[en] We report a study on granular matter with and without small additions of silicon oil, under low-frequency and large amplitude oscillatory shear strain under constant normal pressure, by running experiments with a rotational rheometer with a cup-and-plate geometry. We analysed the expansion with the Chebyshev polynomials of the orthogonal decomposition of stress–strain Lissajous–Bowditch loops. We found the onset of the strain amplitude for the yielding regime indicated a regime change from filament-like structures of grains to grain rearrangements for the dry granulate and from oscillations to the breaking and regeneration of liquid bridges for wet granulates. We have shown that this viscoelastic dynamics can be characterized by a noise temperature following Sollich et al. (Phys Rev Lett https://doi.org/10.1103/PhysRevLett.78.2020, 1997). The analysis of the first harmonics of the Chebyshev expansion showed that the state of disorder of dry and wet granular matter in pre-yielding and yielding regimes involved ensembles of different inherent states; thus, each of them was governed by a different noise temperature. The higher-order harmonics of the Chebyshev expansion revealed a proportionality between the viscous nonlinearity and the variation in the elastic nonlinearity induced by the deformation, which shows the coupling between the elastic deformation and the viscous flow of mesoscopic-scale structures.
M. Becker, H. Lippmann, Plane plastic flow of granular model material. Experimental setup and results. Arch. Mech. 29, 829–846 (1977)
S. Dartevelle, Numerical and granulometric approaches to geophysical granular flows. Dissertation, Michigan Technological University, Michigan, 2003. https://digitalcommons.mtu.edu/cgi/viewcontent.cgi?referer=https://duckduckgo.com/httpsredir=1article=1315context=etds
On dense granular flows, GDR-MiDi. Eur. Phys. J. E 14, 341–365 (2004). 10.1140/epje/i2003-10153-0 DOI: 10.1140/epje/i2003-10153-0
O. Pouliquen, C. Cassar, P. Jop, Y. Forterre, M. Nicolas, Flow of dense granular material: towards simple constitutive laws. J. Stat. Mech. (2006). 10.1088/1742-5468/2006/07/P07020 DOI: 10.1088/1742-5468/2006/07/P07020
P. Jop, Y. Forterre, O. Pouliquen, A constitutive law for dense granular flows. Nature 441, 727–30 (2006). 10.1038/nature04801 DOI: 10.1038/nature04801
Y. Forterre, O. Pouliquen, Flows of dense granular media. Annu. Rev. Fluid Mech. 40(1), 1–24 (2008). 10.1146/annurev.fluid.40.111406.102142 DOI: 10.1146/annurev.fluid.40.111406.102142
S. Luding, The effect of friction on wide shear bands. Part. Sci. Technol. (2007). 10.1080/02726350701759167 DOI: 10.1080/02726350701759167
S. Luding, S. Luding, Cohesive, frictional powders: contact models for tension. Granul. Matter 10, 235–246 (2008). 10.1007/s10035-008-0099-x DOI: 10.1007/s10035-008-0099-x
F. da Cruz, S. Emam, M. Prochnow, J.-N. Roux, F.M.C. Chevoir, Rheophysics of dense granular materials: Discrete simulation of plane shear flows. Phys. Rev. E 72, 021309 (2005). 10.1103/PhysRevE.72.021309 DOI: 10.1103/PhysRevE.72.021309
G. Lois, A. Lemaître, J. Carlson, Numerical tests of constitutive laws for dense granular flows. Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 72, 051303 (2005). 10.1103/PhysRevE.72.051303 DOI: 10.1103/PhysRevE.72.051303
P.G. Rognon, J.-N. Roux, M. Naaïm, F. Chevoir, Dense flows of cohesive granular materials. J. Fluid Mech. 596, 21–47 (2008). 10.1017/S0022112007009329 DOI: 10.1017/S0022112007009329
K. Kamrin, G. Koval, Nonlocal constitutive relation for steady granular flow. Phys. Rev. Lett. 108, 178301 (2012). 10.1103/PhysRevLett.108.178301 DOI: 10.1103/PhysRevLett.108.178301
