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Engineering Damage Mechanics: Jean Lemaitre, Rodrigue Desmorat

Engineering Damage Mechanics:
Ductile, Creep, Fatigue and Brittle Failures
With 135 Figures

Jean Lemaitre, Rodrigue Desmorat

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Content:

1 Background on Continuum Damage Mechanics
1.1 Physics and Damage Variables
1.1.1 Definition of a Scalar Damage Variable
1.1.2 Definition of Several Scalar Damage Variables
1.1.3 Definition of a Tensorial Damage Variable
1.1.4 Effective Stress Concept
1.1.5 Effects of Damage
1.2 Thermodynamics of Damage
1.2.1 General Framework
1.2.2 State Potential for Isotropic Damage
1.2.3 State Potential for Anisotropic Damage
1.2.4 Quasi-Unilateral Conditions of Microdefects Closure
1.3 Measurement of Damage
1.3.1 Isotropic Elasticity Change
1.3.2 Isotropic Elasticity Change by Ultrasonic Waves
1.3.3 Anisotropic Elasticity Change
1.3.4 Hardness Change
1.3.5 Elasticity Field Change
1.4 Kinetic Laws of Damage Evolution
1.4.1 Damage Threshold and Mesocrack Initiation
1.4.2 Formulation of the Isotropic Unified Damage Law
1.4.3 Formulation of the Anisotropic Damage Law
1.4.4 Fast Identification of Damage Material Parameters
1.4.5 Generalization of the Unified Damage Law
1.5 Elasto-(Visco-)Plasticity Coupled with Damage
1.5.1 Basic Equations without Damage Coupling
1.5.2 Coupling with Isotropic Damage
1.5.3 Coupling with Anisotropic Damage
1.5.4 Non-Isothermal Behavior
1.5.5 Two-Scale Model for Damage at Microscale
1.6 Localization and Mesocrack Initiation
1.6.1 Critical Damage Criterion
1.6.2 Strain Damage Localization Criterion
1.6.3 Size and Orientation of the Crack Initiated
2 Numerical Analysis of Damage
2.1 Uncoupled Analysis
2.1.1 Uniaxial Loading
2.1.2 Proportional Loading
2.1.3 Post-processing a (Visco-)Plastic Computation
2.1.4 Post-processing an Elastic Computation
2.1.5 Jump-in-Cycles Procedure in Fatigue
2.2 Fully-Coupled Analysis
2.2.1 Nonlinear Material Behavior FEA
2.2.2 FE Resolution of the Global Equilibrium
2.2.3 Local Integration Subroutines
2.2.4 Single Implicit Algorithm for Damage Models
2.2.5 Damage Models with Microdefects Closure Effect
2.2.6 Performing FE Damage Computations
2.2.7 Localization Limiters
2.3 Locally-Coupled Analysis
2.3.1 Post-Processing a Reference Structure Calculation
2.3.2 Implicit Scheme for the Two-Scale Model
2.3.3 DAMAGE 2000 Post-Processor
2.4 Precise Identification of Material Parameters
2.4.1 Formulation of an Identification Problem
2.4.2 Minimization Algorithm for Least Squares Problems
2.4.3 Procedure for Numerical Identification
2.4.4 Cross Identification of Damage Evolution Laws
2.4.5 Validation Procedure
2.4.6 Sensitivity Analysis
2.5 Hierarchic Approach and Model Updating
2.6 Table of Material Damage Parameters
3 Ductile Failures
3.1 Engineering Considerations
3.2 Fast Calculation of Structural Failures
3.2.1 Uniaxial Behavior and Validation of the Damage Law
3.2.2 Case of Proportional Loading
3.2.3 Sensitivity Analysis
3.2.4 Stress Concentration and the Neuber Method
3.2.5 Safety Margin and Crack Arrest
3.3 Basic Engineering Examples
3.3.1 Plates or Members with Holes or Notches
3.3.2 Pressurized Shallow Cylinders
3.3.3 Post-Buckling in Bending
3.3.4 Damage Criteria in Proportional Loading
3.4 Numerical Failure Analysis
3.4.1 Finite Strains
3.4.2 Deep Drawing Limits
3.4.3 Damage in Cold Extrusion Process
3.4.4 Crack Initiation Direction
3.4.5 Porous Materials – the Gurson Model
