Viscoelastic Structures

Viscoelastic Structures

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Product Details

ISBN-13: 9780122222801
Publisher: Elsevier Science & Technology Books
Publication date: 12/15/1997
Pages: 596
Product dimensions: 6.24(w) x 9.28(h) x 1.29(d)

Table of Contents

1 Kinematics of Continua
1(24)
1.1 Basic Definitions and Formulas
1(22)
1.1.1 Description of Motion
1(2)
1.1.2 Tangent Vectors
3(2)
1.1.3 The Nabla Operator
5(1)
1.1.4 Deformation Gradient
6(1)
1.1.5 Deformation Tensors and Strain Tensors
7(3)
1.1.6 Stretch Tensors
10(1)
1.1.7 Relative Deformation Tensors
11(1)
1.1.8 Rigid Motion
12(1)
1.1.9 Generalized Strain Tensors
13(1)
1.1.10 Volume Deformation
14(1)
1.1.11 Deformation of the Surface Element
15(1)
1.1.12 Objective Tensors
16(2)
1.1.13 Velocity Vector and Its Gradient
18(2)
1.1.14 Corotational Derivatives
20(2)
1.1.15 The Rivlin-Ericksen tensors
22(1)
Bibliography
23(2)
2 Constitutive Models in Linear Viscoelasticity
25(82)
2.1 Differential Constitutive Models
25(9)
2.1.1 Differential Constitutive Models
26(2)
2.1.2 Fractional Differential Models
28(6)
2.2 Integral Constitutive Models
34(20)
2.2.1 Boltzmann's Superposition Principle
35(4)
2.2.2 Connections Between Creep and Relaxation Measures
39(2)
2.2.3 A Model of Adaptive Links
41(3)
2.2.4 Spectral Presentation of the Function X(t, T)
44(4)
2.2.5 Three-Dimensional Loading
48(6)
2.3 Creep and Relaxation Kernels
54(17)
2.3.1 Creep and Relaxation Kernels for Nonaging Media
54(5)
2.3.2 Creep and Relaxation Kernels for Aging Media
59(7)
2.3.3 Properties of Creep and Relaxation Measures
66(5)
2.4 Thermodynamic Potentials and Variational Principles in Linear Viscoelasticity
71(9)
2.4.1 Thermodynamic Potentials of Aging Viscoelastic Media
72(1)
2.4.2 Variational Principles in Viscoelasticity
73(4)
2.4.3 Gibbs' Principle and the Second Law of Thermodynamics
77(2)
2.4.4 Thermodynamic Inequalities in Linear Viscoelasticity
79(1)
2.5 A Model of Adaptive Links for Aging Viscoelastic Media
80(17)
2.5.1 A Model of Adaptive Links
81(8)
2.5.2 Validation of the Model
89(4)
2.5.3 Prediction of Stress-Strain Curves for Time-Varying Loads
93(4)
Bibliography
97(10)
3 Nonlinear Constitutive Models with Small Strains
107(64)
3.1 Nonlinear Differential Models
107(10)
3.2 Nonlinear Integral Models
117(13)
3.2.1 Uniaxial Loading
117(9)
3.2.2 Three-Dimensional Loading
126(4)
3.3 A Model for Crosslinked Polymers
130(15)
3.3.1 A Model of Adaptive Links
131(5)
3.3.2 Determination of Adjustable Parameters
136(4)
3.3.3 Constitutive Equations for Three-Dimensional Loading
140(3)
3.3.4 Correspondence Principles in Nonlinear Viscoelasticity
143(2)
3.4 A Model for Non-Crosslinked Polymers
145(16)
3.4.1 A Model of Adaptive Links
146(3)
3.4.2 A Generalized Model of Adaptive Links
149(4)
3.4.3 Validation of the Model
153(8)
Bibliography
161(10)
4 Nonlinear Constitutive Models with Finite Strains
171(91)
4.1 Differential Constitutive Models
171(6)
4.1.1 The Rivlin-Ericksen Models
172(1)
4.1.2 The Kelvin-Voigt Model
173(1)
4.1.3 The Maxwell Model
174(2)
4.1.4 The Standard Viscoelastic Solid
176(1)
4.2 Fractional Differential Models
177(26)
4.2.1 Fractional Differential Operators with Finite Strains
178(2)
4.2.2 Fractional Differential Models
180(2)
4.2.3 Uniaxial Extension of an Incompressible Bar
182(6)
4.2.4 Radial Deformation of a Spherical Shell
188(7)
4.2.5 Uniaxial Extension of a Compressible Bar
195(3)
4.2.6 Simple Shear of a Compressible Medium
198(5)
4.3 Integral Constitutive Models
203(9)
4.3.1 Linear Constitutive Equations
203(2)
4.3.2 Constitutive Equations in the Form of Taylor Series
205(1)
4.3.3 BKZ-Type Constitutive Equations
206(4)
4.3.4 Semilinear Constitutive Equations
210(2)
4.4 A Model of Adaptive Links
212(14)
4.4.1 A Model of Adaptive Links
212(1)
4.4.2 The Lagrange Variational Principle
213(6)
4.4.3 Thermodynamic Stability of a Viscoelastic Medium
219(2)
4.4.4 Constitutive Equations for Incompressible Media
221(2)
4.4.5 Extension of a Viscoelastic Bar
223(3)
4.5 A Constitutive Model in Finite Viscoelasticity
226(29)
4.5.1 A Model of Adaptive Links
227(4)
4.5.2 Uniaxial Extension of a Viscoelastic Bar