Q. Zhang, K. Kamrin, Microscopic description of the granular fluidity field in nonlocal flow modeling. Phys. Rev. Lett. 118, 058001 (2017). 10.1103/PhysRevLett.118.058001 DOI: 10.1103/PhysRevLett.118.058001
D. Berzi, J.T. Jenkins, Fluidity, anisotropy, and velocity correlations in frictionless, collisional grain flows. Phys. Rev. Fluids 3, 094303 (2018). 10.1103/PhysRevFluids.3.094303 DOI: 10.1103/PhysRevFluids.3.094303
T. Boutreux, P.G. de Geennes, Compaction of granular mixtures: a free volume model. Phys. A Stat. Mech. Appl. 244(1), 59–67 (1997). 10.1016/S0378-4371(97)00236-7 DOI: 10.1016/S0378-4371(97)00236-7
G. Lumay, N. Vandewalle, Experimental study of granular compaction dynamics at different scales: grain mobility, hexagonal domains, and packing fraction. Phys. Rev. Lett. (2005). 10.1103/physrevlett.95.028002 DOI: 10.1103/physrevlett.95.028002
G. D’Anna, G. Gremaud, The jamming route to the glass state in weakly perturbed granular media. Nature 413, 407–9 (2001). 10.1038/35096540 DOI: 10.1038/35096540
G. D’Anna, P. Mayor, G. Gremaud, A. Barrat, V. Loreto, Extreme events driven glassy behaviour in granular media. EPL (Europhys. Lett.) (2002). 10.1209/epl/i2003-00245-y DOI: 10.1209/epl/i2003-00245-y
P. Philippe, D. Bideau, Compaction dynamics of a granular media under vertical tapping. EPL (Europhys. Lett.) 60, 677 (2007). 10.1209/epl/i2002-00362-7 DOI: 10.1209/epl/i2002-00362-7
K. Lu, E. Brodsky, H. Kavehpour, A thermodynamic unification of jamming. Nat. Phys. (2008). 10.1038/nphys934 DOI: 10.1038/nphys934
K. Lu, E. Brodsky, H. Kavehpour, Shear-weakening of the transitional regime for granular flow. J. Fluid Mech. 587, 347–372 (2007). 10.1017/S0022112007007331 DOI: 10.1017/S0022112007007331
P. Sollich, F. Lequeux, P. Hébraud, M.E. Cates, Rheology of soft glassy materials. Phys. Rev. Lett. (1997). 10.1103/PhysRevLett.78.2020 DOI: 10.1103/PhysRevLett.78.2020
S.M. Fielding, Ageing, driving and effective temperatures: from ’soft rheology’ to glassy dynamics. Thesis (Ph.D.), University of Edinburgh, Edinburgh (2000). https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.650886
S.M. Fielding, Elastoviscoplastic rheology and aging in a simplified soft glassy constitutive model. J. Rheol. 64(3), 723–738 (2020). 10.1122/1.5140465 DOI: 10.1122/1.5140465
P. Sollich, M.E. Cates, Thermodynamic interpretation of soft glassy rheology models. Phys. Rev. E 85, 031127 (2012). 10.1103/PhysRevE.85.031127 DOI: 10.1103/PhysRevE.85.031127
J.E. Fiscina, M. Pakpour, A. Fall, N. Vandewalle, C. Wagner, D. Bonn, Dissipation in quasistatically sheared wet and dry sand under confinement. Phys. Rev. E (2012). 10.1103/physreve.86.020103 DOI: 10.1103/physreve.86.020103
J.E. Fiscina, G. Lumay, F. Ludewig, N. Vandewalle, Compaction dynamics of wet granular assemblies. Phys. Rev. Lett. 105, 048001 (2010). 10.1103/PhysRevLett.105.048001 DOI: 10.1103/PhysRevLett.105.048001
N. Vandewalle, G. Lumay, F. Ludewig, J. Fiscina, How relative humidity affects random packing experiments. Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 85, 031309 (2012). 10.1103/PhysRevE.85.031309 DOI: 10.1103/PhysRevE.85.031309
D. Geromichalos, Dynamik Feuchter Granulate. Dissertation zur Erlangung des Doktorgrades Dr. rer. nat. der Fakultät für Naturwissenschaften der Universität Ulm, Ulm, Deutschland (2004). https://doi.org/10.18725/OPARU-95
R. Darby, Chemical Engineering Fluid Mechanics, 2nd edn. (CRC Press, Boca Raton, FL, 2001)
A. Gemant, The conception of a complex viscosity and its application to dielectrics. Trans. Faraday Soc. 31, 1582–1590 (1935). 10.1039/TF9353101582 DOI: 10.1039/TF9353101582
