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1、NonlinearelasticconstantsofsolidswithcracksVeniaminE.NazarovandAlexanderM.SutinInstituteofAppliedPhysics,RussianAcademyofSciences,46UljanovStreet,603600,NizhnyNovgorod,Russia~Received24May1996;revised26February1997;accepted26February1997!Experimentaldataonacrackedmediumexhibitinghighacousticnon
2、linearityisacommonlyobservedphenomenon.Hereaphysicalmodelofamediumwithcracksissuggestedtoexplaintheobservedphenomena.Themodelisbasedontheassumptionofuniformstressthatisvalidforalowconcentrationofcracks.Thecrackbehaviorisdescribedusingthemodelinwhichacrackisrepresentedasanelasticcontactoftworoug
3、hsurfaces,pressedonetotheotherundertheactionofinternalstressesinthesurroundingsolid.Linearandnonlinearacousticconstantsofthefracturedmediumarecalculated.Itisshownthat,inthismedium,negativevaluesofthePoisson'sratioandanomalouslyhighvaluesofthenonlinearconstantsarepossible.©1997AcousticalSocietyo
4、fAmerica.@S0001-4966~97!05910-9#PACSnumbers:43.25.Ba,43.25.Dc@MAB#LISTOFSYMBOLSCt,Clthetransverseandlongitudinalveloci-xiorx,y,ztheCartesiansystemcoordinatetiesofelasticwavessxx,syy,szzthecomponentsofstresstensorrthedensityofthemediumEandntheYoungmodulusandthePoissonra-W(h)thefunctionofpeakdist
5、ributionovertioofasolidtheheightshE*5E/2(12n2)d5h2dÐthedisplacementofthepeakUx,Uy,UzthecomponentsofvectordisplacementfromthemiddlelineUxx,Uyy,Uzzthecomponentsofstraintensorftheforceneededforthecompressionofsnnthenormalstressesthepeakwandutheanglesoforientationofthecrackx8iorx8,y8,z8thenewCartes
6、iancoordinatesystematheradiusofthesphericaltopdU8theadditionalstrainalongthez8axisbtheradiusofthecirclestampz8z8DV(w)thevolumevariationofasinglecrackctheapexangleoftheobtuseconeN(w,u)thefunctionofthecrack'sdistributionnthepeaks'amountinthefullsquareofintheangleswanduthecracksurfaceathelinearcoe
7、f®cientofelasticityoftheh521/2hs0crackh0theeffectiveheightoftheroughnessesbandgthenonlinear~quadraticandcubic!co-Rtheradiusofthecrackef®cientsofelasticityofthecrackU0(r)thenormaldisplacementofcracksur-dUxx,dUyy,dUzztheadditionalst
