Viscoelastic Structures: Mechanics of Growth and Aging
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Table of contents
- Contentsxi
- Chapter 1. Kinematics of Continua1
- 1.1 Basic Definitions and Formulas1
- Bibliography23
- Chapter 2. Constitutive Models in Linear Viscoelasticity25
- 2.1 Differential Constitutive Models25
- 2.2 Integral Constitutive Models34
- 2.3 Creep and Relaxation Kernels54
- 2.4 Thermodynamic Potentials and Variational Principles in Linear Viscoelasticity71
- 2.5 A Model of Adaptive Links for Aging Viscoelastic Media80
- Bibliography97
- Chapter 3. Nonlinear Constitutive Models with Small Strains107
- 3.1 Nonlinear Differential Models107
- 3.2 Nonlinear Integral Models117
- 3.3 A Model for Crosslinked Polymers130
- 3.4 A Model for Non-Crosslinked Polymers145
- Bibliography161
- Chapter 4. Nonlinear Constitutive Models with Finite Strains171
- 4.1 Differential Constitutive Models171
- 4.2 Fractional Differential Models177
- 4.3 Integral Constitutive Models203
- 4.4 A Model of Adaptive Links212
- 4.5 A Constitutive Model in Finite Viscoelasticity226
- Bibliography255
- Chapter 5. Constitutive Relations for Thermoviscoelastic Media262
- 5.1 Constitutive Models in Thermoviscoelasticity262
- 5.2 A Model of Adaptive Links in Thermoviscoelasticity275
- 5.3 Constitutive Models for the Nonisothermal Behavior294
- Bibliography328
- Chapter 6. Accretion of Aging Viscoelastic Media with Finite Strains337
- 6.1 Continuous Accretion of Aging Viscoelastic Media337
- 6.2 Winding of a Cylindrical Pressure Vessel371
- 6.3 Winding of a Composite Cylinder with Account for Resin Flow393
- 6.4 Volumetric Growth of a Viscoelastic Tissue413
- Bibliography436
- Chapter 7. Accretion of Viscoelastic Media with Small Strains446
- 7.1 Accretion of a Viscoelastic Conic Pipe446
- 7.2 Accretion of a Viscoelastic Spherical Dome464
- 7.3 Debonding of Accreted Viscoelastic Beams480
- 7.4 Torsion of an Accreted Elastoplastic Cylinder499
- Bibliography510
- Chapter 8. Optimization Problems for Growing Viscoelastic Media511
- 8.1 An Optimal Rate of Accretion for Viscoelastic Solids511
- 8.2 Optimal Accretion of an Elastic Column532
- 8.3 Preload Optimization for a Wound Cylindrical Pressure Vessel542
- 8.4 Optimal Design of Growing Beams554
- 8.5 Optimal Solidification of a Spherical Pressure Vessel569
- Bibliography589
- Index593
Viscoelastic Structures covers the four basic problems in the mechanics of viscoelastic solids and structural members: construction of constitutive models for the description of thermoviscoelastic behavior of polymers; mathematical modeling of manufacturing advanced composite materials; optimal-design of structural members and technological processes of their fabrication; and stability analysis for thin-walled structural members driven by time-varying loads.
This book familiarizes the reader with state-of-the-art mathematical models for advanced materials and processes, and demonstrates their applications in modeling and simulating specific manufacturing processes. Viscoelastic Structures also demonstrates the effects of material, geometrical, and technological parameters on the characteristic features of viscoelastic structures.
1Presents state-of-the-art mathematical models and methods which serve for the analysis of advanced technological processes
1Includes numerous examples to demonstrate theory which have not been included in previous literature
1Employs one consistent, user-friendly method to study a number of technological processes
1Features unique approach to aging materials
1Appendices cover background material on tensor calculus, kinematics with finite strains, stochastic differential equations, and evolutionary equations with operator coefficients
This book familiarizes the reader with state-of-the-art mathematical models for advanced materials and processes, and demonstrates their applications in modeling and simulating specific manufacturing processes. Viscoelastic Structures also demonstrates the effects of material, geometrical, and technological parameters on the characteristic features of viscoelastic structures.
1Presents state-of-the-art mathematical models and methods which serve for the analysis of advanced technological processes
1Includes numerous examples to demonstrate theory which have not been included in previous literature
1Employs one consistent, user-friendly method to study a number of technological processes
1Features unique approach to aging materials
1Appendices cover background material on tensor calculus, kinematics with finite strains, stochastic differential equations, and evolutionary equations with operator coefficients