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Using a direct shear-box capable of very low shearing rate, we measure the force-displacement curve of cyclic, large-amplitude shear, and also the total plastic displacement residual after each cycle, for samples of glass beads. As the shear rate decreases, we observe a transition from normal, elastoplastic behavior to pure elastic behavior, with reducing residual, or total plastic, displacement after each cycle. Remarkably, this transition is also observed for large amplitude of the cyclic shear, up to 90% of the failure value. The force-displacement relation is necessarily rate-dependent during this transition. These experimental results demonstrate that granular solids may respond in a purely elastic manner, both for low amplitude force oscillations of high frequencies (such as sound) and for large amplitude ones of low frequencies, implying that the granular matter has a purely elastic regime, in which the theory of elasticity holds fully true. This regime has been overlooked in the literature, probably because its deformation rate is nearly two orders of magnitude lower than those typically used. Theoretically, the present measurements support granular solid hydrodynamics, or the fact that strong deviation from elastoplastic dynamics and rate independence take place in the low frequency limit, with a rate-dependent transition to the classic theory of elasticity.
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Keywords:
- granular solid /
- rate-dependence /
- elasticity /
- plasticity
[1] Landau L D, Lifshitz E M 1986 Theory of Elasticity (New York: Pergamon Press)
[2] Zhang Q, Li Y C, Hou M Y, Jiang Y M, Liu M 2012 Phys. Rev. E 85 031306
[3] BonneauL, Andreotti B, Clment E 2008 Phys. Rev. Lett. 101 118001
[4] BonneauL, Andreotti B, Clment E 2007 Phys. Rev. E 75 016602
[5] Jia XCaroli CVelicky B 1999 Phys. Rev. Lett. 82 1863
[6] Wittmer J, Claudin P, Cates M, Bouchaud J 1996 Nature 382 336
[7] Sun Q C, Hou M Y, Jin F 2011 Physics and Mechanics of Granular Materials (Beijing: Sciencs Press) (in Chinese) [孙其诚, 厚美瑛, 金峰 2011 颗粒物质物理与力学(北京:科学出版社)]
[8] Wichtmann T 2005 Ph. D. Dissertation (Bochum: Ruhr-University Bochum)
[9] Schwedes J 2003 Granular Matter 5 1
[10] AgnolinI, Roux J N 2007 Phys. Rev. E 76 061304
[11] Laughlin R B, Pines D 2000 Proc. Natl. Acad. Sci. 97 28
[12] Laughlin R B 2004 A Different Universe (Changsha: Hunan Science and Technology Press) (in Chinese) [王文浩 译 2008 不同的宇宙 (长沙: 湖南科学技术出版社)]
[13] Makse H A, Gland N, Johnson D L, Schwartz L 2004 Phys. Rev. E 70 061302
[14] Mayer M, Liu M 2010 Phys. Rev. E 82 042301
[15] Zheng H P, Jiang Y M, Peng Z, Fu L P 2012 Acta Phys. Sin. 61 214502 (in Chinese) [郑鹤鹏, 蒋亦民, 彭政, 符力平 2012 61 214502]
[16] Jiang Y M, Liu M 2004 Phys. Rev. Lett. 93 148001
[17] Jiang Y M, Liu M 2015 Eur. Phys. J. E 38 15
[18] Chen Q, Wang Q H, Zhao C, Zhang Q, Hou M Y 2015 Acta Phys. Sin. 64 154502 (in Chinese) [陈琼, 王青花, 赵闯, 张祺, 厚美瑛 2015 64 154502]
[19] Ma Q W, Sandali Y, Zhang R N, Ma F Y, Wang H T, Ma S P, Shi Q F 2016 Chin. Phys. Lett. 33 038101
[20] Alonso-Marroquin F, Herrmann H J 2004 Phys. Rev. Lett. 92 054301
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[1] Landau L D, Lifshitz E M 1986 Theory of Elasticity (New York: Pergamon Press)
[2] Zhang Q, Li Y C, Hou M Y, Jiang Y M, Liu M 2012 Phys. Rev. E 85 031306
[3] BonneauL, Andreotti B, Clment E 2008 Phys. Rev. Lett. 101 118001
[4] BonneauL, Andreotti B, Clment E 2007 Phys. Rev. E 75 016602
[5] Jia XCaroli CVelicky B 1999 Phys. Rev. Lett. 82 1863
[6] Wittmer J, Claudin P, Cates M, Bouchaud J 1996 Nature 382 336
[7] Sun Q C, Hou M Y, Jin F 2011 Physics and Mechanics of Granular Materials (Beijing: Sciencs Press) (in Chinese) [孙其诚, 厚美瑛, 金峰 2011 颗粒物质物理与力学(北京:科学出版社)]
[8] Wichtmann T 2005 Ph. D. Dissertation (Bochum: Ruhr-University Bochum)
[9] Schwedes J 2003 Granular Matter 5 1
[10] AgnolinI, Roux J N 2007 Phys. Rev. E 76 061304
[11] Laughlin R B, Pines D 2000 Proc. Natl. Acad. Sci. 97 28
[12] Laughlin R B 2004 A Different Universe (Changsha: Hunan Science and Technology Press) (in Chinese) [王文浩 译 2008 不同的宇宙 (长沙: 湖南科学技术出版社)]
[13] Makse H A, Gland N, Johnson D L, Schwartz L 2004 Phys. Rev. E 70 061302
[14] Mayer M, Liu M 2010 Phys. Rev. E 82 042301
[15] Zheng H P, Jiang Y M, Peng Z, Fu L P 2012 Acta Phys. Sin. 61 214502 (in Chinese) [郑鹤鹏, 蒋亦民, 彭政, 符力平 2012 61 214502]
[16] Jiang Y M, Liu M 2004 Phys. Rev. Lett. 93 148001
[17] Jiang Y M, Liu M 2015 Eur. Phys. J. E 38 15
[18] Chen Q, Wang Q H, Zhao C, Zhang Q, Hou M Y 2015 Acta Phys. Sin. 64 154502 (in Chinese) [陈琼, 王青花, 赵闯, 张祺, 厚美瑛 2015 64 154502]
[19] Ma Q W, Sandali Y, Zhang R N, Ma F Y, Wang H T, Ma S P, Shi Q F 2016 Chin. Phys. Lett. 33 038101
[20] Alonso-Marroquin F, Herrmann H J 2004 Phys. Rev. Lett. 92 054301
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