Energy based damage criterion

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Table of contents

Table of contents
Introduction
1 Context and motivation
1.1 Experimental characterization of damage spreading and quasi-brittle failure
1.1.1 At the specimen scale: Average mechanical response of quasi-brittle materials
1.1.2 At the scale of damage and microstructure: Temporal and spatial organization of precursors to failure
1.1.3 Conclusions
1.2 Damage models
1.2.1 At the continuum scale: Damage mechanics
1.2.2 At the microstructure scale: Statistical models of quasi-brittle fracture
1.2.3 Our approach: A mesoscopic description of damage spreading in heterogeneous media
1.3 Conclusions
2 Model formulation and limit cases analysis
2.1 Non-local damage model description of a heterogeneous material
2.1.1 Energy based damage criterion
2.1.2 Material parameters
2.1.3 Interaction function
2.1.4 Numerical integration
2.2 On the relevance of the combination of interactions and disorder
2.2.1 Interacting homogeneous system response
2.2.2 Non-interacting heterogeneous system response
2.3 Conclusions
3 Damage localization and failure predictions of the quasi-brittle material
3.1 Failure behavior of the heterogeneous system: numerical observations
3.1.1 Macroscopic response
3.1.2 Deviation from the homogeneous system response and failure damage thresholds
3.1.3 Damage field spatial organization
3.1.4 Conclusions
3.2 Critical loadings prediction: linear stability analysis
3.2.1 Stability analysis of the homogeneous damage states
3.2.2 Application to 1D media
3.2.3 Application to 2D media
3.3 Critical damage at failure: global energy minimization
3.3.1 Before localization: Prediction of the homogeneous material evolution and its loss of stability
3.3.2 After localization: Failure prediction
3.4 Conclusions
4 Damage spreading toward failure: Statistics of fluctuations
4.1 Statistics of fluctuations in damage models with positive load redistributions ( = 0)
4.1.1 Avalanche definition
4.1.2 Temporal behavior: avalanche size evolution
4.1.3 Spatial structure of the avalanches
4.1.4 Spatial organization of the cumulated damage field
4.2 Statistics of fluctuations in damage models with finite wavelength at localization (> c)
4.3 Theoretical analysis of the damage growth fluctuations: A disordered elastic interface analogy
4.3.1 Analogy between damage growth and driven disordered elastic interface
4.3.2 Linearized evolution equation for the damage growth
4.3.3 Exponents prediction
4.4 Conclusions
5 Comparison with experiments: Compression of a 2D array of hollow soft cylinders
5.1 Experimental setup
5.2 Mechanical behavior
5.2.1 Macroscopic Force-Displacement response
5.2.2 Intermittent dynamics of the compaction process: Avalanches definitions
5.3 Characterization and prediction of localization
5.3.1 Determination of the localization threshold from the deformation field
5.3.2 Analytical investigation of localization
5.4 Temporal fluctuations study
5.5 Conclusions
Conclusions
Bibliography