Review Article

Continuum Modeling of Granular Media

[+] Author and Article Information
J. D. Goddard

Professor of Applied Mechanics
and Engineering Science,
Department of Mechanical
and Aerospace Engineering,
University of California, San Diego,
La Jolla, CA 92093
e-mail: jgoddard@ucsd.edu

The Introduction draws heavily on Ref. [2].

Viewed elsewhere [67] as the “quicksand” of continuum mechanics, in a metaphor particularly appropriate to the present setting.

Manuscript received August 13, 2013; final manuscript received October 26, 2013; published online May 13, 2014. Editor: Harry Dankowicz.

Appl. Mech. Rev 66(5), 050801 (May 13, 2014) (18 pages) Paper No: AMR-13-1060; doi: 10.1115/1.4026242 History: Received August 13, 2013; Revised October 26, 2013

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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Fig. 1

Schematic diagram of granular-flow regimes

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Fig. 2

2D DEM simulations (courtesy of W. Ehlers).

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Fig. 3

Axial compression of dry Hostun sand specimen (courtesy of W. Ehlers).

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Fig. 4

Schematic diagram of triaxial stress/dilatation-strain curves for initially dense (solid curves) and loose (dashed curves) sands

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Fig. 5

Dashpot/spring/slide-block analog of viscoelastoplasticity

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Fig. 6

2D version of dilatancy constraint (after Ref. [85])




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