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利用能以极慢变形率直接剪切颗粒固体的实验装置, 测量了(玻璃珠)样品对大幅度循环剪切的力-位移曲线, 以及一个循环周期后的塑性位移残留. 发现随着循环频率的降低, 样品会从有限塑性残留的弹塑行为转变到几乎没有塑性的纯弹性行为, 同时伴随有率相关性. 该转变在剪切力幅度高达样品破坏值的90%时依然存在, 但需要极小的变形率(10-5 Hz)或惯性数(10-8). 这意味着无论是高频小幅度的声波扰动, 还是极低频大幅度的直接剪切, 静态颗粒固体都可做出纯弹性的力学响应. 在足够慢的状态变化范围里, 它仍是属于经典弹性理论范畴的一类材料. 这个弹性区域一直未被报道和关注, 可能是观测它时需要样品的变形率远比通常此类研究中所采用的慢变形还要小许多(大约两个数量级)的缘故. 理论上本文测量结果支持描述颗粒固体宏观动力学的基本方程组, 不能只有弹塑和率无关行为, 它们必须在极慢变形极限下退化为经典弹性理论, 并且在这个转变过程中表现出率相关特性.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 物理学报 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 物理学报 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 物理学报 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 物理学报 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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