S. Rogers, Large amplitude oscillatory shear: simple to describe, hard to interpret. Phys. Today 71(7), 34–40 (2018). 10.1063/PT.3.3971 DOI: 10.1063/PT.3.3971
M.A. Kanso, A.J. Giacomin, C. Saengow, Large-amplitude oscillatory shear flow loops for long-chain branching from general rigid bead-rod theory. Phys. Fluids 32(5), 053102 (2020). 10.1063/5.0009752 DOI: 10.1063/5.0009752
K.S. Cho, K. Hyun, K. Ahn, S. Lee, A geometrical interpretation of large amplitude oscillatory shear response. J. Rheol. 49, 747 (2005). 10.1122/1.1895801 DOI: 10.1122/1.1895801
R. Ewoldt, A. Hosoi, G. McKinley, New measures for characterizing nonlinear viscoelasticity in large amplitude oscillatory shear. J. Rheol. 52(6), 1427–1458 (2008). 10.1122/1.2970095 DOI: 10.1122/1.2970095
J.D. Ferry, H.S. Myers, Viscoelastic properties of polymers. J. Electrochem. Soc. 108(7), 142 (1961). 10.1149/1.2428174 DOI: 10.1149/1.2428174
R.H. Ewoldt, Defining nonlinear rheological material functions for oscillatory shear. J. Rheol. 57(1), 177–195 (2013). 10.1122/1.4764498 DOI: 10.1122/1.4764498
K. Hyun, M. Wilhelm, C.O. Klein, K.S. Cho, J.G. Nam, K.H. Ahn, S.J. Lee, R.H. Ewoldt, G.H. McKinley, A review of nonlinear oscillatory shear tests: analysis and application of large amplitude oscillatory shear (laos). Prog. Polym. Sci. 36(12), 1697–1753 (2011). 10.1016/j.progpolymsci.2011.02.002 DOI: 10.1016/j.progpolymsci.2011.02.002
J. Läuger, H. Stettin, Differences between stress and strain control in the non-linear behavior of complex fluids. Rheol. Acta 49(9), 909–930 (2010). 10.1007/s00397-010-0450-0 DOI: 10.1007/s00397-010-0450-0
S.A. Rogers, B.M. Erwin, D. Vlassopoulos, M. Cloitre, A sequence of physical processes determined and quantified in LAOS: application to a yield stress fluid. J. Rheol. 55(2), 435–458 (2011). 10.1122/1.3544591 DOI: 10.1122/1.3544591
S.A. Rogers, M.P. Lettinga, A sequence of physical processes determined and quantified in large-amplitude oscillatory shear (LAOS): application to theoretical nonlinear models. J. Rheol. 56(1), 1–25 (2012). 10.1122/1.3662962 DOI: 10.1122/1.3662962
S.A. Rogers, In search of physical meaning: defining transient parameters for nonlinear viscoelasticity. Rheol. Acta 56, 501–525 (2017). 10.1007/s00397-017-1008-1 DOI: 10.1007/s00397-017-1008-1
J.D. Park, S.A. Rogers, A sequence of physical processes determined and quantified in large-amplitude oscillatory shear (LAOS): application to theoretical nonlinear models. J. Rheol. 62(4), 869–888 (2018). 10.1122/1.5024701 DOI: 10.1122/1.5024701
R.B. Bird, J.M. Wiest, Constitutive equations for polymeric liquids. Ann. Rev. Fluid Mech. 27(1), 169–193 (1995). 10.1146/annurev.fl.27.010195.001125 DOI: 10.1146/annurev.fl.27.010195.001125
M. Wilhelm, D. Maring, H.-W. Spiess, Fourier-transform rheology. Rheol. Acta 37(4), 399–405 (1998). 10.1007/s003970050126 DOI: 10.1007/s003970050126
M.R.B. Mermet-Guyennet, J. Gianfelice de Castro, M. Habibi, N. Martzel, M.M. Denn, D. Bonn, LAOS: the strain softening/strain hardening paradox. J. Rheol. 59(1), 21–32 (2015). 10.1122/1.4902000 DOI: 10.1122/1.4902000
M. Scheel, R. Seemann, M. Brinkmann, M. Di Michiel, A. Sheppard, B. Breidenbach, S. Herminghaus, Morphological clues to wet granular pile stability. Nat. Mater. 7, 189–93 (2008). 10.1038/nmat2117 DOI: 10.1038/nmat2117
M. Badetti, A. Fall, F. Chevoir, J.-N. Roux, Shear strength of wet granular materials: macroscopic cohesion and effective stress. Eur. Phys. J. E 41(5), 68 (2018). 10.1140/epje/i2018-11677-8 DOI: 10.1140/epje/i2018-11677-8
J.P.D. Clewett, K. Roeller, R.M. Bowley, S. Herminghaus, M.R. Swift, Emergent surface tension in vibrated, noncohesive granular media. Phys. Rev. Lett. 109, 228002 (2012). 10.1103/PhysRevLett.109.228002 DOI: 10.1103/PhysRevLett.109.228002