231(5)
4.5.3 Biaxial Extension of a Viscoelastic Sheet
236(12)
4.5.4 Torsion of a Viscoelastic Cylinder
248(7)
Bibliography
255(7)
5 Constitutive Relations for Thermoviscoelastic Media
262(75)
5.1 Constitutive Models in Thermoviscoelasticity
262(13)
5.1.1 Thermorheologically Simple Media
262(8)
5.1.2 The Proportionality Hypothesis
270(2)
5.1.3 The McCrum Model
272(3)
5.2 A Model of Adaptive Links in Thermoviscoelasticity
275(19)
5.2.1 Governing Equations
275(9)
5.2.2 A Refined Model of Adaptive Links
284(10)
5.3 Constitutive Models for the Nonisothermal Behavior
294(34)
5.3.1 Constitutive Equations for Isothermal Loading
297(5)
5.3.2 Constitutive Equations for Nonisothermal Loading
302(4)
5.3.3 Three-Dimensional Loading
306(1)
5.3.4 The Standard Thermoviscoelastic Solid
307(6)
5.3.5 Cooling of a Cylindrical Pressure Vessel
313(15)
Bibliography
328(9)
6 Accretion of Aging Viscoelastic Media with Finite Strains
337(109)
6.1 Continuous Accretion of Aging Viscoelastic Media
337(34)
6.1.1 A Model for Continuous Accretion
338(9)
6.1.2 Continuous Accretion of a Viscoelastic Cylinder
347(6)
6.1.3 Continuous Accretion of an Elastoplastic Bar
353(18)
6.2 Winding of a Cylindrical Pressure Vessel
371(22)
6.2.1 The Lame Problem for an Accreted Cylinder
375(18)
6.3 Winding of a Composite Cylinder with Account for Resin Flow
393(20)
6.3.1 Kinematics of Deformation
394(4)
6.3.2 Governing Equations
398(6)
6.3.3 Accretion on a Rigid Mandrel
404(2)
6.3.4 Accretion with Small Strains
406(7)
6.4 Volumetric Growth of a Viscoelastic Tissue
413(23)
6.4.1 A Brief Historical Survey
414(3)
6.4.2 Constitutive Equations
417(6)
6.4.3 Compression of a Growing Bar
423(7)
6.4.4 The Lame Problem for a Growing Cylinder
430(6)
Bibliography
436(10)
7 Accretion of Viscoelastic Media with Small Strains
446(65)
7.1 Accretion of a Viscoelastic Conic Pipe
446(18)
7.1.1 Formulation of the Problem
446(1)
7.1.2 Kinematics of Accretion
447(3)
7.1.3 Constitutive Equations
450(1)
7.1.4 Governing Equations (Model 1)
451(4)
7.1.5 Governing Equations (Model 2)
455(3)
7.1.6 Numerical Analysis
458(6)
7.2 Accretion of a Viscoelastic Spherical Dome
464(16)
7.2.1 Formulation of the Problem
465(2)
7.2.2 Governing Equations
467(5)
7.2.3 Determination of Preload
472(2)
7.2.4 Displacements in an Accreted Dome
474(1)
7.2.5 Numerical Analysis
475(5)
7.3 Debonding of Accreted Viscoelastic Beams
480(19)
7.3.1 Accretion of a Two-Layered Beam
480(9)
7.3.2 Accretion of an Elastic Beam on a Nonlinear Winkler Foundation
489(10)
7.4 Torsion of an Accreted Elastoplastic Cylinder
499(11)
7.4.1 Formulation of the Problem
499(2)
7.4.2 Stresses and Strains in a Growing Cylinder
501(1)
7.4.3 Accretion of an Elastic Cylinder
502(3)
7.4.4 An Elastoplastic Cylinder with Plastic Region
505(4)
7.4.5 An Elastoplastic Cylinder with Two Plastic Regions
509(1)
Bibliography
510(1)
8 Optimization Problems for Growing Viscoelastic Media
511(82)
8.1 An Optimal Rate of Accretion for Viscoelastic Solids
511(21)
8.1.1 Torsion of an Accreted Viscoelastic Cylinder With Small Strains
512(11)
8.1.2 Extension of an Accreted Elastic Bar with Finite Strains
523(9)
8.2 Optimal Accretion of an Elastic Column
532(10)
8.2.1 Formulation of the Problem and Governing Equations
532(4)
8.2.2 Optimal Regime of Loading
536(2)
8.2.3 Optimal Regime of Accretion
538(4)
8.3 Preload Optimization for a Wound Cylindrical Pressure Vessel
542(12)
8.3.1 Formulation of the Problem and Governing Equations
542(6)
8.3.2 Winding of a Nonaging Cylindrical Pressure Vessel
548(2)
8.3.3 Winding of an Aging Cylindrical Pressure Vessel
550(4)
8.4 Optimal Design of Growing Beams
554(15)
8.4.1 Formulation of the Problem and Governing Equations
555(3)
8.4.2 Optimal Thickness of a Nonaging Elastic Beam
558(4)
8.4.3 Optimal Thickness of an Aging Elastic Beam
562(7)
8.5 Optimal Solidification of a Spherical Pressure Vessel
569(20)
8.5.1 Formulation of the Problem
570(2)
8.5.2 Temperature Distribution
572(1)
8.5.3 Stresses and Displacements
573(6)
8.5.4 Stresses in a Pressure Vessel after Cooling
579(3)
8.5.5 Numerical Analysis
582(7)
Bibliography
589(4)
Index 593

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