, these types of Simulation and preparational files are provided in "input_files":
                ' "potentials.lmpmod" – atom definitions and interatomic potentials
                ' "silica_quench_1_c_SPP.data" – initial atoms IDs, molecule IDs, atom types, atom positions, and image flags from the setup after quenching
                ' "silica_quench_1_c_SPP-sdx.data" – initial atoms IDs, molecule IDs, atom types, atom positions, and image flags after reduction of dipole moment in x direction
                ' "silica.data" – initial atoms IDs, molecule IDs, atom types, atom positions, and image flags following an energy minimazation procedure described in [6]