Abstract
We study the rheological response at low temperature of a sheared model disordered material as a function of the bond rigidity. We find that the flow curves follow a Herschel-Bulkley law, whatever is the bond rigidity, with an exponent close to 0.5. Interestingly, the apparent viscosity can be related to a single relevant time scale t rel, suggesting a strong connection between the local dynamics and the global mechanical behaviour. We propose a model based on the competition between the nucleation and the avalanche-like propagation of spatial strain heterogeneities. This model can explain the Herschel-Bulkley exponent on the basis of the size dependence of the heterogeneities on the shear rate.
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References
N.P. Bailey, J. Schiøtz, A. Lemaitre, K.W. Jacobsen, Phys. Rev. Lett. 98, 095501 (2007).
R. Besseling, E.R. Weeks, A.B. Schofield, W.C.K. Poon, Phys. Rev. Lett. 99, 028301 (2007).
L. Berthier, J.-L. Barrat, J. Chem. Phys. 116, 6228 (2002).
L. Berthier, J. Phys.: Condens. Matter 15, S933 (2003).
M. Möbius, G. Katgert, M. van Hecke, EPL 90, 44003 (2010).
P. Schall, D.A. Weitz, F. Spaepen, Science 318, 1895 (2007).
T. Gibaud, D. Frelat, S. Manneville, Soft Matter 6, 3482 (2010).
F. Da Cruz, F. Chevoir, D. Bonn, P. Coussot, Phys. Rev. E 66, 051305 (2002).
M. Dennin, Phys. Rev. E 70, 041406 (2004).
T. Majmudar, R. Behringer, Nature 435, 1079 (2005).
F. Varnik, O. Henrich, Phys. Rev. B 73, 174209 (2006).
Y. Shi, M.L. Falk, Phys. Rev. Lett. 95, 095502 (2005).
A. Tanguy, F. Lèonforte, J.-L. Barrat, Eur. Phys. J. E 20, 355 (2006).
M. Tsamados, Eur. Phys. J. E 32, 165 (2010).
C. Fusco, T. Albaret, A. Tanguy, Phys. Rev. E 82, 066116 (2010).
F. Delogu, Phys. Rev. Lett. 100, 255901 (2008).
T. Divoux, D. Tamarii, C. Barentin, S. Teitel, S. Manneville, Soft Matter 8, 4151 (2012).
P. Schall, M. van Hecke, Annu. Rev. Fluid Mech. 42, 67 (2010).
E.R. Weeks, Statistical Physics of Complex Fluids (Tohoku University Press, Sendai, Japan, 2007) pp. 243--255.
R. Höhler, S.C. Addad, J. Phys.: Condens. Matter 17, 1041 (2005).
P. Coussot, Soft Matter 3, 528 (2007).
H.A. Barnes, J.F. Hutton, K. Walters, An introduciton to Rheology (Elsevier, Amsterdam, 1989).
P. Sollich, F. Lequeux, P. Hébraud, M.E. Cates, Phys. Rev. Lett. 78, 2020 (1997).
M.L. Falk, J.S. Langer, Phys. Rev. E 57, 7192 (1998).
M.L. Falk, J.S. Langer, Annu. Rev. Condens. Matter Phys. 2, 353 (2011).
L. Berthier, L. Cugliandolo, J.L. Iguain, Phys. Rev. E 63, 051302 (2001).
K. Martens, L. Bocquet, J.-L. Barrat, Soft Matter 8, 4197 (2012).
D. Vandembroucq, S. Roux, Phys. Rev. B 84, 134210 (2011).
K.A. Dahmen, Y. Ben-Zion, J.T. Uhl, Phys. Rev. Lett. 102, 175501 (2009).
S.J. Plimpton, J. Comput. Phys. 117, (1995) see also http://lammps.sandia.gov.
D. Rodney, A. Tanguy, D. Vandembroucq, Modelling Simul. Mater. Sci. Eng. 19, 083001 (2011).
F.H. Stillinger, T.A. Weber, Phys. Rev. B 31, 5262 (1985).
J.M. Pelletier, B. Van de Moortele, I.R. Lu, Mater Sci. Eng. A 336, 190 (2002).
A. Lemaitre, C. Caroli, Phys. Rev. Lett. 103, 065501 (2009).
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Fusco, C., Albaret, T. & Tanguy, A. Rheological properties vs. local dynamics in model disordered materials at low temperature. Eur. Phys. J. E 37, 43 (2014). https://doi.org/10.1140/epje/i2014-14043-0
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DOI: https://doi.org/10.1140/epje/i2014-14043-0