# Comparison of shear and compression jammed packings of frictional disks

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## Abstract

We compare the structural and mechanical properties of mechanically stable (MS) packings of frictional disks in two spatial dimensions (2D) generated with isotropic compression and simple shear protocols from discrete element modeling (DEM) simulations. We find that the average contact number and packing fraction at jamming onset are similar (with relative deviations \(< 0.5\%\)) for MS packings generated via compression and shear. In contrast, the average stress anisotropy \(\langle {{\hat{\varSigma}}}_{xy} \rangle = 0\) for MS packings generated via isotropic compression, whereas \(\langle {{\hat{\varSigma}}}_{xy} \rangle >0\) for MS packings generated via simple shear. To investigate the difference in the stress state of MS packings, we develop packing-generation protocols to first unjam the MS packings, remove the frictional contacts, and then rejam them. Using these protocols, we are able to obtain rejammed packings with nearly identical particle positions and stress anisotropy distributions compared to the original jammed packings. However, we find that when we directly compare the original jammed packings and rejammed ones, there are finite stress anisotropy deviations \(\varDelta {{\hat{\varSigma }}}_{xy}\). The deviations are smaller than the stress anisotropy fluctuations obtained by enumerating the force solutions within the null space of the contact networks generated via the DEM simulations. These results emphasize that even though the compression and shear jamming protocols generate packings with the same contact networks, there can be residual differences in the normal and tangential forces at each contact, and thus differences in the stress anisotropy.

## Keywords

Granular materials Jamming Friction Shear jamming Force chains## Notes

### Acknowledgements

The authors (P.W., N.T.O. and C.S.O.) thank the Army Research Laboratory for supporting the research carried out in this work. This work also benefited from the facilities and staff of the Yale University Faculty of Arts and Sciences High Performance Computing Center. P.W. and F.X. contributed equally to the paper.

### Funding

This research was sponsored by the Army Research Laboratory under Grant No. W911NF-17-1-0164 (P.W., N.T.O., and C.S.O.). Computing resources were provided by the Army Research Laboratory Defense University Research Instrumentation Program Grant No. W911NF-18-1-0252. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Laboratory or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein. In addition, we acknowledge support from the China Scholarship Council Grant No. 201806210283 (F. X.).

### Compliance with ethical standards

### Conflict of interest

The authors declare that they have no conflict of interest.

