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arXiv 0711.4243cond-mat.softcond-mat.dis-nncond-mat.mtrl-sci
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摩擦和无序对颗粒固体在局部力作用下准静态响应的影响

Effects of Friction and Disorder on the Quasi-Static Response of Granular Solids to a Localized Force

C. Goldenberg, I. Goldhirsch

摘要:

对局部力的响应为颗粒固体中不同的应力传递模型提供了灵敏的测试。工程师传统上使用的弹塑性模型受到了理论和实验结果的挑战,这些结果表明应力的波动(双曲线)传播,而不是静态弹性的椭圆方程。数值模拟的二维颗粒系统受到本地化的外力的性质,研究在这些系统中的应力传递作为施加的力的大小,摩擦参数和无序(多分散性)的函数。结果表明,在大型系统(通常认为由工程师),响应是接近各向同性弹性预测,而小系统的响应(或当足够大的力施加)是强烈的各向异性。在后一种情况下,所施加的力引起接触网络的变化,并伴随着摩擦滑动。静摩擦的静摩擦系数越大,响应为弹性的力的范围越宽,各向异性越小。增加多分散性的程度(对于所研究的范围,高达25%)减小弹性响应的范围。这篇文章是以前发表的一封信的延伸[1]。

英文摘要:

The response to a localized force provides a sensitive test for different models of stress transmission in granular solids. The elasto-plastic models traditionally used by engineers have been challenged by theoretical and experimental results which suggest a wave-like (hyperbolic) propagation of the stress, as opposed to the elliptic equations of static elasticity. Numerical simulations of two-dimensional granular systems subject to a localized external force are employed to examine the nature of stress transmission in these systems as a function of the magnitude of the applied force, the frictional parameters and the disorder (polydispersity). The results indicate that in large systems (typically considered by engineers), the response is close to that predicted by isotropic elasticity whereas the response of small systems (or when sufficiently large forces are applied) is strongly anisotropic. In the latter case the applied force induces changes in the contact network accompanied by frictional sliding. The larger the coefficient of static friction, the more extended is the range of forces for which the response is elastic and the smaller the anisotropy. Increasing the degree of polydispersity (for the range studied, up to 25%) decreases the range of elastic response. This article is an extension of a previously published letter [1].

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