Abstract
This paper reviews the emergence of non-local flow phenomena in granular materials and discusses a range of models that have been proposed to integrate an intrinsic length-scale into granular rheology. The frameworks discussed include micro-polar modeling, kinetic theory, three particular order-parameter-based models, and strongly non-local integral-based models. An extensive commentary is included discussing the current capabilities of these existing models as well as their implementational ease, physical motivation, and breadth of predictive ability.
Highlights
Let us define a local rheology as a constitutive model whose well-developed strain-rate response depends only on the stress and no higher-gradients of kinematic quantities or stress
In the case of granular media, it is evident that the mean grain size d provides this microscopic length unit, and the observed length-scale of non-local effects should be some multiple of d
Another non-local effect is connected to the reverse problem— rather than material flowing even though the stress seems too small, there are cases where material does not flow even though the stress appears to be above the yield limit
Summary
Let us define a local rheology as a constitutive model whose well-developed strain-rate response depends only on the stress and no higher-gradients of kinematic quantities or stress. It is widely accepted that such models lack robustness in their ability to predict all flow phenomena and, in many cases, predictions of local models disagree with experiments by nontrivial amounts [14,15,16,17,18,19] This is true even though such models predict uniform flows well, such as steady simple shearing. It is the fact that these models succeed in homogeneous cases but break down in the presence of spatial inhomogeneity that the origin of this difference can be attributed to a non-local effect. In such models, a microscopic length-scale emerges on dimensional grounds. In the case of granular media, it is evident that the mean grain size d provides this microscopic length unit, and the observed length-scale of non-local effects should be some multiple of d
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