Analytical aspects of relaxation for single-slip models in finite crystal plasticity [Elektronische Ressource] / vorgelegt von Carolin Kreisbeck
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Analytical aspects of relaxation for single-slip models in finite crystal plasticity [Elektronische Ressource] / vorgelegt von Carolin Kreisbeck

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Univ2010onaspIectssburgofeckrelaxationderfoMathematikrRegesingle-sliporgelegtmorolindelsLappinanniteNWFcrystal-plasticitderyersitätDissertationnzurvErlangungvdesCaDoktorgradesKreisbderausNaturwissenscersdorfhaftenAnalytical(Dr.rer.nat.)Prof.SergionPromotionsgesucPrüfer:hProf.wurdeheingereicersitäthGarctAbamGeorg18.05.2010.2.DieProf.ArbtieitwwurdeDr.angeleitetevHelmoniiProf.Dr.Dr.DolzmaGeorgnDolzmaGutacnter:n.Dr.PrüfungsausscConh(Univuss:Bonn)Veitererorsitzender:Prof.Prof.HaraldDr.kBerndErsatzprüfer:AmmannDr.1.utGutacelshDaster:uW-GrenzwMoVdernegescmathematischhehenZugängeKräfte.zuhelasto-plastiscinhemundMaterialveinererhaltenalsoführenen.übhertermauerteinenstütztzeitdiskretenStrukturEhennergieansatzt.zuwirnicohzugehöriget-kerformonkzuführenveinerexenelastiscVtariationsproblemen,diedietsiconheisdterenenaufStandardmethodiedenundderVVdenariationsrecilitätsbhnKungolgeenmittziehen.imDieseVArbersceittebgeescashäftigtEnergiedicsicFhtmitigeometriscdellhcnicalischFt-lineareropiscKristallpMikrostrukturenlastizitätwundeinehierbmittelseiergenzspDereziellKmitder2DhrankMohdellenalgebra-mitAbsceinemanisotropaktivProblemsenaufGleitsystem.

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ersit?tAnalyticalanaspCaects-ofvrelaxationausfoNWFrdersingle-slipnmovdelsKreisbinersdorfnitedercrystalIplasticitMathematikyUnivDissertationRegezursburgErlangungorgelegtdesonDoktorgradesrolindereckNaturwissenscLapphaften2010(Dr.rer.nat.)Dr.DasConPromotionsgesucnhProf.wurdeDr.eingereicter:hBonn)tkamels18.05.2010.DolzmaDieGutacArbDr.eit(UnivwurdeeitererangeleitetHaraldvErsatzpr?fer:onutProf.Prof.Dr.GeorgGeorgnDolzma2.nhn.Prof.Pr?fungsausscSergiohtiuss:ersit?tVworsitzender:Pr?fer:Prof.Dr.Dr.GarcBerndeAmmannProf.1.HelmGutacAbhiiter:ndZusammenfassungacMoertderneerfestigungmathematischihetetZug?ngedemzuiiielasto-plastiscehemderMaterialvOrienerhaltengro?enf?hrenn?bAusereineeinenwird.zeitdiskretensicEdesnergieansatzdiv-curlzuF?rniclokhct-krelaxierteonungsgradien-vist.exengutenVherariationsproblemen,bdieBildungsicwhvdderenScStandardmethosorgf?ltigedendiederandererseitsVerallgemeinerungariationsrecGrenz-hnedingungungonstruktionenvtziehen.ortsabh?ngigenDieseMoArberfestigungeithbvescvh?ftigtaufsichhallmitvgeometriscmhundnichenhhert-linearerehlenKristallpherlastizit?tundundeichierbgro?eei-KspuneziellBewmitompaktheit2DunMoedelleneinerseitsmitisceinemh?tzungen,aktiveenerfassen,Gleitsystem.eineUmkteInformationenklassisc?bdieerergangdasompressibmakroskhopiiescdenheFVendenerhaltenLaminatesolceriodenherSobaldMaterialienjedzuauferhalten,erzicwirdvdiedieRelaxierunghderaufeinzelnennInkremenVtproblemewunsublineareter-dersuczur?chdiesemt,annwhobneixwirzwiscunsMohiermitausscgesprohlie?licerdhysikaufheinendasZeitsconhrimikroskttalabonescopischr?nktremen.MaterialanUnseraufAugen-externermerkmittelslionegergenzttermauertdabDereieisaufKderuFderrage,terenobhrankaufst?tztstarrerhElastizit?taufbasierendealgebra-MohdelleAbscalsdieguteanisotropApproStrukturxProblemsiundmaufationgescf?rcphVysikdesahenlLemmas,iscdenh?brealistiscinhereInkSystemeilit?tsbmiterm?glicelastisct.herdEnergieKdieneneinerk-Grenzw?nnen,realisierendenzumindesolgeterwfallswirletzterealeelastiscmithePVunderzerrungtierungen.energetiscimhdellhinreicohendhstarkVbve-hstrafen.wird,Dieerscinwindetteressanzugeh?rigeteEnergiedicEntetdecollst?ndigkungeineristMengeun,ondasserformdieten,AnastdaswWorthstumenEnergiedictscteheidendkzuf?hrendaInvFonkab-alsoh?ngt,icobtmanoeineinerMoApprodellimitationohenderstarrenohnedellVdemerfestigungelastiscbEnergieetracchwtet.en.UnphteraliscBer?cSicksicthewirkttigungFlinearervVVerfestigungaufbopiscekSkommdietvmanMikrostruktureneinmakroskimhobigenexSinnewpheosi-ttivorteseineErgebnis,KlassedasKr?fte.mathematischtheAbstractinMoisdernomathematicalcaseapproacelastichesvtoonplasticitcalyblead,toimpliesnon-conmathematicallyvandextheminimizationlemmaprob-recolemspforassowhicahthethethestandardhere.methosoftdsexternalofuptherocalculuserofestimatesvfariationsofareernottheapplicable.wInosition-thisorienthesiswwenergyetoconsiderappliedgeometricallysublinearnonlinearycrystalbelastoplasticitandydoineaking,tmicrostructurewvioroadimensionshwithkoneyactivTheeofsliplosystem.oundIncarefulorderaptostructurederivproblemesubtleinformationclassicalarecobyoutFmacroscopicofmaterialerybuseehawithviorendenthedrelaxationInofhardening,theer,singlerelaxincremenytalshoproblems,anishwhicclasshwhicresulttofromwththedenap-Consequenplieddesiredtime-discretewvmoariationaloneapproacergh,notneedsysicallytoofboevinbvtheestionsegrangeated.es.Hereisourbacstudiesedarebrestricted-contoergence.theprstoftimecompactnesssteptheonlyw.bWreliesenespalgebraiceciallycfoturingcusanisotropiconothethequestionandofawhethergeneralizationre-thealisticdiv-curlsystemstowithvanincompressibilitelasticinenergylimit.leadingortoconstructionlargeapvenalizationsequenceofesmallloelasticlaminatesstrainspcandepbteeriowandell-approtation.ximatedthebwithoutyhomoevdelsthebasedciatedonedthedensitassumptioncanoferigidwnelasticitvyfor.largeThofeloads,inhterestiduengthendingrogofisenergythatsitthere.aretlyqualitativtheelyrelationdierenetteenanswrigidersdeldeptheendiwithngenonywhethereshardeningholdisPhincludspedabsenceorhardeningnot.formationInfpresenceandoferylinearmacroscopichardeningehawofesampleobtainrespatopwideositivofeforcresult,ivwhicp 1L L
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