M. Scheel, R. Seemann, M. Brinkmann, M.D. Michiel, A. Sheppard, S. Herminghaus, Liquid distribution and cohesion in wet granular assemblies beyond the capillary bridge regime. J. Phys. Condens. Matter 20(49), 494236 (2008) DOI: 10.1088/0953-8984/20/49/494236
F. Fan, E.J.R. Parteli, T. Pöschel, Origin of granular capillarity revealed by particle-based simulations. Phys. Rev. Lett. 118, 218001 (2017). 10.1103/PhysRevLett.118.218001 DOI: 10.1103/PhysRevLett.118.218001
Y.I. Rabinovich, M.S. Esayanur, B.M. Moudgil, Capillary forces between two spheres with a fixed volume liquid bridge: theory and experiment. Langmuir 21(24), 10992–10997 (2005). 10.1021/la0517639 DOI: 10.1021/la0517639
O. Pitois, P. Moucheront, X. Chateau, Rupture energy of a pendular liquid bridge. Eur. Phys. J. B 23(1), 79–86 (2001). 10.1007/s100510170084 DOI: 10.1007/s100510170084
S. Herminghaus, Dynamics of wet granular matter. Adv. Phys. 54, 221–261 (2005). 10.1080/00018730500167855 DOI: 10.1080/00018730500167855
S. Fielding, M. Cates, P. Sollich, Shear banding, aging and noise dynamics in soft glassy materials. Soft Matter (2009). 10.1039/B812394M DOI: 10.1039/B812394M
C. Ness, Z. Xing, E. Eiser, Oscillatory rheology of dense, athermal suspensions of nearly hard spheres below the jamming point. Soft Matter 13(19), 3664–3674 (2017). 10.1039/c7sm00039a
M. Bouzid, A. Izzet, M. Trulsson, E. Clément, P. Claudin, B. Andreotti, Non-local rheology in dense granular flows. Eur. Phys. J. E (2015). 10.1140/epje/i2015-15125-1 DOI: 10.1140/epje/i2015-15125-1
F. Ludewig, S. Dorbolo, T. Gilet, N. Vandewalle, Energetic approach for the characterization of taps in granular compaction. EPL (Europhys. Lett.) 84, 44001 (2008). 10.1209/0295-5075/84/44001 DOI: 10.1209/0295-5075/84/44001
S. Song, F. Zhu, M. Chen, Universal scaling law of glass rheology. Nat. Mater. (2022). 10.1038/s41563-021-01185-y DOI: 10.1038/s41563-021-01185-y
H. Hayakawa, D.C. Hong, Thermodynamic theory of weakly excited granular systems. Phys. Rev. Lett. 78, 2764–2767 (1997). 10.1103/PhysRevLett.78.2764 DOI: 10.1103/PhysRevLett.78.2764
J.E. Fiscina, M.O. Cáceres, Fermi-like behavior of weakly vibrated granular matter. Phys. Rev. Lett. 95, 108003 (2005). 10.1103/PhysRevLett.95.108003 DOI: 10.1103/PhysRevLett.95.108003
D. Janković-Ilić, J. Fiscina, C. Oliver, N. Ilić, F. Muecklich, Self formed cu-w functionally graded material produced via powder segregation. Adv. Eng. Mater. 9, 542–546 (2007). 10.1002/adem.200700095 DOI: 10.1002/adem.200700095
D. Janković-Ilić, J. Fiscina, C. Oliver, N. Ilić, F. Mücklich, Electrical and elastic properties of cu-w graded material produced by vibro compaction. J. Mater. Sci. 43, 6777–6783 (2008). 10.1007/s10853-008-2941-2 DOI: 10.1007/s10853-008-2941-2
J. Rafelski, Connecting qgp-heavy ion physics to the early universe, in Proceedings of the IV International Conference on Particle and Fundamental Physics in Space Nuclear Physics B: Proceedings Supplements (243–244, 155–162, 2013). https://doi.org/10.1016/j.nuclphysbps.2013.09.017
Q. Sun, F. Jin, G. Wang, S. Song, G. Zhang, On granular elasticity. Sci. Rep. (2015). 10.1038/srep09652 DOI: 10.1038/srep09652
N. Kumar, S. Luding, Memory of jamming-multiscale models for soft and granular matter. Granul. Matter (2016). 10.1007/s10035-016-0624-2 DOI: 10.1007/s10035-016-0624-2
H. Shi, S. Roy, T. Weinhart, V. Magnanimo, S. Luding, Steady state rheology of homogeneous and inhomogeneous cohesive granular materials. Granul. Matter (2019). 10.1007/s10035-019-0968-5 DOI: 10.1007/s10035-019-0968-5
