PLASTICITY THEORY

By CHARLOTTE CLARK

CONTENTS CHAPTER 1: INTRODUCTION TO CONTINUUM THERMOME- CHANICS SECTION 11 MATHEMATICAL FUNDAMENTALS 111 NOTATION 112 CARTESIAN TENSORS 113 VECTOR AND TENSOR CALCULUS 114 CURVILINEAR COORDINATES SECTION 12 CONTINUUM DEFORMATION 121 DISPLACEMENT 122 STRAIN 123 PRINCIPAL STRAINS 124 COMPATIBILITY CONDITIONS SECTION 13 MECHANICS OF CONTINUOUS BODIES 131 INTRODUCTION 132 STRESS 133 MOHR’S CIRCLE 134 PLANE STRESS 135 BOUNDARY-VALUE PROBLEMS SECTION 14 CONSTITUTIVE RELATIONS: ELASTIC 141 ENERGY AND THERMOELASTICITY 142 LINEAR ELASTICITY 143 ENERGY PRINCIPLES SECTION 15 CONSTITUTIVE RELATIONS: INELASTIC 151 INELASTICITY 152 LINEAR VISCOELASTICITY 153 INTERNAL VARIABLES: GENERAL THEORY 154 FLOW LAW AND FLOW POTENTIAL CHAPTER 2: THE PHYSICS OF PLASTICITY SECTION 21 PHENOMENOLOGY OF PLASTIC DEFORMATION 211 EXPERIMENTAL STRESS-STRAIN RELATIONS 212 PLASTIC DEFORMATION 213 TEMPERATURE AND RATE DEPENDENCE SECTION 22 CRYSTAL PLASTICITY 221 CRYSTALS AND SLIP 222 DISLOCATIONS AND CRYSTAL PLASTICITY 223 DISLOCATION MODELS OF PLASTIC PHENOMENA SECTION 23 PLASTICITY OF SOILS, ROCKS AND CONCRETE 231 PLASTICITY OF SOIL 232 “PLASTICITY” OF ROCK AND CONCRETE CHAPTER 3: CONSTITUTIVE THEORY SECTION 31 VISCOPLASTICITY 311 INTERNAL-VARIABLE THEORY OF VISCOPLASTICITY 312 TRANSITION TO RATE-INDEPENDENT PLASTICITY 313 VISCOPLASTICITY WITHOUT A YIELD SURFACE SECTION 32 RATE-INDEPENDENT PLASTICITY 321 FLOW RULE AND WORK-HARDENING 322 MAXIMUM-DISSIPATION POSTULATE AND NORMALITY 323 STRAIN-SPACE PLASTICITY SECTION 33 YIELD CRITERIA, FLOW RULES AND HARDENING RULES 331 INTRODUCTION 332 YIELD CRITERIA INDEPENDENT OF THE MEAN STRESS 333 YIELD CRITERIA DEPENDENT ON THE MEAN STRESS 334 YIELD CRITERIA UNDER SPECIAL STATES OF STRESS OR DEFORMATION 335 HARDENING RULES SECTION 34 UNIQUENESS AND EXTREMUM THEOREMS 341 UNIQUENESS THEOREMS 342 EXTREMUM AND VARIATIONAL PRINCIPLES 343 RIGID–PLASTIC MATERIALS SECTION 35 LIMIT-ANALYSIS AND SHAKEDOWN THEOREMS 351 STANDARD LIMIT-ANALYSIS THEOREMS 352 NONSTANDARD LIMIT-ANALYSIS THEOREMS 353 SHAKEDOWN THEOREMS CHAPTER 4: PROBLEMS IN CONTAINED PLASTIC DEFOR- MATION SECTION 41 ELEMENTARY PROBLEMS 411 INTRODUCTION: STATICALLY DETERMINATE PROBLEMS 412 THIN-WALLED CIRCULAR TUBE IN TORSION AND EXTENSION 413 THIN-WALLED CYLINDER UNDER PRESSURE AND AXIAL FORCE 414 STATICALLY INDETERMINATE PROBLEMS SECTION 42 ELASTIC–PLASTIC TORSION 421 THE TORSION PROBLEM 422 ELASTIC TORSION 423 PLASTIC TORSION SECTION 43 THE THICK-WALLED HOLLOW SPHERE AND CYLINDER 431 ELASTIC HOLLOW SPHERE UNDER INTERNAL AND