Shearing flows of a dry granular material—hypoplastic constitutive theory and numerical simulations
Shearing flows of a dry granular material—hypoplastic constitutive theory and numerical simulations
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干燥颗粒材料的剪切流动——亚塑性本构理论和数值模拟
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发表时间：
2006
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影响因子：
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通讯作者：
K. Hutter
中科院分区：
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作者：
C. Fang;Yongqi Wang;K. Hutter
本文将Goodman-Cowin理论推广到考虑塑性特征的情况下，建立了干散粒材料流动的弹粘塑性本构模型。根据Müler-Liu熵原理进行了热力学分析，得到了本构变量的平衡表达式。利用拟线性理论提出了非平衡响应，特别是引入了亚塑性关系来模拟内耗和塑性效应。结果表明，Goodman-Cowin理论可以适当地推广到体积分数的演化方程(即所谓的平衡力平衡)和柯西应力张量的平衡表达式中考虑摩擦效应。将所实现的模型分别用于研究常规的定常等温颗粒不可压缩颗粒流，即简单平面剪切流、倾斜重力驱动流和垂直槽道流。数值结果表明，亚塑性效应对流动颗粒材料的行为有重要影响。具有亚塑性特征的速度分布和体积分数分布通常比没有这种塑性特征的速度分布和体积分数分布更尖锐，剪切变薄效应更明显。这表明本模型在颗粒材料和土力学领域具有广泛的适用性。此外，本文还为亚塑性理论的进一步扩展提供了一个可能的框架。版权所有©2006 John Wiley&Sons，Ltd.
In the present study, the Goodman–Cowin theory is extended to incorporate plastic features to construct an elasto‐visco‐plastic constitutive model for flowing dry granular materials. A thermodynamic analysis, based on the Müller–Liu entropy principle, is performed to derive the equilibrium expressions of the constitutive variables. Non‐equilibrium responses are proposed by use of a quasi‐linear theory, in particular a hypoplastic‐type relation is introduced to model the internal friction and plastic effects. It is illustrated that the Goodman–Cowin theory can appropriately be extended to include frictional effects into the evolution equation of the volume fraction (i.e. the so‐called balance of equilibrated force) and the equilibrium expression of the Cauchy stress tensor. The implemented model is applied to investigate conventional steady isothermal granular flows with incompressible grains, namely simple plane shear, inclined gravity‐driven and vertical channel‐flows, respectively. Numerical results show that the hypoplastic effect plays a significant role in the behaviour of a flowing granular material. The obtained profiles of the velocity and the volume fraction with hypoplastic features are usually sharper and the shear‐thinning effect is more significant than that without such plastic effects. This points at the possible wide applicability of the present model in the fields of granular materials and soil mechanics. In addition, the present paper also provides a framework for a possible extension of the hypoplastic theories which can be further undertaken. Copyright © 2006 John Wiley & Sons, Ltd.