Viscoelastic Modeling for Structural Analysis.

Cover -- Half-Title Page -- Title Page -- Copyright Page -- Contents -- Preface -- Acknowledgment -- List of Notations -- List of main notations as they appear in the book -- 1. One-dimensional Viscoelastic Modeling -- 1.1. Experimental observations -- 1.2. Fundamental uniaxial tests -- 1.2.1. Creep test, creep function -- 1.2.2. Stress relaxation test, relaxation function -- 1.2.3. First comments -- 1.2.4. Recovery -- 1.2.5. Stress fading -- 1.3. Functional description -- 1.4. Aging -- 1.4.1. Aging phenomenon -- 1.4.2. Non-aging materials -- 1.5. Linear behavior -- 1.5.1. Superposition principle: Boltzmannian materials -- 1.5.2. Linear elasticity -- 1.6. Linear viscoelastic material -- 1.6.1. Instantaneous behavior -- 1.6.2. Creep and relaxation functions -- 1.6.3. Recovery and stress fading -- 1.6.4. Instantaneous behavior -- 1.6.5. Validation of the linearity hypothesis: an example -- 1.7. Linear viscoelastic constitutive equation -- 1.7.1. Arbitrary stress history -- 1.7.2. Arbitrary deformation history -- 1.7.3. Linear elastic material -- 1.7.4. Boltzmann's formulas, integral operator -- 1.7.5. Comments -- 1.8. Non-aging linear viscoelastic constitutive equation -- 1.8.1. Creep and relaxation functions -- 1.8.2. Boltzmann's formulas -- 1.8.3. Recovery and stress fading -- 1.8.4. Operational calculus -- 1.9. One-dimensional linear viscoelastic behavior -- 1.9.1. Uniaxial viewpoint and one-dimensional modeling -- 1.9.2. Structural elements -- 1.10. Harmonic loading process -- 1.10.1. The loading process -- 1.10.2. Asymptotic harmonic regime -- 1.10.3. Complex modulus -- 1.10.4. Loss angle, specific loss -- 2. Rheological Models -- 2.1. Rheological models -- 2.2. Basic elements -- 2.2.1. Linear elastic element -- 2.2.2. Linear viscous element -- 2.3. Classical models -- 2.3.1. Maxwell model -- 2.3.2. Kelvin model.

2.3.3. The standard linear solid -- 2.4. Generalized Maxwell and Kelvin models -- 2.4.1. Generalized Maxwell model -- 2.4.2. Generalized Kelvin model -- 2.4.3. Equivalence -- 2.4.4. Continuous spectra -- 3. Typical Case Studies -- 3.1. Presentation and general features -- 3.2. "Creep-type" problems -- 3.2.1. Homogeneous cantilever beam subjected to a uniformly distributed load -- 3.2.2. Homogeneous cantilever beam subjected to a concentrated load -- 3.2.3. Homogeneous statically indeterminate beam -- 3.2.4. A statically indeterminate system -- 3.3. Prestressing of viscoelastic systems or structures -- 3.3.1. Prestressed cantilever beam -- 3.3.2. Prestressed hyperstatic system -- 3.3.3. Prestressed hyperstatic arc -- 3.3.4. The example of a rheological model -- 3.3.5. Practical applications -- 3.4. A complex loading process -- 3.4.1. A practical problem -- 3.4.2. Mathematical treatment -- 3.4.3. Comments -- 3.5. Heterogeneous viscoelastic structures -- 4. Three-dimensional Linear Viscoelastic Modeling -- 4.1. Multidimensional approach -- 4.2. Fundamental experiments -- 4.2.1. The three-dimensional continuum framework -- 4.2.2. General definition of the creep and relaxation tests -- 4.2.3. The linearity hypothesis -- 4.2.4. Tensorial creep and relaxation functions -- 4.2.5. Instantaneous elasticity -- 4.3. Boltzmann's formulas -- 4.3.1. Integral operator -- 4.3.2. Important identities -- 4.4. Isotropic linear viscoelastic material -- 4.4.1. Material symmetries, principle of material symmetries -- 4.4.2. Isotropic linear viscoelastic material: creep test -- 4.4.3. Isotropic linear viscoelastic material: relaxation test -- 4.4.4. Boltzmann's formulas -- 4.4.5. Uniaxial tension relaxation test -- 4.4.6. Constant Poisson's ratio -- 4.5. Non-aging linear viscoelastic material -- 4.5.1. Boltzmann's formulas -- 4.5.2. Operational calculus.

4.5.3. Isotropic material -- 5. Quasi-static Linear Viscoelastic Processes -- 5.1. Quasi-static linear viscoelastic processes -- 5.1.1. Isothermal quasi-static processes -- 5.1.2. Isothermal quasi-static linear viscoelastic processes -- 5.1.3. Superposition principle -- 5.1.4. Loading parameters, kinematic parameters -- 5.2. Solution to the linear viscoelastic quasi-static evolution problem -- 5.2.1. Statically admissible stress histories, kinematically admissible displacement histories -- 5.2.2. Solution methods -- 5.3. Homogeneous isotropic material with constant Poisson's ratio -- 5.3.1. Creep-type problems, creep-type evolutions -- 5.3.2. Relaxation-type problems, relaxation-type evolutions -- 5.3.3. Mixed data problems -- 5.3.4. Comments -- 5.4. Non-aging linear viscoelastic material -- 5.4.1. Correspondence principle -- 5.4.2. Comments -- 6. Some Practical Problems -- 6.1. Presentation -- 6.2. Uniaxial tension-compression of a cylindrical rod -- 6.2.1. Statement of the problem -- 6.2.2. Solution -- 6.3. Bending of a cylindrical rod -- 6.3.1. Statement of the problem -- 6.3.2. Solution -- 6.4. Twisting of a cylindrical rod -- 6.4.1. Preliminary comments -- 6.4.2. Statement of the problem -- 6.4.3. Solution -- 6.4.4. Comment -- 6.5. Convergence of a spherical cavity -- 6.5.1. Statement of the problem -- 6.5.2. Solution -- Appendix -- Laplace transforms of usual functions and distributions -- References -- Index -- Other titles from iSTE in Materials Science -- EULA.

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