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1、ONCONCEPTOFFRACTALINFRACTUREMECHANICSOUZhuocheng,LIGuanying,DUANZhuoping,HUANGFenglei(StateKeyLaboratoryofExplosionScienceandTechnology,BeijingInstituteofTechnology,Beijing100081)Abstract:Fractal,orgenerallyaself-similar(orself-affine)structureofinfiniteorder,hasbe
2、enextensivelyusedasanonlinearmathematicaltooltodescribevariousirregularandcomplexphenomenainfracturemechanics.However,therearestillcriticalissuesremainingambiguous,leadingtoinherentdifficultiesmainlyresultedfromthecontradictionbetweentheintegraldimensionimmeasurabi
3、lityofafractalandtheintegraldimensioncharacteristicofaphysicalobjectinnature・Herewedemonst「atethatconceptuallyaphysicalobjectinnaturecanneverbedescribedasafractal,ratheraubiquitiform(aterminologycoinedhereforafinileorderself-similarorself-affinestructure),andshowma
4、thematicallythataubiquitiformmustbeofintegraldimensioninEuclideanspace,whichisradicallydifferentfromafractalinthesenseoftheHausdorffmeasureandmakesthefractalapproximationofaubiquitiformunavailable・Ourresultimpliesthatanaturalobjectisofubiquitiformratherthanfractal,
5、andthus,insteadoftheexistingfractaltheory,anewtypeofubiquitiformtheorymustbeestablishedinfuture.Weanticipatethisresulttobeastartingpointforthecominguniversalubiquitiformtheoryinfracturemechanics・Moreover,itcanbeexpectedthatthecomingubiquitiformtheorywillbemoreeasy-
6、to-useinpracticethanthefractalone,sinceitcanbeconstructedcompletelyonthebaseof“classical"mathematics,andhencesomeintrinsicdifficultiesinappliedfractalsciencecanbeavoided・Keywords:solidmechanics;ubiquitiform;fractal0IntroductionSincethepioneerworkofMandelbrotisj,fra
7、ctalhasbeenwidelyusedasanonlinearmathematicaltooltodescribevariousirregularandcomplexphenomenainmanyfieldsofscienceandtechnologyp-9].Infracturemechanics,Mandelbrotetal.Hverifiedexperimentallythefractalityofanimpactingfracturesurfaceinmetalbytheslitislandanalysisand
8、obtainedanegativecorrelationbetweenthefractaldimensionofthefracturesurfaceandthefractureenergy,whichbecomesthecomerstoneofcontemporaryfractalfrac
