Plane mechanics and kinematics of compressible ideal granular materials

Spencer, A. J. M.; Kingston, M. R.

doi:10.1007/bf01635103

Cited by 16 publications

(1 citation statement)

References 9 publications

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“…However, this latter approach predicts unrealisti cally large dilatation rates (see Collins 1990;Spencer 1984) and accordingly this theory is also limited in its application. Experim ental evidence of Halldin (1981), F a tt (1957) and Randall (1989) indicates th a t in general granular materials are compressible such th at their density is a function of the applied pressure and in an attem pt to more accurately account for material compressibility de Josselin de Jong (1971,1977), Spencer & Kingston (1973) and Butterfield & Harkness (1972) have proposed modifications of the double-shearing theory. Roscoe, Schofield & W roth (1958) and Atkinson & Bransby (1978) abandon the Coulomb-Mohr yield criterion but utilize the associated plastic flow rule with a new family of yield functions as the plastic potential.…”

Section: Introductionmentioning

confidence: 99%

Some axially symmetric flows of Mohr–Coulomb compressible granular materials

Hill

1992

Proc. R. Soc. Lond. A

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In this paper we consider a number of axially symmetric flows of compressible granular materials obeying the Coulomb–Mohr yield condition and the associated flow rule. We pay particular attention to those plastic régimes and flows not included in the seminal work of Cox, Eason & Hopkins (1961). For certain plastic régimes, the velocity equations uncouple from the stress equations and the flow is said to be kinematically determined. We present a number of kinematically determined flows and the development given follows the known solutions applicable to the so-called ‘double-shearing’ model of granular materials which assumes incompressibility and for which the governing equations are almost the same. Similarly, for certain other plastic régimes the stresses may be completely determined without reference to the velocity equations and these are referred to as statically determined flows. In the latter sections of the paper we examine statically determined flows arising from the assumption that the shear stress in either cylindrical or spherical polar coordinates is zero. In the final section we present a numerical solution, which incorporates gravitational effects, for the flow of a granular material in a converging hopper. In addition, we examine the Butterfield & Harkness (1972) modification of the double-shearing model of granular materials which formally includes both the double-shearing theory and the Coulomb–Mohr flow rule theory as special cases. Moreover, for kinematically determined régimes, the velocity equations are the same apart from a different constant, while for statically determined régimes the governing velocity equations are slightly more complicated, involving another constant which is a different combination of the basic physical parameters. Thus some of the solutions presented here can be immediately extended to this alternative theory of granular material behaviour and therefore the prospect arises of devising experiments which might validate or otherwise one theory or the other.

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Section: Introductionmentioning

confidence: 99%