phonons in honeycomb and auxetic two-dimensional latticesnew

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1、Phononsinhoneycombandauxetictwo-dimensionallatticesA.SparavignaDipartimentodiFisicaPolitecnicodiTorinoC.soDucadegliAbruzzi24,10129Torino,ItalyThemodesofvibrationsinhoneycombandauxeticstructuresarestudied,withmodelsinwhichthelatticeisrepresentedbyaplanarnetworkwheresitesareconnectedbystr

2、ingsandrigidrods.TheauxeticnetworkisobtainedmodifyingamodelproposedbyEvansetal.in1991,andusedtoexplainthenegativePoisson'sratioofauxeticmaterials.Thisrelevantpropertymeansthatthematerialshavealateralextension,insteadtoshrink,whentheyarestretched.Forwhatconcernstheacousticpropertiesofthe

3、sestructures,theyabsorbnoiseandvibrationsmoreefficientlythannon-auxeticequivalents.Theacousticandopticaldispersionsobtainedinthecaseoftheauxeticmodelarecomparedwiththedispersionsdisplayedbyaconventionalhoneycombnetwork.Itispossibletoseethatthephonondispersionsoftheauxeticmodelpossessaco

4、mpletebandgapandthattheGoldstonemodegroupvelocityisstronglydependentonthedirectionofpropagation.Thepresenceofacompletebandgapcanexplainsomeexperimentalobservationsonthesoundpropagationpropertiesoftheauxeticmaterials.PACS:62.20,63.20IntroductionAuxeticmaterialarecharacterisedtohaveaPoiss

5、on'sratiothatturnsouttobenegative[1]:thisrelevantpropertymeansthatthesematerialshavealateralextension,insteadtoshrink,whentheyarestretched.Thesematerialsaremoreresistanttoindentationsthatordinarymaterialsbecauseatthesiteofimpacttheybecomemoredenseandthereforemoreresistant.Naturalauxetic

6、materialsandstructuresoccurinbiologicalsystems,inskinandbonetissues.Manmadeauxeticmaterialshavebeenproducedfromthenanoscaletillthemicro-andmacroscalesandcoverthemajorclassofmaterials,suchasmetals,ceramics,polymersandcomposites[2].AlthoughanegativePoisson'sratioisnotforbiddenbythermodyna

7、mics,thispropertyisusuallybelievedtoberareincrystallinematerials:incontrasttothisbelieve,69%ofcubicelementalmetalshaveanegativePoisson'sratio[3].Foamswithauxeticstructuresbuiltwithpolymericmaterialsareinsteadwellknown[4]andactuallyproducedbyScottIndustrial[5,6].Theseauxeticmate