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The pressure distribution beneath a conical sandpile, created by pouring sandfrom a point source onto a rough rigid support, shows a pronounced minimumbelow the apex (`the dip'). Recent work of the authors has attempted to explainthis phenomenon by invoking local rules for stress propagation that depend onthe local geometry, and hence on the construction history, of the medium. Wediscuss the fundamental difference between such approaches, which lead tohyperbolic differential equations, and elastoplastic models, for which theequations are elliptic within any elastic zones present .... This displacementfield appears to be either ill-defined, or defined relative to a referencestate whose physical existence is in doubt. Insofar as their predictions dependon physical factors unknown and outside experimental control, suchelastoplastic models predict that the observations should be intrinsicallyirreproducible .... Our hyperbolic models are based instead on a physicalpicture of the material, in which (a) the load is supported by a skeletalnetwork of force chains ("stress paths") whose geometry depends on constructionhistory; (b) this network is `fragile' or marginally stable, in a sense that wedefine. .... We point out that our hyperbolic models can nonetheless bereconciled with elastoplastic ideas by taking the limit of an extremelyanisotropic yield condition.Comment: 25 pages, latex RS.tex with rspublic.sty, 7 figures in Rsfig.ps.  Philosophical Transactions A, Royal Society, submitted 02/9

philosophical transactions - royal society. mathematical, physical and engineering sciences/philosophical transactions - royal society. mathematical, physical and engineering sciences

Development of stresses in cohesionless poured sand