Role of contact couples and couple stress in the behaviour of granular media

This is a survey of the interesting phenomenology and the prominent regimes of granular flow, followed by a unified mathematical synthesis of continuum modeling. The unification is achieved by means of “parametric” viscoelasticity and hypoplasticity based on elastic and inelastic potentials. Fully nonlinear, anisotropic viscoelastoplastic models are achieved by expressing potentials as functions of the joint isotropic invariants of kinematic and structural tensors. These take on the role of evolutionary parameters or “internal variables,” whose evolution equations are derived from the internal balance of generalized forces. The resulting continuum models encompass most of the mechanical constitutive equations currently employed for granular media. Moreover, these models are readily modified to include Cosserat and other multipolar effects. Several outstanding questions are identified as to the contribution of parameter evolution to dissipation; the distinction between quasielastic and inelastic models of material instability; and the role of multipolar effects in material instability, dense rapid flow, and particle migration phenomena.

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Role of contact heterogeneities on macroscopic elastic properties of granular media

10.1190/1.3513340 ◽

2010 ◽

Cited By ~ 1

Author(s):

Ratnanabha Sain ◽

Gary Mavko ◽

Tapan Mukerji

Keyword(s):

Elastic Properties ◽

Granular Media

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Buoyancy driven flow of a couple stress fluid from an isothermal vertical plate: the role of spatially periodic magnetic field

Physica Scripta ◽

10.1088/1402-4896/ac2af3 ◽

2021 ◽

Author(s):

Mahesh Kumar ◽

Pranab Kumar Mondal

Keyword(s):

Magnetic Field ◽

Couple Stress ◽

Vertical Plate ◽

Couple Stress Fluid ◽

Periodic Magnetic Field ◽

Spatially Periodic

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Fracture pattern formation in frictional, cohesive, granular material

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2009.0199 ◽

2010 ◽

Vol 368 (1910) ◽

pp. 95-118 ◽

Cited By ~ 16

Author(s):

Alison Ord ◽

Bruce E. Hobbs

Keyword(s):

Pattern Formation ◽

Granular Media ◽

Large Scale ◽

High Stress ◽

Reaction Diffusion ◽

Fracture Pattern ◽

Reaction Diffusion Equations ◽

Three Dimensions ◽

Localized Deformation

Naturally, deformed rocks commonly contain crack arrays (joints) forming patterns with systematic relationships to the large-scale deformation. Kinematically, joints can be mode-1, -2 or -3 or combinations of these, but there is no overarching theory for the development of the patterns. We develop a model motivated by dislocation pattern formation in metals. The problem is formulated in one dimension in terms of coupled reaction–diffusion equations, based on computer simulations of crack development in deformed granular media with cohesion. The cracks are treated as interacting defects, and the densities of defects diffuse through the rock mass. Of particular importance is the formation of cracks at high stresses associated with force-chain buckling and variants of this configuration; these cracks play the role of ‘inhibitors’ in reaction–diffusion relationships. Cracks forming at lower stresses act as relatively mobile defects. Patterns of localized deformation result from (i) competition between the growth of the density of ‘mobile’ defects and the inhibition of these defects by crack configurations forming at high stress and (ii) the diffusion of damage arising from these two populations each characterized by a different diffusion coefficient. The extension of this work to two and three dimensions is discussed.

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