SHEARING FLOWS IN A GOODMAN-COWIN TYPE GRANULAR MATERIAL—THEORY AND NUMERICAL RESULTS
SHEARING FLOWS IN A GOODMAN-COWIN TYPE GRANULAR MATERIAL—THEORY AND NUMERICAL RESULTS
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GOODMAN-COWIN 型粒状材料中的剪切流动——理论和数值结果
DOI：
10.1080/02726359908906807
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发表时间：
1999
影响因子：
2.5
通讯作者：
K. Hutter
中科院分区：
文献类型：
--
作者：
Yongqi Wang;K. Hutter
古德曼和考文(1972)提出了干燥的无粘性颗粒材料的连续体理论，其中固体体积分数被视为一个独立的运动场，并假定了一个附加的平衡力平衡定律。将M-˜方法应用到熵不等式中，证明了在以“，_”和“Grad”为自变量的本构模型中，只有在Helmholtz自由能不依赖于“时，结果才与经典的Colman-Noll方法一致，从而得到了Goodman-Cowin方程。然后将这一简化理论应用于颗粒材料沿斜面和垂直平行板之间的定常、充分发展的水平剪切∞ow和重力∞ows的分析。证明了Passman等人提出的方程和数值结果。(1980)是错误的，它们被更正了。结果表明，这些材料的动力学行为与粘性∞UID有很大不同。在某些情况下，膨胀剪切层只存在于边界附近的狭窄带中。
Goodman and Cowin (1972) proposed a continuum theory of a dry cohesionless granular material in which the solid volume fraction ” is treated as an independent kinematic fleld for which an additional balance law of equilibrated forces is postulated. By adopting the M˜ uller-Liu approach to the exploitation of the entropy inequality we show that in a constitutive model containing ”, _ ” and grad” as independent variables results agree with the classical Coleman-Noll approach only provided the Helmholtz free energy does not depend on _ ”, for which the Goodman-Cowin equations are reproduced. This reduced theory is then applied to analyses of steady fully-developed horizontal shearing ∞ow and gravity ∞ows of granular materials down an inclined plane and between vertical parallel plates. It is demonstrated that the equations and numerical results, presented by Passman et al. (1980) are false, and they are corrected. The results show that the dynamical behaviour of these materials is quite difierent from that of a viscous ∞uid. In some cases the dilatant shearing layers exist only in the narrow zones near the boundaries.