Cover -- Title Page -- Copyright Page -- Contents -- Foreword by Franz-Josef Ulm -- Foreword by Pierre Labbé -- List of Notations -- Introduction -- Chapter 1. Mechanisms of Deformation and Failure of Concrete -- 1.1. Concrete: a material that is both widespread and misunderstood -- 1.2. Composition and behavior of concrete at an early age -- 1.2.1. Concrete curing -- 1.2.2. Consequences of curing and phenomena related to the aging of concrete -- 1.3. Main aspects of the mechanical behavior of concrete -- 1.3.1. Concrete under uniaxial loading -- 1.3.2. Concrete under multiaxial loading -- Chapter 2. Damage Concept and Its Applicability to Concrete -- 2.1. Damage concept -- 2.1.1. Miner cumulative damage law -- 2.1.2. Katchanov's progressive damage law -- 2.1.3. Elasticity-damage coupling -- 2.2. Theoretical bases of damage mechanics -- 2.2.1. Elasticity-damage coupling -- 2.2.2. Isotropic damage theory -- 2.2.3. Damage threshold and notion of loading surface -- Chapter 3. Damage Modeling -- 3.1. Mazars models for monotonous loadings -- 3.1.1. Constitutive equations -- 3.1.2. Using the model (uniaxial case) -- 3.1.3. Strengths and weaknesses of the Mazars model -- 3.2. Model for cyclic loadings: the ì model -- 3.2.1. Concept of effective damage variable -- 3.2.2. Constitutive equations -- 3.2.3. Response of the ì model under various types of loading -- 3.2.4. Adaptation of the ì model to the case of confined loadings -- Chapter 4. Numerical Calculation of Damage -- 4.1. Reminders on concepts governing the use of finite elements -- 4.2. Principle flowcharts -- 4.2.1. Flowchart for the Mazars model -- 4.2.2. Flowchart for the ì model -- 4.3. Data preparation -- 4.3.1. Identification of modeling parameters -- 4.4. Concrete fracturing energy -- 4.4.1. Intrinsic and extrinsic energy -- 4.4.2. Crack band concept, Hillerborg regularization.

4.5. Non-local damage concept -- Chapter 5. Applications to Common Reinforced Concrete Structural Elements Cases -- 5.1. 2D FE calculation -- 5.1.1. Details of the experimental program -- 5.1.2. Numerical processing -- 5.1.3. Results -- 5.2. Calculations by Timoshenko enriched beam elements -- 5.2.1. Strengths and weaknesses of the multifiber beam description -- 5.2.2. Bias of results from the choice of material parameters -- 5.2.3. Multifiber beams and strain localization -- 5.2.4. Enriched multifiber description and use of suitable parameters -- 5.2.5. Simulations based on the enriched multifiber description -- 5.3. Multifiber calculations and access to cracking indicators -- 5.3.1. Damage fields -- 5.3.2. Opening of cracks -- Chapter 6. Modeling of Situations Related to Specific Loadings -- 6.1. Simulation of velocity effects -- 6.1.1. Analysis resulting from the experiment -- 6.1.2. High-velocity loading: application to Spalling tests -- 6.1.3. Loading at medium velocity: impact on a reinforced concrete beam -- 6.2. Simulation of the effects of concrete maturation -- 6.2.1. Problems posed by the behavior of concrete at an early age -- 6.2.2. Case of a beam in a situation of restrained shrinkage -- 6.2.3. Thermomechanical model of concrete at an early age -- 6.2.4. RG8 test: application and results -- Chapter 7. Structures Combining Beams and Planar Elements -- 7.1. Simulation of the behavior of a reinforced concrete wall -- 7.1.1. Model for structural walls: equivalent reinforced concrete -- 7.1.2. Application to the SAFE experiment shear wall case -- 7.2. Application to a structure combining walls, beams and columns -- 7.2.1. Enriched ERC modeling -- 7.2.2. Modeling the response of the SMART model -- 7.3. Calculation combining 2D finite elements and multifiber beams -- 7.3.1. Case study: loss of bearing capacity of a column in a structure.

7.3.2. Calculation-experiment comparison results -- 7.4. Conclusion -- Chapter 8. Assessment of Cracking by Limit Analysis -- 8.1. Characterization of cracking: case of homogeneous fields of tensile elements -- 8.1.1. Limit analysis and yield design theory -- 8.1.2. Case of reinforced concrete beams in bending -- 8.2. Tie rod cracking -- 8.2.1. Localized cracking and diffuse damage -- 8.2.2. Behavioral law for concrete in the diffuse scheme -- 8.2.3. Application to an experiment on tie rods carried out at EPFL -- 8.3. Homogeneous field created by concrete maturation within a cylindrical wall -- 8.3.1. VeRCoRs program and model -- 8.3.2. Mesh of the gusset and temperature conditions -- 8.3.3. Creep, shrinkage and mechanical properties -- 8.3.4. Mechanical calculation -- 8.3.5. Principal results and comparisons with in situ measurements -- 8.4. Conclusion -- Chapter 9. Exercises and Supplements -- 9.1. Determining mechanical characteristics from experimental curves -- 9.2. Mazars model: axisymmetric triaxial loading under compression -- 9.3. Local and non-local damage -- 9.3.1. Example of a concrete bar under direct tension -- 9.3.2. Local model response: impact of the number of elements -- 9.3.3. Non-local damage problem -- 9.3.4. Objective calculation with a local model: Hillerborg method -- 9.3.5. Conclusion -- 9.4. On the ì model -- 9.4.1. Reaching the damage threshold, load-unload criterion -- 9.4.2. On the stress triaxiality factor -- 9.4.3. Response to triaxial axisymmetric compression loading -- 9.5. On the restraint degree R in situations of restrained shrinkage -- 9.6. Solving a simple structure using the PVP* -- 9.6.1. Problem position -- 9.6.2. Using PVP* (assembling the contributions of the elements): preliminary comments for solving -- Appendix: Prerequisites in Solid Mechanics and Finite Element Methods -- References -- Index -- EULA.