DOI: 10.5281/zenodo.13768063
title: Assessing the Capriccio Method via One-dimensional Systems for Coupled Continuum-Particle Simulations in Various Uniaxial Load Cases using a Novel Interdimensional Comparison Approach – data set

description: 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, W. Felix, and S. Pfaller, "Assessing the Capriccio Method via One-dimensional Systems for Coupled Continuum-Particle Simulations in Various Uniaxial Load Cases using a Novel Interdimensional Comparison Approach", Computer Methods in Applied Mechanics and Engineering, in press, 2025.[2] L. Laubert, "One-dimensional framework imitating the Capriccio method for coupling the finite element method with particle-based techniques", Software, Zenodo, 2024. DOI: https://doi.org/10.5281/zenodo.13766914[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, 2024. DOI: https://doi.org/10.5281/zenodo.13767469[4] S. Pfaller, M. Ries, W. Zhao, C. Bauer , F. Weber, L. Laubert, "CAPRICCIO - Tool to run concurrent Finite Element-Molecular Dynamics Simulations", https://doi.org/10.5281/zenodo.12606758, Software, Zenodo, 2024.[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", https://doi.org/10.5281/zenodo.7924368, Project Thesis, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), 2023. DOI: [1] 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. DOI: https://doi.org/10.5281/zenodo.7924367

Abstract (from [1])

This contribution investigates sources of insufficiencies observed with the Capriccio method for concurrent continuum-particle coupling using a novel comparison technique. This approach maps the deformation states of three-dimensional (3D) coupled domains into a concise one-dimensional (1D) representation, which allows for a separate evaluation of the domain strains in a unified representation, enabling facile comparisons of the domain states during deformation. For the investigation, we employ both a 1D coupled system resembling the most relevant features of the full 3D Capriccio method as well as a corresponding 3D setup. Our analysis explores interactions between different material models in finite element (FE) and molecular dynamics (MD) domains. Based on various load cases studied in the 1D setup, we identify a resistance of the coupling region to spatial movement as the fundamental cause of strain convergence problems when applying the staggered solution scheme. Using the developped mapping approach, examination of the corresponding 3D setup reveals that these strain inconsistencies are even exacerbated by adverse relaxation effects in viscous MD models, particularly when coupled to a corresponding viscoelastic-viscoplastic FE model, leading to divergence from optimal strain. Our findings confirm that smaller strain increments in combination with larger load step numbers significantly improve strain convergence in all domains. Overall, this indicates the need for detailed sensitivity analysis of coupling parameter influences to reduce the identified motion resistance of the coupling region. Based on promising results in 1D, we further recommend exploring monolithic solving schemes for 3D systems to achieve optimal strain convergence for all types of Capriccio-based coupled particle and continuum material models. Moreover, our systematic approach of system definition and interdimensional comparison may serve as a model to assess other domain-decomposition coupling techniques.

Contact

Lukas LaubertInstitute of Applied MechanicsFriedrich-Alexander-Universiät Erlangen-NürnbergEgerlandstraße 591058 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-Cap1Dreview.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-Cap1Dreview.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-Cap1Dreview.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], corresponding one-dimensional imitations using [2], and a documentation:        - The spreadsheet "Documentation_data3d-Cap1Dreview.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.        - The subfolders "AA_numLS" and "AB_numBDs" refer to the two initial system setups used:            * only data from "AA_numLS" is covered by diagrams and elaborate discussion in [1]            * "AB_numBDs" refers to setups using more than one layer (here: four layers) of FE elements inside the coupling region        - "1dImitationOf3dSystems" comprises one-dimensional imitations of the three-dimensional deformation tests; the notation is equal to the one from "1dDataSet" above; further notation refers to designations from "Documentation_data3d-Cap1Dreview.xlsx" referring to 3D simulations.        - "3dSandwich_resultData" comprises results from three-dimensional Capriccio-based coupled simulations:            * "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., "01a", refers to the substudy name, which is listed in "Documentation_data3d-Cap1Dreview.xlsx". Please note that some data for the original 02b, which is referred to in the paper, got lost; therefore, the simulation was rerun months later, yielding only nearly identical results, most likely due to random terms in the DPD region. Only Appendix B shows the system state of the rerun result, while all other sections refer to the originally obtained data. Qualitatively, both results are similar.                ' ".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_sysPrepData" contains input, output, and postprocessing files from the 3D system setups related to system data from before and after the equilibration process, split across the folders "beforeEquilibration" and "afterEquilibration", respectively:            * "input_files" contains similar files as in [simulation input files] above, but related to the system state before the equilibration            * "input_parameters" contains parameter files for the simulation parameters in LAMMPS and the FEM package from [4]            * "equMD_files" contains the system files as in [simulation input files] related to its the MD domain's state after the equilibration            * "bounds.dat" states the x, y, and z dimensions of the MD setups            * "lammps_log.table" contains thermodynamic output (e.g. temperature, energy, pressure)            * ".fig" and ".pdf" files contain visualization files as in [file types] above:            * "KinEng.*", "PotEng.*", "Pressure.*", and "TotEng.*" respectively comprise the total kinetic energy, the total potential energy, the pressure averaged over the total system, and the total energy over the simulation time, respectively