3.4.6 Frames Analysis by Lumped Damage Mechanics
3.4.7 Predeformed and Predamaged Initial Conditions
3.4.8 Hierarchic Approach up to Full Anisotropy
4 LowCycleFatigue
4.1 Engineering Considerations
4.2 Fast Calculation of Structural Failures
4.2.1 Uniaxial Behavior and Validation of the Damage Law
4.2.2 Case of Proportional Loading
4.2.3 Sensitivity Analysis
4.2.4 Cyclic Elasto-Plastic Stress Concentration
4.2.5 Safety Margin and Crack Growth
4.3 Basic Engineering Examples
4.3.1 Plate or Members with Holes or Notches
4.3.2 Pressurized Shallow Cylinders
4.3.3 Cyclic Bending of Beams
4.4 Numerical Failure Analysis
4.4.1 Effects of Loading History
4.4.2 Multiaxial and Multilevel Fatigue Loadings
4.4.3 Damage and Fatigue of Elastomers
4.4.4 Predeformed and Predamaged Initial Conditions
4.4.5 Hierarchic Approach up to Non-Proportional Effects
5 Creep, Creep-Fatigue, and Dynamic Failures
5.1 Engineering Considerations
5.2 Fast Calculation of Structural Failures
5.2.1 Uniaxial Behavior and Validation of the Damage Law
5.2.2 Case of Proportional Loading
5.2.3 Sensitivity Analysis
5.2.4 Elasto-Visco-Plastic Stress Concentration
5.2.5 Safety Margin and Crack Growth
5.3 Basic Engineering Examples
5.3.1 Strain Rate and Temperature-Dependent Yield Stress
5.3.2 Plates or Members with Holes or Notches
5.3.3 Pressurized Shallow Cylinder
5.3.4 Adiabatic Dynamics Post-Buckling in Bending
5.4 Numerical Failure Analysis
5.4.1 Hollow Sphere under External Pressure
5.4.2 Effect of Loading History: Creep-Fatigue
5.4.3 Creep-Fatigue and Thermomechanical Loadings
5.4.4 Dynamic Analysis of Crash Problems
5.4.5 Ballistic Impact and Penetration of Projectiles
5.4.6 Predeformed and Predamaged Initial Conditions
5.4.7 Hierarchic Approach up to Viscous Elastomers
6 High Cycle Fatigue
6.1 Engineering Considerations
6.2 Fast Calculation of Structural Failures
6.2.1 Characteristic Effects in High-Cycle Fatigue
6.2.2 Fatigue Limit Criteria
6.2.3 Two-Scale Damage Model in Proportional Loading
6.2.4 Sensitivity Analysis
6.2.5 Safety Margin and Crack Growth
6.3 Basic Engineering Examples
6.3.1 Plates or Members with Holes or Notches
6.3.2 Pressurized Shallow Cylinders
6.3.3 Bending of Beams
6.3.4 Random Loadings
6.4 Numerical Failure Analysis
6.4.1 Effects of Loading History
6.4.2 Non-Proportional Loading of a Thinned Shell
6.4.3 Random Distribution of Initial Defects
6.4.4 Stochastic Resolution by Monte Carlo Method
6.4.5 Predeformed and Predamaged Initial Conditions
6.4.6 Hierarchic Approaches up to Surface and Gradient Effects
7 Failure of Brittle and Quasi-Brittle Materials
7.1 Engineering Considerations
7.2 Fast Calculations of Structural Failures
7.2.1 Damage Equivalent Stress Criterion
7.2.2 Interface Debonding Criterion
7.2.3 The Weibull Model
7.2.4 Two-Scale Damage Model for Quasi-Brittle Failures
7.2.5 Sensitivity Analysis
7.2.6 Safety Margin and Crack Propagation
7.3 Basic Engineering Examples
7.3.1 Plates or Members with Holes and Notches
7.3.2 Pressurized Shallow Cylinders
7.3.3 Fracture of Beams in Bending
7.4 Numerical Failure Analysis
7.4.1 Quasi-Brittle Damage Models
7.4.2 Failure of Pre-stressed Concrete 3D Structures
7.4.3 Seismic Response of Reinforced Concrete Structures
7.4.4 Damage and Delamination in Laminate Structures
7.4.5 Failure of CMC Structures
7.4.6 Single and Multifragmentation of Brittle Materials
7.4.7 Hierarchic Approach up to Homogenized Behavior

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