Abstract
We find that in simulations of quasi-statically sheared frictional disks, the shear jamming transition can be characterized by an abrupt jump in the number of force bearing contacts between particles. This mechanical coordination number increases discontinuously from Z = 0 to \(Z \gtrsim d +1\) at a critical shear value \(\gamma _c\), as opposed to a smooth increase in the number of geometric contacts. This is accompanied by a diverging timescale \(\tau ^*\) that characterizes the time required by the system to attain force balance when subjected to a perturbation. As the global shear \(\gamma \) approaches the critical value \(\gamma _c\) from below, one observes the divergence of the time taken to relax to a state where all the inter-particle contacts have uniformly zero force. Above \(\gamma _{c}\), the system settles into a state characterized by finite forces between particles, with the timescale also increasing as \(\gamma \rightarrow \gamma _{c}^{+}\). By using two different protocols to generate force balanced configurations, we show that this timescale divergence is a robust feature that accompanies the shear jamming transition.
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Chaikin, P.M., Lubensky, T.C.: Principles of Condensed Matter Physics. Cambridge University Press, Cambridge (2000)
Debenedetti, P.G., Stillinger, F.H.: Supercooled liquids and the glass transition. Nature 410, 259 (2001)
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)
Cates, M., Wittmer, J., Bouchaud, J.-P., Claudin, P.: Jamming, force chains, and fragile matter. Phys. Rev. Lett. 81, 1841 (1998)
Bi, D., Zhang, J., Chakraborty, B., Behringer, R.: Jamming by shear. Nature 480, 355 (2011)
Wyart, M., Cates, M.: Discontinuous shear thickening without inertia in dense non-Brownian suspensions. Phys. Rev. Lett. 112, 098302 (2014)
Sarkar, S., Bi, D., Zhang, J., Behringer, R., Chakraborty, B.: Origin of rigidity in dry granular solids. Phys. Rev. Lett. 111, 068301 (2013)
Vinutha, H.A., Sastry, S.: Disentangling the role of structure and friction in shear jamming. Nat. Phys. 12, 578 (2016)
Baity-Jesi, M., Goodrich, C.P., Liu, A.J., Nagel, S.R., Sethna, J.P.: Emergent SO(3) symmetry of the frictionless shear jamming transition. J. Stat. Phys. 167, 735 (2017)
Urbani, P., Zamponi, F.: Shear yielding and shear jamming of dense hard sphere glasses. Phys. Rev. Lett. 118, 038001 (2017)
Behringer, R.P., Chakraborty, B.: The physics of jamming for granular materials: a review. Rep. Prog. Phys. 82, 012601 (2018)
Otsuki, M., Hayakawa, H.: Shear jamming, discontinuous shear thickening, and fragile state in dry granular materials under oscillatory shear. arXiv preprint arXiv:1810.03846 (2018)
Howell, D., Behringer, R., Veje, C.: Stress fluctuations in a 2D granular Couette experiment: a continuous transition. Phys. Rev. Lett. 82, 5241 (1999)
Majmudar, T., Sperl, M., Luding, S., Behringer, R.P.: Jamming transition in granular systems. Phys. Rev. Lett. 98, 058001 (2007)
Sarkar, S., Chakraborty, B.: Shear-induced rigidity in athermal materials: a unified statistical framework. Phys. Rev. E 91, 042201 (2015)
Henkes, S., Quint, D.A., Fily, Y., Schwarz, J.: Rigid cluster decomposition reveals criticality in frictional jamming. Phys. Rev. Lett. 116, 028301 (2016)
Vinutha, H., Sastry, S.: Force networks and jamming in shear-deformed sphere packings. Phys. Rev. E 99, 012123 (2019)
Morone, F., Burleson-Lesser, K., Vinutha, H., Sastry, S., Makse, H.A.: The jamming transition is a k-core percolation transition. Physica A 516, 172 (2019)
Olsson, P., Teitel, S.: Critical scaling of shear viscosity at the jamming transition. Phys. Rev. Lett. 99, 178001 (2007)
Ramola, K., Chakraborty, B.: Disordered contact networks in jammed packings of frictionless disks. J. Stat. Mech. Theory Exp. 2016, 114002 (2016)
Ramola, K., Chakraborty, B.: Scaling theory for the frictionless unjamming transition. Phys. Rev. Lett. 118, 138001 (2017)
Vinutha, H.A.: Ph.D. Thesis, Tata Institute of Fundamental Research (2018)
Cundall, P.A., Strack, O.D.: A discrete numerical model for granular assemblies. Geotechnique 29, 47 (1979)
Silbert, L.E.: Jamming of frictional spheres and random loose packing. Soft Matter 6, 2918 (2010)
Grob, M., Zippelius, A., Heussinger, C.: Rheological chaos of frictional grains. Phys. Rev. E 93, 030901 (2016)
Plimpton, S.: Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 117, 1 (1995)
Vinutha, H., Sastry, S.: Geometric aspects of shear jamming induced by deformation of frictionless sphere packings. J. Stat. Mech. Theory Exp. 2016, 094002 (2016)
Péter, H., Libál, A., Reichhardt, C., Reichhardt, C.J.: Crossover from jamming to clogging behaviours in heterogeneous environments. Sci Rep 8, 10252 (2018)
Ikeda, A., Kawasaki, T., Berthier, L., Saitoh, K., Hatano, T.: arXiv Preprint arXiv:1904.07359 (2019)
Das, P., Vinutha, H. A., Sastry, S.: Unified phase diagram of reversible-irreversible, jamming and yielding transitions in cyclically sheared soft sphere packings. arXiv preprint arXiv:1907.08503 (2019)
Seto, R., Singh, A., Chakraborty, B., Denn, M. M., Morris, J. F.: Shear jamming and fragility in dense suspensions. arXiv preprint arXiv:1902.04361 (2019)
Acknowledgements
We dedicate this work to the memory of Bob Behringer whose insightful experiments with granular matter are an inspiration to us all. We acknowledge support from the Indo-US Science and Technology Forum (grant no. IUSSTF/JC-026/2016). The work of BC and KR has been supported by NSF-CBET 1605428. BC acknowledges a fellowship from the Simons Foundation. SS and HAV gratefully acknowledge TUE-CMS, SSL, JNCASR, for computational resources and support. SS acknowledges support through the J C Bose Fellowship, DST, India.
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Vinutha, H.A., Ramola, K., Chakraborty, B. et al. Timescale divergence at the shear jamming transition. Granular Matter 22, 16 (2020). https://doi.org/10.1007/s10035-019-0983-6
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DOI: https://doi.org/10.1007/s10035-019-0983-6