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Stress correlations in near-crystalline packings
by Roshan Maharana and Kabir Ramola
Submission summary
| Authors (as registered SciPost users): | Roshan Maharana |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202311_00022v2 (pdf) |
| Date submitted: | 2024-04-16 11:45 |
| Submitted by: | Maharana, Roshan |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
We derive exact results for stress-correlations in near-crystalline systems in two and three dimensions. We study energy minimized configurations of particles interacting through Harmonic as well as Lennard-Jones potentials, for varying degrees of microscopic disorder and quenched forces on grains. Our findings demonstrate that the macroscopic elastic properties of such near-crystalline packings remain unchanged within a certain disorder threshold, yet they can be influenced by various factors, including packing density, pressure, and the strength of inter-particle interactions. We show that the stress-correlations in such systems display anisotropic behavior at large lengthscales and are significantly influenced by the pre-stress of the system. The anisotropic nature of these correlations remains unaffected as we increase the strength of the disorder. Additionally, we derive the large lengthscale behavior for the change in the local stress components that shows a $1/r^d$ radial decay for the case of particle size disorder and a $1/r^{d-1}$ behavior for quenched forces introduced into a crystalline network. Finally, we verify our theoretical results numerically using energy-minimised static particle configurations.
Author comments upon resubmission
List of changes
Below we write the list of changes in the revised manuscript.
1. Both Figure 1 and Figure 9 are cited in the main text.
2. The sequence of figures now corresponds to the order of citation.
3. Definitions for variables such as $\lambda_{SS},\lambda_{SL},\lambda_{LL}$ in Eq. (4) and $\mathcal{P}_1,\mathcal{P}_2$ in Eq. (23) are provided in sections 2.2 and 5, respectively.
4. Figure 2 has been updated to include the variation of the difference $B_{theory}-\langle B \rangle$ and $G_{theory}-\langle G \rangle$ in logarithmic scale.
5. Previous numerical finding regarding the variation of elastic modulus with disorder is cited on Page 7 as reference [31].
6. Centrosymmetry order parameter for near-crystalline packings are measured and written in Page 8.
7. Relevant citations for measuring the centrosymmetry order parameter are included as references [67], [68], and [69].
8. Appendix D now provides a comprehensive explanation of the measurement of Inversion symmetry order parameter.
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