## References

- 1.O’Hern, C.S., Silbert, L.E., Liu, A.J., Nagel, S.R.: Jamming at zero temperature and zero applied stress: the epitome of disorder. Phys. Rev. E
**68**, 011306 (2003)CrossRefADSGoogle Scholar - 2.Makse, H.A., Johnson, D.L., Schwartz, L.M.: Packing of compressible granular materials. Phys. Rev. Lett.
**84**, 4160 (2000)CrossRefADSGoogle Scholar - 3.Bertrand, T., Behringer, R.P., Chakraborty, B., O’Hern, C.S., Shattuck, M.D.: Protocol dependence of the jamming transition. Phys. Rev. E
**93**, 012901 (2016)CrossRefADSGoogle Scholar - 4.Bililign, E.S., Kollmer, J.E., Daniels, K.E.: Protocol dependence and state variables in the force-moment ensemble. Phys. Rev. Lett.
**122**, 038001 (2019)CrossRefADSGoogle Scholar - 5.Silbert, L.E.: Jamming of frictional spheres and random loose packing. Soft Matter
**6**, 2918–2924 (2010)CrossRefADSGoogle Scholar - 6.Miskin, M.Z., Jaeger, H.M.: Evolving design rules for the inverse granular packing problem. Soft Matter
**10**, 3708–3715 (2014)CrossRefADSGoogle Scholar - 7.Inagaki, S., Otsuki, M., Sasa, S.: Protocol dependence of mechanical properties in granular systems. Eur. Phys. J. E
**34**, 124 (2011)CrossRefGoogle Scholar - 8.Ciamarra, M.P., Nicodemi, M., Coniglio, A.: Recent results on the jamming phase diagram. Soft Matter
**6**, 2871–2874 (2010)CrossRefADSGoogle Scholar - 9.Majmudar, T.S., Behringer, R.P.: Contact force measurements and stress-induced anisotropy in granular materials. Nature
**435**, 1079 (2005)CrossRefADSGoogle Scholar - 10.Bi, D., Zhang, J., Chakraborty, B., Behringer, R.P.: Jamming by shear. Nature
**480**, 355 (2011)CrossRefADSGoogle Scholar - 11.Zhang, J., Majmudar, T., Behringer, R.: Force chains in a two-dimensional granular pure shear experiment. Chaos: an interdisciplinary journal of nonlinear science
**18**, 041107 (2008)CrossRefGoogle Scholar - 12.Zhang, J., Majmudar, T.S., Tordesillas, A., Behringer, R.P.: Statistical properties of a 2D granular material subjected to cyclic shear. Granul. Matter
**12**, 159–172 (2010)CrossRefGoogle Scholar - 13.Kondic, L., Goullet, A., O’Hern, C.S., Kramar, M., Mischaikow, K., Behringer, R.P.: Topology of force networks in compressed granular media. EPL (Europhys. Lett.)
**97**, 54001 (2012)CrossRefADSGoogle Scholar - 14.Gao, G.-J., Blawzdziewicz, J., O’Hern, C.S.: Frequency distribution of mechanically stable disk packings. Phys. Rev. E
**74**, 061304 (2006)CrossRefADSGoogle Scholar - 15.Gao, G.-J., Blawzdziewicz, J., O’Hern, C.S.: Geometrical families of mechanically stable granular packings. Phys. Rev. E
**80**, 061303 (2009)CrossRefADSGoogle Scholar - 16.Chen, S., Bertrand, T., Jin, W., Shattuck, M.D., O’Hern, C.S.: Stress anisotropy in shear-jammed packings of frictionless disks. Phys. Rev. E
**98**, 042906 (2018)CrossRefADSGoogle Scholar - 17.Papanikolaou, S., O’Hern, C.S., Shattuck, M.D.: Isostaticity at frictional jamming. Phys. Rev. Lett.
**110**, 198002 (2013).CrossRefADSGoogle Scholar - 18.Song, C., Wang, P., Makse, H.A.: A phase diagram for jammed matter. Nature
**453**, 629 (2008)CrossRefADSGoogle Scholar - 19.Shen, T., Papanikolaou, S., O Hern, C.S., Shattuck, M.D.: Statistics of frictional families. Phys. Rev. Lett.
**113**, 128302 (2014)CrossRefADSGoogle Scholar - 20.Shaebani, M.R., Unger, T., Kertész, J.: Extent of force indeterminacy in packings of frictional rigid disks. Phys. Rev. E
**79**, 052302 (2009)CrossRefADSGoogle Scholar - 21.Handin, J.: On the Coulomb Mohr failure criterion. J. Geophys. Res.
**74**, 5343–5348 (1969)CrossRefADSGoogle Scholar - 22.Cundall, P.A., Strack, O.D.: A discrete numerical model for granular assemblies. Geotechnique
**29**, 47–65 (1979)CrossRefGoogle Scholar - 23.Xu, N., Blawzdziewicz, J., O Hern, C.S.: Random close packing revisited: ways to pack frictionless disks. Phys. Rev. E
**71**, 061306 (2005)CrossRefADSGoogle Scholar - 24.Silbert, L.E., Ertas, D., Grest, G.S., Halsey, T.C., Levine, D.: Geometry of frictionless and frictional sphere packings. Phys. Rev. E
**65**, 031304 (2002)MathSciNetCrossRefADSGoogle Scholar - 25.Silbert, L.E., Ertas, D., Grest, G.S., Halsey, T.C., Levine, D., Plimpton, S.J.: Granular flow down an inclined plane: Bagnold scaling and rheology. Phys. Rev. E
**64**, 051302 (2001)CrossRefADSGoogle Scholar - 26.Clark, A.H., Shattuck, M.D., Ouellette, N.T., O’Hern, C.S.: Role of grain dynamics in determining the onset of sediment transport. Phys. Rev. Fluids
**2**, 034305 (2017)CrossRefADSGoogle Scholar - 27.Peyneau, P.E., Roux, J.N.: Frictionless bead packs have macroscopic friction, but no dilatancy. Phys. Rev. E
**78**, 011307 (2008)CrossRefADSGoogle Scholar - 28.Tighe, B.P., Snoeijer, J.H., Vlugt, T.J., van Hecke, M.: The force network ensemble for granular packings. Soft Matter
**6**, 2908–2917 (2010)CrossRefADSGoogle Scholar - 29.Shundyak, K., van Hecke, M., van Saarloos, W.: Force mobilization and generalized isostaticity in jammed packings of frictional grains. Phys. Rev. E
**75**, 010301 (2007)CrossRefADSGoogle Scholar - 30.Vinutha, H.A., Sastry, S.: Force networks and jamming in shear-deformed sphere packings. Phys. Rev. E
**99**, 012123 (2019)CrossRefADSGoogle Scholar - 31.Coleman, T.F., Li, Y.: A reflective Newton method for minimizing a quadratic function subject to bounds on some of the variables. SIAM J. Optim.
**6**, 1040–1058 (1996)MathSciNetCrossRefGoogle Scholar - 32.Royer, J.R., Chaikin, P.M.: Precisely cyclic sand: self-organization of periodically sheared frictional grains. Proc. Natl. Acad. Sci.
**112**, 49–53 (2015)CrossRefADSGoogle Scholar