European Journal of Mechanics / A Solids

Data accompanying the research paper: Čanađija, M., Košmerl, V., Zlatić, M., Vrtovšnik, D., Munjas, N.: A computational framework for nanotrusses: input convex neural networks approach, European Journal of Mechanics - A/Solids (2023) Trained neural networks for true-stress vs. true strain uniaxial tension/compression curves and diameter vs. true strain for 818 different single-walled carbon nanotubes at 300 K. Datasets obtained by molecular dynamics (MD) are also enclosed. Results used in the second example in the above paper, obtained by MD are provided. In the case you find this dataset useful, please cite the above paper. Full bibliographic data can be found at the DOI link: https://doi.org/10.1016/j.euromechsol.2023.105195

These are the source files for the finite-strain Raviart-Thomas element, making use of Mathematica and Acegen.

Abaqus Python scripts for the analysis of laminar and fibrous infinite media undergoing a jamming transition

A Method for Selection of Structural Theories for Low to High Frequency Vibration Analyses HIGHER-ORDER WAVE PARAMETERS OF FLEXURAL BEAM VIBRATION FROM LOW TO HIGH FREQUENCIES

A tutorial for the improved Loewner Framework for modal analysis.

Abstract: from [1] Polymer nanocomposites (PNCs) have shown great potential to meet the ever-growing requirements of modern engineering applications. Nowadays, molecular dynamics (MD) simulations are increasingly employed to complement experimental work and thereby gain a deeper understanding of the complex structure–property relations of PNCs. However, with respect to the thermoplastic’s mechanical behavior, the role of its average molar mass is rarely addressed, and many MD studies only consider uniform (monodispersed) polymers. Therefore, this contribution investigates the impact that and the dispersity Đ have on the stiffness and strength of PNCs through coarse-grained MD. To this end, we employed a Kremer–Grest bead–spring model and observed the expected increase in the mechanical performance of the neat polymer for larger . Our results indicated that the unimodal molar mass distribution does not impact the mechanical behavior in the investigated dispersity range Đ. For the PNC, we obtained the same -dependence and Đ-independence of the mechanical properties over a wide range of filler sizes and contents. This contribution proves that even simple MD models can reproduce the experimentally well researched effect of the molar mass. Hence, this work is an important step in understanding the complex structure–property relations of PNCs, which is essential to unlock their full potential. Contact: Maximilian Ries Institute of Applied Mechanics Friedrich-Alexander-Universität Erlangen-Nürnberg Egerlandstr. 5 91058 Erlangen Software: All MD simulations were performed with LAMMPS [2,3], version: 23 Oct 2022 / 20220623 Compiled with Compiler: GNU C++ 11.2.0 with OpenMP not enabled C++ standard: C++11 Active compile time flags: -DLAMMPS_GZIP -DLAMMPS_SMALLBIG Installed packages: CLASS2 DPD-BASIC EXTRA-DUMP INTEL KSPACE MANYBODY MC MISC MOLECULE MOLFILE MPIIO NETCDF OPT PERI Polymer and polymer composite samples generated with self-avoiding random-walk algorithm [4] Post-processing Matlab R2019b License: Creative Commons Attribution 4.0 International Context: Data set supplementing journal paper: [1] M. Ries, L. Laubert, P. Steinmann, & S. Pfaller, “Impact of the unimodal molar mass distribution on the mechanical behavior of polymer nanocomposites below the glass transition temperature: A generic, coarse-grained molecular dynamics study,” European Journal of Mechanics - A/Solids, vol. 107, p. 105 379, 2024. Content: structure of data set: -01_neat containing the neat polymer simulations -01_uniform containing samples with uniform chain lengths -02_distributed containing samples with distributed chain lengths -100-dist samples with mean molar mass 100 -200-dist samples with mean molar mass 200 -02_PNC containing the polymer nanocomposite simulations -01_uniform containing samples with uniform chain lengths -T_0.2 simulations at temperature 0.2 -T_0.3 simulations at temperature 0.3 -T_0.4 simulations at temperature 0.4 -02_distributed containing samples with distributed chain lengths -T_0.2 simulations at temperature 0.2 -T_0.3 simulations at temperature 0.3 -T_0.4 simulations at temperature 0.4 naming convention for simulation folders - neat polymer simulations example: GTP_UT_num_chains-80_num_beads_per_chain-500-8 * num_chains: number of polymer chains * num_beads_per_chain: molar mass (chain length) * distribution: standard deviation of gauss distribution govering dispersity * "trailing number": batch number of sample - polymer nanocomposite simulations example: GTP_rF-5_nF-10_chainlen-5_7-T_0.2 * rF: nanofiller radius * nF: number of nanofillers * chainlen: molar mass (chain length) Each simulation directory contains: lammps input file (*.in) of the specific simulation data file (*.data) containing the initial sample configuration input.prm: input parameters of the specific simulation (read by the input file) meta.info: meta data of the specific simulation run LAMMPS_out: simulation results (lammps thermo_out) in tabulated form, an overview of columns is given below thermo_out.Dat: raw output thermo_out_SG.Dat: smoothed output (Savitzky-Golay filter) thermo_out_STD.Dat: standard deviation of raw output Output quantities (columns of *.Dat files): Please note that the normalized Lennard-Jones unit set is used, so all quantities are normalized to fundamental mass, length, energy, time and the Boltzmann constant. Thus all entries are unitless [1]. Step: time step Time: time TotEng: total energy PotEng: potential energy KinEng: kinetic energy E_pair: pair energy E_bond: bond energy E_angle: angle energy E_dihed: dihedral energy Temp: temperature Press: hydrostatic pressure Pxx: xx component of pressure tensor Pyy: yy component of pressure tensor Pzz: zz component of pressure tensor Pxy: xy component of pressure tensor Pxz: xz component of pressure tensor Pyz: yz component of pressure tensor Volume: volume of simulation box Lx: box length in x direction Ly: box length in y direction Lz: box length in z direction Density: density c_RG: radius of gyration scalar c_RG[1]: squared radius of gyration tensor (xx component) c_RG[2]: squared radius of gyration tensor (yy component) c_RG[3]: squared radius of gyration tensor (zz component) c_RG[4]: squared radius of gyration tensor (xy component) c_RG[5]: squared radius of gyration tensor (xz component) c_RG[6]: squared radius of gyration tensor (yz component) c_bondave[1]: bond energy averaged over all atoms c_bondave[2]: bond distance averaged over all atoms c_bondave[3]: squared bond distance averaged over all atoms c_angleave[1]: angle energy averaged over all atoms c_angleave[2]: angle averaged over all atoms degree c_angleave[3]: cosine of angle c_angleave[4]: squared cosine of angle c_MSD[1]: mean squared displacement x-direction c_MSD[2]: mean squared displacement y-direction c_MSD[3]: mean squared displacement z-direction c_MSD[4]: total mean squared displacement c_COM[1]: x coordinate of center of mass c_COM[2]: y coordinate of center of mass c_COM[3]: z coordinate of center of mass v_strain_xx: xx component of engineering strain tensor v_strain_yy: yy component of engineering strain tensor v_strain_zz: zz component of engineering strain tensor v_vMisesequivstress: von Mises equivalent stress v_Cauchy_xx: xx component of stress tensor v_Cauchy_yy: yy component of stress tensor v_Cauchy_zz: zz component of stress tensor v_Cauchy_xy: xy component of stress tensor v_Cauchy_xz: xz component of stress tensor v_Cauchy_yz: yz component of stress tensor v_strain_xy: xy component of engineering strain tensor v_strain_xz: xz component of engineering strain tensor v_strain_yz: yz component of engineering strain tensor References: [1] M. Ries, L. Laubert, P. Steinmann, & S. Pfaller, “Impact of the unimodal molar mass distribution on the mechanical behavior of polymer nanocomposites below the glass transition temperature: A generic, coarse-grained molecular dynamics study,” European Journal of Mechanics - A/Solids, vol. 107, p. 105 379, 2024. [2] S. Plimpton, “Fast parallel algorithms for short-range molecular dynamics,” Journal of computational physics, 1995, 117, 1-19. [3] A. P. Thompson 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. 108171, 2022. [4] J. Roksvaag, M.Ries . “A fast self-avoiding random walk algorithm (SARW) for generic thermoplastic polymers and nanocomposites”, manuscript in preparation

