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1、AContinuumTheoryforGranularMaterialsM.A.GOODMANS.C.COWINCommunicatedbyJ.L.ERICKSEN1.IntroductionIn1776,COULOMB[1]presentedthefirstyieldcriterioninmechanics,ayieldcriterionforsoils,includinggranularmaterials.TheCoulombcriterionstatesthatslipisimpendingonaplaneinthematerialwhenS=bT+c
2、,(1.1)whereSandTaretheshearstressandnormalstress,respectively,actingontheplane,bisacoefficientofstaticfriction,andcisacoefficientofcohesion.TheMohr-Coulombtheoryoflimitingequilibrium,basedontheCoulombcriterionandtheequationsofstaticequilibrium,wasformulatedbyK6~n~R[2]andextendedand
3、summarizedbySOKOLOVSKn[3].TheCoulombcriterionalsoservesasthestartingorfocalpointformostexistingthree-dimensionaldeformationtheoriesforsoilswhich,forthemostpart,areextensionsormodificationsofthetheoryofelastic-plasticbodies[4,5,6,7,8,9].Suchtheories,however,donotrecognizethetwo(orth
4、ree)phasenatureofgranularmaterialsand,consequently,yieldresultswhichareindependentofthemagnitudeanddistributionofthevoidvolume.Inthispaper,wepresentatheoryforgranularmaterialsformulatedfromformalargumentsofcontinuummechanics.Thebasicpremiseunderlyingthepaperisthattheconceptofmassdi
5、stributionmustbeextendedtoadmitgranularmaterials.Inparticular,thedistributionofmassmustberelatedtothevolumedistributionofgranules.Toachievethis,weintroduceanindependentkinematicalvariable,calledthevolumedistributionfunction.Thefollowingphysicallymotivatedassumptionsassociatedwithth
6、evolumedistributionofgranulesinagranularmaterialformthebasisfortheproposedtheoryofgranularmaterials.I.ThevolumeofgranulesinagranularmaterialisregardedasameasureonEuclideanspace.Themeasureisequallyvalidforsolid,porousmaterials(rock,cork,sponge,etc.)aswellasgranularmaterials(sand,gra
7、in,powder,etc.)2.Themassmeasureisassumedabsolutelycontinuouswithrespecttothevolumedistributionmeasure.Thisassumptionistantamounttoneglectingthevoidmassandisconsistentwithone'sintuitivenotionofgranularmaterials;e.g.considerdrysand.Sincethevoidmassisneglected,onlyonetypeofmaterialpoi
8、ntneedbeconsideredfordescr
