Predicting Defects in Soft Sphere Packings near Jamming Using the Force Network Ensemble

James D. Sartor and Eric I. Corwin

Phys. Rev. Lett. 129, 188001 – Published 24 October 2022

Abstract

Amorphous systems of soft particles above jamming have more contacts than are needed to achieve mechanical equilibrium. The force network of a granular system with a fixed contact network is thus underdetermined and can be characterized as a random instantiation within the space of the force network ensemble. In this Letter, we show that defect contacts that are not necessary for stability of the system can be uniquely identified by examining the boundaries of this space of allowed force networks. We further show that, for simulations in the near jamming limit, this identification is nearly always correct and that defect contacts are broken under decompression of the system.

Received 8 September 2021
Accepted 23 September 2022

DOI:https://doi.org/10.1103/PhysRevLett.129.188001

Physics Subject Headings (PhySH)

Defects Jamming

Polymers & Soft Matter

Authors & Affiliations

James D. Sartor^* and Eric I. Corwin

Department of Physics and Materials Science Institute, University of Oregon, Eugene, Oregon 97403, USA

^*Corresponding author. jsartor7@uoregon.edu

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 129, Iss. 18 — 28 October 2022

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Scatter plot of the loads on each contact in the two states of self stress $F_{1}$ and $F_{2}$ (shown with arbitrary rotation) for a typical system ( $N = 128$ ) at 2SSS. Each point represents a contact in the system, with the $x$ coordinate determined by the load in $F_{1}$ and the $y$ coordinate determined by the load in $F_{2}$ for that contact. Positive values represent compressive loads, and negative values represent tensile loads. A sloped line passing through the origin (at angle $α$ ) represents the linear combination $F_{1} \sin α + F_{2} \cos α$ . The load on each contact in this linear combination can be understood as the distance from the line to each point. The black lines represent the two linear combinations of force eigenvectors at the boundary of the allowed region of force space (shaded green), i.e., the set of linear combinations for which all loads are compressive (or zero). These two linear combinations necessarily each bring a different set of contacts to zero force, shown highlighted in red. The green line shows the linear combination of the states of self stress that corresponds to the measured physical forces in the packing. Inset: a region near the origin in greater detail. For a more pedagogical explanation of this manner of visualizing the FNE, see Fig. 1 in [19].
Reuse & Permissions
Figure 2
(a) Evolution of mixing angle representation of the force space under decompression for the system in Fig. 1 over the range of pressures for which the system is at 2SSS. Position in force space is shown as mixing angles $α - α^{*}$ , where $α^{*}$ is the mixing angle of the system at the contact breaking event. Green shaded region shows all mixing angles for positive-definite force networks. Green line shows the physical forces. Red lines show the boundaries of the force network ensemble. Gray lines show mixing angles that would bring other contacts to zero force. (b) Evolution of the system in force space, shown as in the inset to Fig. 1. The highest and lowest pressures at which the system is at 2SSS are shown as gray circles and black $x$ ’s respectively, with arrows between them. Breakable contacts on the edge of force space are shown in red.
Reuse & Permissions
Figure 3
Probability of predicting contact breaking versus scaled pressure, for systems decompressing from 2SSS to 1SSS. The prediction is counted as a success if one of the two predicted sets of contacts are broken when the system reaches 1SSS. Data shown for FNE predictions in $N = 128$ (blue), 1024 (green), 8192 (red), for pressures at which at least 25 systems remain at 2SSS. The shaded region around each curve shows the 95% confidence interval for the estimation of the probability. Success of the affine response prediction of the smallest two contacts is shown for $N = 128$ (dark gray), 1024 (medium gray), 8192 (light gray).
Reuse & Permissions
Figure 4
Probability of correctly predicting contact breaking by FNE versus scaled pressure, for systems of $N = 1024$ particles decompressing from 2, 3, 4, and 5SSS to 1SSS. Colors represent number of states of self stress as indicated. At each pressure, the prediction is counted as a success if one of the $N_{cj}$ predicted sets of contacts are broken when the system reaches 1SSS. As in Fig. 3, data are shown only for pressures at which at least 25 systems remain at the indicated number of SSS. The shaded region around each curve shows the 95% confidence interval for the estimation of the probability. Probability of any of the $N_{cj}$ combinations of the smallest forces in the system breaking is shown in gray, from 2SSS (darkest gray) to 5SSS (lightest gray).
Reuse & Permissions

Physical Review Letters