Ductile fracture through void growth to coalescence occurs at the grain scale in numerous metallic alloys encountered in engineering applications. Classical models used to perform numerical simulations of ductile fracture, like the Gurson-Tvergaard-Needleman model and its extensions, are relevant for the case of large voids compared to the grain size, in which a homogenization of the material behavior over a large number of grains is used. Such modelling prevents assessing the effects of microstructure on both crack path and propagation resistance. Therefore, in this upload, a material law based on homogenized constitutive equations for porous single crystals plasticity is proposed, featuring void growth and void coalescence stages, hardening and void shape evolutions. This finite strain material law is implemented within MFront code generator framework with an original numerical solving method based on the coupling of Newton-Raphson and fixed point algorithms. Void growth is accounted for by a mono-surface plastic yield criterion and void coalescence by another criterion derived from the classical yield function of Thomason. Three strain hardening modes are available and the finite strain paradigm used is logarithmic strain. Mfront material laws are suitable for mechanical solver codes with a UMAT-type routine, which enables the use of external material laws. Among such codes are Z-set, AMITEX_FFTP, CAST3M, Code_Aster, Abaqus...

Ductile fracture through void growth to coalescence occurs at the grain scale in numerous metallic alloys encountered in engineering applications. In order to perform mechanical homogenization of porous single crystals, a database of porous single crystal unit-cell simulation results has been gathered through Finite Element Modeling and Fast-Fourrier Transform simulations, respectively performed on Z-set and Amitex_FFTP. In these simulations, a cubic unit-cell with a unique central spherical void undergo axisymmetric mechanical loading. Mechanical simulations are performed within finite strain theory. Input parameters of interest are stress triaxiality, crystallographic orientation, initial porosity and strain hardening law type; results include macroscopic stress, macroscopic deformation gradient, porosity, void aspect ratio, ligament size and cell aspect ratio.