kstress: a LAMMPS package for calculating the 2D wavevector-dependent stress tensor and its anisotropy in amorphous solids
Abstract
The stress tensor resolved in wavevector qvec and time t, σαβ(qvec,t), gives access to the elastic moduli of amorphous solids as a function of the probed length scale, and to the long-range stress correlations that distinguish an amorphous solid from a liquid. Its evaluation requires the contribution of every interacting pair and therefore an interface to the force loop of the molecular dynamics code. In the current work, we present: i) an optimized implementation of the LAMMPS~\cite{lammps} module for calculating σαβ(qvec,t), in which trigonometric functions are calculated only for the basic wavevectors and, in addition, all the relevant wavevectors are supplied as an explicit list rather than generated as a full grid, so that only the wavevectors of interest are computed and stored, and ii) a validation protocol for the code illustrated for a two-dimensional polydisperse Lennard-Jones (2DpLJ) glass-forming liquid. Based on these technical achievements we elucidated how the affine moduli for the 2DpLJ model depend on the norm q of the wavevector. In particular, we demonstrate that the longitudinal affine modulus shows a minimum near qmax corresponding to the main peak of the structure factor. Our data also point to the peaks in the q-dependencies of vibrational frequencies well below qmax for both transverse and longitudinal modes. The potential relevance of this feature to the ``boson peak'' is discussed as well.
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BibTeX
@misc{benzerara2026kstress,
title = {{kstress: a LAMMPS package for calculating the 2D wavevector-dependent stress tensor and its anisotropy in amorphous solids}},
author = {Olivier Benzerara and Jörg Baschnagel and Alexander N. Semenov and Liudmyla Klochko},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.34206},
eprint = {2610.34206},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.34206},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - kstress: a LAMMPS package for calculating the 2D wavevector-dependent stress tensor and its anisotropy in amorphous solids
AU - Olivier Benzerara
AU - Jörg Baschnagel
AU - Alexander N. Semenov
AU - Liudmyla Klochko
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2610.34206
UR - https://arxiv.org/abs/2610.34206
AB - The stress tensor resolved in wavevector qvec and time t, σ_αβ(qvec,t), gives access to the elastic moduli of amorphous solids as a function of the probed length scale, and to the long-range stress correlations that distinguish an amorphous solid from a liquid. Its evaluation requires the contribution of every interacting pair and therefore an interface to the force loop of the molecular dynamics code. In the current work, we present: i) an optimized implementation of the LAMMPS~\cite{lammps} module for calculating σ_αβ(qvec,t), in which trigonometric functions are calculated only for the basic wavevectors and, in addition, all the relevant wavevectors are supplied as an explicit list rather than generated as a full grid, so that only the wavevectors of interest are computed and stored, and ii) a validation protocol for the code illustrated for a two-dimensional polydisperse Lennard-Jones (2DpLJ) glass-forming liquid. Based on these technical achievements we elucidated how the affine moduli for the 2DpLJ model depend on the norm q of the wavevector. In particular, we demonstrate that the longitudinal affine modulus shows a minimum near q_max corresponding to the main peak of the structure factor. Our data also point to the peaks in the q-dependencies of vibrational frequencies well below q_max for both transverse and longitudinal modes. The potential relevance of this feature to the ``boson peak'' is discussed as well.
ER -