EXTERNAL PRESSURE 432 ELASTIC–PLASTIC HOLLOW SPHERE UNDER INTERNAL PRESSURE 433 THERMAL STRESSES IN AN ELASTIC–PLASTIC HOLLOW SPHERE 434 HOLLOW CYLINDER: ELASTIC SOLUTION AND INITIAL YIELD PRESSURE 435 ELASTIC–PLASTIC HOLLOW CYLINDER SECTION 44 ELASTIC–PLASTIC BENDING 441 PURE BENDING OF PRISMATIC BEAMS 442 RECTANGULAR BEAMS UNDER TRANSVERSE LOADS 443 PLANE-STRAIN PURE BENDING OF WIDE BEAMS OR PLATES SECTION 45 NUMERICAL METHODS 451 INTEGRATION OF RATE EQUATIONS 452 THE FINITE-ELEMENT METHOD 453 FINITE-ELEMENT METHODS FOR NONLINEAR CONTINUA CHAPTER 5: PROBLEMS IN PLASTIC FLOW AND COLLAPSE I: THEORIES AND “EXACT” SOLUTIONS INTRODUCTION SECTION 51 PLANE PROBLEMS 511 SLIP-LINE THEORY 512 SIMPLE SLIP-LINE FIELDS 513 METAL-FORMING PROBLEMS SECTION 52 COLLAPSE OF CIRCULAR PLATES 521 INTRODUCTION TO PLATE THEORY 522 ELASTIC PLATES 523 YIELDING OF PLATES SECTION 53 PLASTIC BUCKLING 531 INTRODUCTION TO STABILITY THEORY 532 THEORIES OF THE E?ECTIVE MODULUS 533 PLASTIC BUCKLING OF PLATES AND SHELLS CHAPTER 6: PROBLEMS IN PLASTIC FLOW AND COLLAPSE II: APPLICATIONS OF LIMIT ANALYSIS INTRODUCTION SECTION 61 LIMIT ANALYSIS OF PLANE PROBLEMS 611 BLOCKS AND SLABS WITH GROOVES OR CUTOUTS 612 PROBLEMS IN BENDING 613 PROBLEMS IN SOIL MECHANICS SECTION 62 BEAMS UNDER COMBINED STRESSES 621 GENERALIZED STRESS 622 EXTENSION AND BENDING 623 COMBINED EXTENSION, BENDING AND TORSION 624 BENDING AND SHEAR SECTION 63 LIMIT ANALYSIS OF TRUSSES, BEAMS AND FRAMES 631 TRUSSES 632 BEAMS 633 LIMIT ANALYSIS OF FRAMES 634 LIMIT DESIGN OF FRAMES SECTION 64 LIMIT ANALYSIS OF PLATES AND SHELLS 641 LIMIT ANALYSIS OF PLATES 642 LIMIT ANALYSIS OF SHELLS: THEORY 643 LIMIT ANALYSIS OF SHELLS: EXAMPLES CHAPTER 7: DYNAMIC PROBLEMS SECTION 71 DYNAMIC LOADING OF STRUCTURES 711 INTRODUCTION 712 DYNAMIC LOADING OF BEAMS 713 DYNAMIC LOADING OF PLATES AND SHELLS SECTION 72 ONE-DIMENSIONAL PLASTIC WAVES 721 THEORY OF ONE-DIMENSIONAL WAVES 722 WAVES IN ELASTIC–PLASTIC BARS 723 RATE DEPENDENCE 724 APPLICATION OF THE METHOD OF CHARACTERISTICS SECTION 73 THREE-DIMENSIONAL WAVES 731 THEORY OF ACCELERATION WAVES 732 SPECIAL CASES CHAPTER 8: LARGE-DEFORMATION PLASTICITY SECTION 81 LARGE-DEFORMATION CONTINUUM MECHANICS 811 CONTINUUM DEFORMATION 812 CONTINUUM MECHANICS AND OBJECTIVITY SECTION 82 LARGE-DEFORMATION CONSTITUTIVE THEORY 821 THERMOELASTICITY 822 INELASTICITY: KINEMATICS 823 INELASTICITY: THERMOMECHANICS 824 YIELD CONDITION AND FLOW RULE SECTION 83 NUMERICAL METHODS IN LARGE-DEFORMATION PLASTIC- ITY 831 RATE-BASED FORMULATIONS 832 “HYPERELASTIC” NUMERICAL METHODS REFERENCES