Viscoelasticity — Basic Theory and Applications to Concrete Structures

I: Basic Concepts Integral Representation.- I. 1. Constitutive relations.- I. 2. Basic experimental results.- I. 2.1. Linearity.- I. 2.2. Aging.- I. 3. Integral representation of linear aging viscoelasticity.- I. 3.1. Alternative forms of the integral representation.- I. 4. Determination of the relaxation function from the creep function.- I. 5. Numerical solution of Volterra equation.- I. 6. Notes and references.- II: Rheological Models Differential Representation.- II. 1. The basic elements: spring and dashpot.- II. 2. Maxwell model.- II. 3. Kelvin model.- II. 3.1. Numerical solution for the Kelvin model.- II. 4. Generalized models.- II. 5. Models with variable parameters.- II. 6. Representation by means of state variables.- II. 7. Identification.- II. 8. A nonlinear model.- II. 9. Notes and references.- III: Examples of Viscoelastic behavior.- III. 1. Tests with constant stress rate.- III. 2. Tests with constant strain rate.- III. 3. Tests with periodic loading.- III. 4. Solids and fluids.- III. 4.1. Stability.- III. 4.2. Fading memory.- III. 5. Reduced modulus.- III. 5.1. Trost-Bazant modulus.- III. 6. Notes and references.- IV: Viscoelasticity in Three Dimensions.- IV. 1. Constitutive relations.- IV. 2. Cor re spondence method.- IV. 3. Asymptotic behavior.- IV. 4. Notes and references.- V: Representation of Concrete's behavior.- V. 1. Concrete as a porous-adsorbent material.- V. 2. Basic experimental facts and definitions.- V. 3. Some basic mathematical expressions.- V. 4. Prediction of creep.- V. 5. Formulas for structural analysis.- V. 5.1. Dischinger's formula.- V. 5.2. Improved Dischinger's formula.- V. 5.3. Arutyunyan's formula.- V. 5.4. Exponential series.- V. 5.5. Bazant-Panula formula.- V. 5.6. Expressions used in the Codes.- V. 6. Nonlinear behavior.- V. 7. Notes and references.- VI: Structural Analysis.- VI. 1. General method.- VI. 1.1. Basic relations.- VI. 1.2. Correspondence method.- VI. 1.3. General results classification of problems.- VI. 2. Generalized force method.- VI. 3. Approximate solutions more examples.- VI. 3.1. Effective modulus and TB-modulus.- VI. 3.2. Redistribution of stresses in a concrete column.- VI. 3.3. Single elastic restraint.- VI. 4. Notes and references.- VII: Finite Elements Viscoelastic Analysis.- VII. 1. Finite elements basic equations.- VII. 2. Constitutive relations.- VII. 3. Incremental formulation for viscoelasticity problems.- VII. 4. A computer program for viscoelastic analysis of trusses.- VII. 5. Notes and references.- VIII: Viscoelastic Buckling.- VIII. 1. The stability concept.- VIII. 2. Simplified column analysis.- VIII. 2.1. Elastic analysis.- VIII. 2.2. Linear viscoelastic analysis.- VIII. 3. Beam-column analysis.- VIII. 4. Nonlinear viscoelastic analysis.- VIII. 5. Practical formulas and Codes.- VIII. 6. Notes and references.- Appendix A: Some Mathematical Formulae.- Appendix B: Some Elasticity Formulae.- References.