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Sachverzeichnis

Anderungsgeschwindigkeit materielle 90

Ableitung direkte 90 Lie-Ableitung 98 materielle 90 objektive 97

Anfangsspannungsmatrix 261 Anfangsverschiebungsmatrix 261 Aufpunktgr6Be

abgeleitete 52 primare 52

Ausgangslage 60

Basis duale 11 kontravariante 11 kovariante 11

Basissystem kartesisches 4

Bauschinger Effekt 181 Belastung

Grenzpunktder 295 kinematisch konsistente 254 nicht konservative 257 thermische 267

Beschreibung Eulersche 63 Lagrangesche 62 materielle 62

Bewegungsgesetz erstes Bewegungsgesetz von

Cauchy 119, 121 zweites Bewegungsgesetz von

Cauchy 119 Bogenlangenverfahren 297

Cayley-Hamilton Theorem 35,77 charakteristische Gleichung 34 Clausius-Duhem-Ungleichung 126,

131

Deformation dilatatorische 85 isochore 85

Deformation 62 Deformationsgradient 63

materieller 63 raumlicher 64

Deformationsrate 92 Deformationstensor

Cauchy-Green- 67 linker 67,74 rechter 66, 73

Deformationstheorie 178 Dehnung

natiirliche 84 Dehnungsenergiefunktion 137 Deviator 23 Dissipationsarbeit

plastische 175

366

Drehgeschwindigkeitstensor 92 Drei-Feldansatz 318 Druckersche Ungleichung 183

Eigenform 327 Eigentensor 33

der Ausgangskonfiguration 71 der Momentankonfiguration

75 Eigenvektor 32, 70 Eigenwertaufgabe 32 Eigenwerte 32 Elemente

isoparametrische 252 Energie

freie 133 innere 125 latente 175 Rate der inneren 127, 129

Evolutionsgesetz 178

Feld-problem 51 theorie 51

Feldgr6Ben energetisch konjugierte 55 konjugierte 54

FlieB-flache 178 funktion 179 regel, assoziierte 184 spannung 176 theorie 179

FlieBflache 180 Flussgr6Be

abstrakte 52 primare 52f. resultierende 52, 54

Formulierung

Sachverzeichnis

Total Lagrangesche 250 Freiwerte

des Finiten Elementes 252 Funktion

skalarwertige 38 tensorwertige 38 vektorwertige 38

Funktional 242 thermisches 265

Geschwindigkeitsgradient raumlicher 91

Gleichgewicht schwache Form 119,247 strenge Form 119 thermisches Gleichgewicht III

schwacher Form 265 Gradient

des Skalarfeldes 40 des Vektorfeldes 40

GrenzflieBspannung 177

Haupt-achsensystem 71 richtungen 32 system 71 werte 32,71

Hourglass-Instabilitat 316

lacobimatrix des Gleichungssystems 293

Korper 50 Knotenvektor

der eingepragten Krafte 254 der eingepragten Tragheitskraft

254 des integrierten Kraftflusses

254 Konduktivitatsmatrix 268

Sachverzeichnis

Konfiguration 60 Ausgangs- 60 Momentan- 60 Referenz- 60

konstitutive Gleichung 55 Kontinuumshypothese 50 Kontinuumsmechanik

analytische 242 klassische 242

Konvergenz geschwindigkeit 284 globale 284 lokale 284 rate 284

Koordinaten des Tensors 4 des Vektors 3 materielle 60 raumliche 60

Kraftftussvektor 109 Kugeltensor 23 Kuhn-Tucker Bedingung

der Plastizitat 188

Lastkorrekturmatrix 262 Linearisierung

konsistente 205,210 locking siehe Sperren

Massenmatrix kinematisch konsistente 255

Material Cauchy-elastisches 137 Green-elastisches 137 hyperelastisches 137

Material-entfestigung 177 verfestigung 177

Materialgesetz

Mooney-Rivlin 159 Ogden 160

Materialkoordinaten 60 Materialpunkt 50 Materialtangente

algorithmische 227 elastoplastische 206 konsistente 210

367

im Hauptachsensystem 228 Metrik 13, 68

Naherungsfeld 57 Nullmode 316

objektiv 59, 87 materiell 88

Operation pull back 65, 67 push forward 64, 67

Ortsvektor 59

Plastizitat assoziierte 184 dehnratenabhangig 175 dehnratenunabhangig 175 ideale 177

Potential elastisches 138 plastisches 184

Prinzip der virtuellen Arbeit 244,247 der virtuellen Leistung 245

Radiale Riickkehrmethode radial return 179,208

Randbedingung Spannungs- 122 Verschiebungs- 122

Randwertaufgabe mechanische 122

368

thennische 264 Rate 92 Restlasten 293 Rotationstensor 66, 73

schwache Fonn der Bilanzerfiillung 58

schwachen Fonn des Gleichgewichts 244

Spannung des ersten FlieBens 177 materielle 113 nominale 112

Spannungsrate Iaumannsche 118 Oldroydsche 119

Spannungstensor Biot 115 Cauchy 109 erster Piola-Kirchhoff 112 Kirchhoff 113 zweiter Piola-Kirchhoff 112

Spatprodukt 16 Sperren

eines Elementes 312 globales Netz- 313 Membran- 313 Schub- 312 volumetrisches 313

Spintensor 92 Steifigkeit

geometrische 261 tangentiale 262 Materialsteifigkeit 261 tangentiale 205,257,293

Streckgeschwindigkeitstensor 92 Strecktensor

linker 66, 73 rechter 66, 73

Streckung 64 Summationsregel

Einsteinsche 5 System

diskretes 57

Tensor Definitheit 24

Sachverzeichnis

eigentlich orthogonal 29 hOherer Stufe 24 Invarianten des 35 isotroper 30 kartesischer 4 Matrixdarstellung 8 orthogonal 29 potenzierten 36 schiefsymmetrischer 22 Spur des 22 symmetrischer 22 tensorielles Produkt 19 transponierte 22 verjiingendes Produkt 20 zweifache Verjiingung 21

Tensorfeld Eulersches 63 Lagrangesches 63

Testfunktion 246 Thennodynamik

erster Hauptsatz 128 zweiter Hauptsatz 131

thermoelastischer Effekt 229 Transfonnation

eigentlich orthogonale 29

Ungleichgewichtslasten 293

Variable innere 174, 178

Variation kinematisch vertragliche 244

Sachverzeichnis

Vektor liuBeres oder dyadisches Pro­

dukt 19 affiner 3 euklidscher 3

Vektorprodukt 15 Verfahren

line search 285 Verfestigung

isotrope 181 kinematische 181

Verfestigungsmodul 226 Verschiebungs-

feld virtuelles 244 methode 242 modell 248, 252

Verzerrungstensor Almansi 79 Greenscher 79 Hencky 84

Volumendilatation 163

Wlirmekapazitlit 134 Wlirmeleistung

369

die eingeprligte Wlirmeleistung 267

die integrierte 267 WeggroBen-

element 248 verfahren 242

Zerlegung polare 66

Zustandsgleichung kalorische 132

Zwei-Feldansatz 324 Zweifeld Tensor 64

Doppeltensor 64 two-point tensor 64

Zwischenkonfiguration plastische 192