THEORETICAL AND APPLIED RHEOLOGY
CONTENT 1 INTRODUCTION RHEOLOGY: SUBJECT AND LANGUAGE 2 STRESSES 21 GENERAL THEORY 22 LAW OF EQUALITY OF CONJUGATED SHEAR STRESSES 23 PRINCIPAL STRESSES 24 INVARIANTS 25 HYDROSTATIC PRESSURE AND DEVIATOR 26 EQUILIBRIUM (BALANCE) EQUATIONS 27 EXAMPLES 271 A BAR LOADED BY THE CONSTANT FORCE 272 A BAR LOADED BY ITS OWN WEIGHT 273 SAGGING OF A FLEXIBLE BAR OR A FIBER 274 INTERNAL PRESSURE IN A THIN-WALLED CYLINDER 275 HEMISPHERICAL MEMBRANE UNDER ITS OWN WEIGHT 276 TORSION OF A THIN-WALLED CYLINDER 277 TORSION OF A CONE OVER A PLATE 278 STRESSES IN A MEDIA MOVING ALONG A CYLINDER 279 STRESSES AROUND A CIRCULAR HOLE IN A SHEET 28 CONCLUDING REMARKS 29 REFERENCES 3 DEFORMATION AND DEFORMATION RATE 31 DISPLACEMENTS AND DEFORMATIONS 32 DEFORMATION RATE 33 LARGE DEFORMATIONS 34 PRINCIPAL VALUES AND INVARIANTS OF THE DEFORMATION TENSORS 35 UNIAXIAL ELONGATION POISSON RATIO 36 SIMPLE SHEAR AND PURE SHEAR 37 EXAMPLES 371 UNIAXIAL EXTENSION OF A BAR (BEAM, FIBER) 372 SHEAR 373 PLANE DEFORMATION (STRAIN) STATE 374 THREE-DIMENSIONAL DEFORMED STATE 38 CONCLUDING REMARKS 39 REFERENCES 4 RHEOLOGICAL EQUATIONS OF STATE 41 MAIN RHEOLOGICAL EFFECTS 411 NON-NEWTONIAN VISCOSITY 412 PLASTIC BEHAVIOR 413 WEISSENBERG EFFECT 414 TRANSIENT DEFORMATIONS IN SHEAR (OF LIQUIDS) 415 UNIAXIAL EXTENSION 416 INSTABILITIES AND SECONDARY FLOWS 4161 EXTRUDATE DISTORTIONS (MELT FRACTURE) 4162 SECONDARY FLOW 4163 WAVING IN EXTENSIONAL FLOWS 4164 INTERFACIAL AND SURFACE INSTABILITY 4165 RHEOLOGICAL PHENOMENON IN INERTIAL TURBULENCE (TOMS EFFECT) 417 THIXOTROPY AND RHEOPEXY 418 NON-LINEAR ELASTICITY 419 VISCOELASTIC BEHAVIOR 4110 FLOW AROUND SOLID OBSTACLES 4111 PHASE TRANSITIONS INDUCED BY DEFORMATIONS 42 GENERAL PRINCIPLES 43 CONCLUDING REMARKS 44 REFERENCES 5 RHEOLOGICAL VISCOUS FLUIDS 51 DEFINITIONS 52 NEWTONIAN LIQUID 53 NON-NEWTONIAN LIQUIDS 54 VISCO-PLASTIC LIQUIDS 55 SOME BASIC PROBLEMS 551 INTRODUCTION 552 PLANE UNIDIMENSIONAL FLOW 553 FLOW THROUGH STRAIGHT TUBES UNDER PRESSURE 554 PENETRATION OF A CYLINDER INTO A VISCOUS MEDIUM 555 RESISTANCE TO ROTATION OF A THIN DISK IN A LIQUID 556 CONVERGING (DIVERGING) FLOWS 557 MOVEMENT OF A BALL THROUGH A VISCOUS FLUID 558 COMPRESSION OF A LIQUID BETWEEN TWO PARALLEL DISKS 559 HYDRODYNAMICS OF ROLLING 5510 FLOW IN LUBRICANT LAYER 56 CONCLUDING REMARKS 57 REFERENCES 6 ELASTIC SOLIDS 61 DEFINITIONS 62 HOOKEAN ELASTIC MATERIAL 63 LINEAR ANISOTROPIC MATERIALS 64 LARGE ELASTIC DEFORMATIONS IN SOLIDS 65 LIMITS OF ELASTICITY 66 SOME BASIC PROBLEMS 661 GENERAL FORMULATION 662 UNIAXIAL EXTENSION 663 BENDING BY A TORQUE 664 BENDING BY A TRANSVERSE FORCE 665 TORSION OF A BAR 666 TEMPERATURE STRESSES 667 CYLINDER UNDER INTERNAL PRESSURE 668 PRESSURE INSIDE A SPHERE 669 STRESSES AND DEFORMATIONS IN MEMBRANES 6610 CONTACT (LOCAL) STRESSES 67 CONCLUDING REMARKS 7 VISCOELASTICITY 71 INTRODUCTION 72 DEFINITIONS 721 CREEP 722 RELAXATION 723 PERIODIC OSCILLATIONS 73 PRINCIPLE OF SUPERPOSITION 74 RELAXATION AND RETARDATION SPECTRA 741 CALCULATION OF CONTINUOUS SPECTRUM 742 CALCULATING DISCRETE SPECTRUM 75 DYNAMIC AND RELAXATION PROPERTIES - CORRELATIONS 76 RELATIONSHIPS BETWEEN CONSTANTS 761 VISCOELASTIC SOLID 762 VISCOELASTIC LIQUID 77 MECHANICAL MODELS OF VISCOELASTIC BEHAVIOR 78 SUPERPOSITION 79 APPLICATIONS OF LINEAR VISCOELASTICITY 791 COMPARISON OF MATERIALS BY THEIR VISCOELASTIC PROPERTIES 792 CALCULATION OF THE RESPONSE 710 NON-LINEAR VISCOELASTICITY INTRODUCTION 7101 LARGE DEFORMATIONS IN NON-LINEAR VISCOELASTICITY 7102 RELAXATION PROPERTIES DEPENDENT ON DEFORMATION 711 CONCLUDING REMARKS 712 REFERENCES