Mechanics of Viscoelastic Solids

Transcription

1 Mechanics of Viscoelastic Solids Aleksey D. Drozdov Institute for Industrial Mathematics, Beersheba, Israel JOHN WILEY & SONS Chichester New York Weinheim Brisbane Toronto Singapore

2 Contents Preface xi 1 Constitutive Models in Linear Viscoelasticity THE BOLTZMANN SUPERPOSITION PRINCIPLE THE SHORT-TERM RESPONSE IN PHYSICALLY AGED POLYMERS A MODEL OF ADAPTIVE LINKS A BALANCE EQUATION FOR THE NUMBER OF LINKS COMPARISON WITH EXPERIMENTS TIME-VARYING LOADING THE LONG-TERM RESPONSE IN PHYSICALLY AGED POLYMERS A MODEL OF ADAPTIVE LINKS A FREE VOLUME CONCEPT CONSTITUTIVE EQUATIONS COMPARISON WITH EXPERIMENTS CONSTITUTIVE RELATIONS FOR THREE-DIMENSIONAL LOADING THERMODYNAMIC POTENTIALS OF A TRANSIENT NETWORK STRAIN ENERGY DENSITY THERMODYNAMIC POTENTIALS AND CONSTI TUTIVE EQUATIONS PROPERTIES OF RELAXATION FUNCTIONS VARIATIONAL PRINCIPLES IN VISCOELASTICITY VARIATIONAL PRINCIPLES AND GOVERNING EQUATIONS GIBBS' PRINCIPLE AND THE SECOND LAW OF THERMODYNAMICS DEBONDING OF A STRIP LINKED TO A RIGID FOUNDATION BY A VISCOELASTIC ADHESIVE LAYER 90

3 viii CONTENTS 1.7 PHASE TRANSITIONS IN VISCOELASTIC MEDIA FORMULATION OF THE PROBLEM AN INTEGRAL OVER A VARYING DOMAIN INTERFACIAL EQUILIBRIUM EQUATIONS LOCAL MELTING OF A VISCOELASTIC MEDIUM. 120 References Constitutive Models in Nonlinear Viscoelasticity A TRANSIENT NETWORK WITH NONLINEAR LINKS CONSTITUTIVE EQUATIONS COMPARISON WITH EXPERIMENTS THREE-DIMENSIONAL LOADING TORSION OF A CONICAL PIPE THE CORRESPONDENCE PRINCIPLES A NETWORK WITH AN EYRING-TYPE CLOCK STRESS-STRAIN RELATIONS THE GENERALIZED ARRHENIUS EQUATION COMPARISON WITH EXPERIMENTS A NETWORK WITH AN ENTROPY-DRIVEN CLOCK THERMODYNAMIC POTENTIALS A DISSIPATION-DRIVEN INTERNAL CLOCK COMPARISON WITH EXPERIMENTS CONSTITUTIVE RELATIONS IN VISCOELASTOPLAS- TICITY A MODEL OF ADAPTIVE LINKS COMPARISON WITH EXPERIMENTS 196 References Constitutive Models in Finite Viscoelasticity OPERATOR LINEAR CONSTITUTIVE RELATIONS KINETIC EQUATIONS STRAIN ENERGY DENSITY THERMODYNAMIC POTENTIALS COMPARISON WITH EXPERIMENTS THE PRINCIPLE OF MINIMUM FREE ENERGY THERMODYNAMIC STABILITY THE MOONEY-RIVLIN MODEL DIFFERENTIAL CONSTITUTIVE EQUATIONS UNIAXIAL EXTENSION SIMPLE SHEAR TORSION OF A CIRCULAR CYLINDER STRAIN ENERGY DENSITY OF A NETWORK UNIAXIAL EXTENSION 256

4 CONTENTS ix BIAXIAL EXTENSION CONSTITUTIVE EQUATIONS BASED ON THE FREE VOLUME CONCEPT THE TIME-STRAIN SUPERPOSITION PRINCIPLE A NEO-HOOKEAN VISCOELASTIC MEDIUM UNIAXIAL EXTENSION SIMPLE SHEAR RADIAL DEFORMATION OF A SPHERICAL SHELL A NETWORK WITH AN ENTROPY-DRIVEN CLOCK A CONCEPT OF TRANSIENT NETWORKS THERMODYNAMIC POTENTIALS SIMPLE SHEAR 317 References Constitutive Models in Thermoviscoelasticity THERMORHEOLOGICALLY SIMPLE MEDIA TIME-TEMPERATURE SUPERPOSITION PRINCI PLE ' THERMAL SHIFT FACTOR NONISOTHERMAL LOADING THERMORHEOLOGICALLY COMPLEX MEDIA BASIC HYPOTHESES A CONCEPT OF TRANSIENT NETWORKS (MODEL I) A CONCEPT OF TRANSIENT NETWORKS (MODEL I) NONISOTHERMAL LOADING THE NONISOTHERMAL RESPONSE IN NONAGING POLYMERS THREE-DIMENSIONAL LOADING THE STANDARD THERMOVISCOELASTIC SOLID COOLING OF A RECTILINEAR BAR COOLING OF A CYLINDRICAL SHELL LINEAR MEDIA SUBJECTED TO PHYSICAL AGING CONSTITUTIVE EQUATIONS COOLING OF A SPHERICAL PRESSURE VESSEL NONLINEAR MEDIA SUBJECTED TO PHYSICAL AGING STRAIN ENERGY DENSITY OF A NETWORK (ISOTHERMAL LOADING) STRAIN ENERGY DENSITY OF A NETWORK (NONISOTHERMAL LOADING) THERMODYNAMIC POTENTIALS CONSTITUTIVE RELATIONS (FINITE STRAINS) CONSTITUTIVE RELATIONS (SMALL STRAINS). 425

5 x CONTENTS CONSTITUTIVE RELATIONS FOR PHYSICALLY AGED POLYMERS THE AGING SHIFT FACTOR UNIAXIAL EXTENSION COOLING OF A PLATE 446 References 459 Index 465