Viscoelasticity - Basic Theory and Applications to Concrete Structures

This book contains notes for a one-semester graduate course which is an introduction to the study of viscoelasticity and creep of concrete. Emphasis was set on the conceptual aspects rather than on the mathematical or computational refinements. The mathematical structure of viscoelasticity is discussed with some care because it clarifies the basic concepts and has important consequences in computa­ tional applications. Basic ideas are exemplified using the simplest problems and constitutive models in order to be able to show complete solutions. In the computational applications we have also chosen to present the sim­ plest situations with the greatest possible detail. It has been the author's experience that once the basic concepts are well understood the students are able to follow the rest of the course more easily and to accede to more advanced literature and applications. Chapters I to III furnish the foundations for the course, that may be expanded in diverse ways. If we are interested in finite elements applications we should look at Chapter IV and then go direct­ ly to Chapter VII. If we are interested in the simplified analysis of frame structures we should study Chapter VI in detail. Chapter V re­ views the viscoelastic behavior of concrete and Chapter VIII studies the problem of creep buckling. At the end of each chapter we give se­ lected references to works that complete and extend the subject matter.

Contenu

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.