Multiscale modeling of heterogenous materials : from microstructure to macro-scale properties

Foreword. Chapter 1. Accounting for Plastic Strain Heterogenities in Modeling Polycrystalline Plasticity: Microstructure-based Multi-laminate Approaches ( Patrick FRANCIOSI ). 1.1. Introduction.1 1.2. Polycrystal morphology in terms of grain and sub-grain boundaries. .1.3. Sub-boundaries and multi-laminate structure for heterogenous plasticity. 1.4. Application to polycrystal plasticity within the affine approximation. 1.5. Conclusion. 1.6. Bibliography. Chapter 2. Discrete Dislocation Dynamics: Principles and Recent Applications ( Marc FIVEL ). 2.1. Discrete Dislocation Dynamics as a link in multiscale modeling. 2.2. Principle of Discrete Dislocation Dynamics. 2.3. Example of scale transition: from DD to Continuum Mechanics. 2.4. Example of DD analysis: simulations of crack initiation in fatigue. 2.5. Conclusions. 2.6. Bibliography. Chapter 3. Multiscale Modeling of Large Strain Phenomena in Polycrystalline Metals ( Kaan INAL and Raj. K. MISHRA ). 3.1. Implementation of polycrystal plasticity in finite element analysis. 3.2. Kinematics and constitutive framework. 3.3. Forward Euler algorithm. 3.4. Validation of the forward Euler algorithm. 3.5. Time step issues in the forward Euler scheme. 3.6. Comparisons of CPU times: the rate tangent versus the forward Euler methods. 3.7. Conclusions. 3.8. Acknowledgements. 3.9. Bibliography. Chapter 4. Earth Mantle Rheology Inferred from Homogenization Theories ( Olivier CASTELNAU, Ricardo LEBENSOHN, Pedro Ponte CASTANEDA and Donna BLACKMAN ). 4.1. Introduction. 4.2. Grain local behavior. 4.3. Full-field reference solutions. 4.4. Mean-field estimates. 4.5. Concluding observations. 4.6. Bibliography. Chapter 5. Modeling Plastic Anistropy and Strength Differential Effects in Metallic Materials ( Oana CAZACU and Frederic BARLAT ). 5.1. Introduction. 5.2. Isotropic yield criteria. 5.3. Anisotropic yield criteria with SD effects. 5.4. Modeling anisotropic hardening due to texture evolution. 5.5. Conclusions and future perspectives. 5.6. Bibliography. Chapter 6. Shear Bands in Steel Plates under Impact Loading ( George Z. VOYIADJIS and Amin H. ALMASRI ). 6.1. Introduction. 6.2. Viscoplasticity and constitutive modeling. 6.3. Higher order gradient theory. 6.4. Two-dimensional plate subjected to velocity boundary conditions. 6.5. Shear band in steel plate punch. 6.6. Conclusions. 6.7. Bibliography. Chapter 7. Viscoplastic Modeling of Anisotropic Textured Metals ( Brian PLUNKETT and Oana CAZACU ). 7.1. Introduction. 7.2. Anisotropic elastoviscoplastic model. 7.3. Application to zirconium. 7.4. High strain-rate deformation of tantalum. 7.5. Conclusions. 7.6. Bibliography. Chapter 8. Non-linear Elastic Inhomogenous Materials: Uniform Strain Fields and Exact Relations ( Qi-Chang HE, B. BARY and Hung LE QUANG ). 8.1. Introduction. 8.2. Locally uniform strain fields. 8.3. Exact relations for the effective elastic tangent moduli. 8.4. Cubic polycrystals. 8.5. Power-law fibrous composites. 8.6. Conclusion. 8.7. Bibliography. Chapter 9. 3D Continuous and Discrete Modeling of Bifurcations in Geomaterials ( Florent PRUNIER, Felix DARVE, Luc SIBILLE and Francois NICOT ). 9.1. Introduction. 9.2. 3D bifurcations exhibited by an incrementally non-linear constitutive relation. 9.3. Discrete modeling of the failure mode related to second-order work criterion. 9.4. Conclusions. 9.5. Acknowledgements. 9.6. Bibliography. Chapter 10. Non-linear Micro-cracked Geomaterials: Anisotropic Damage and Coupling with Plasticity ( Djimedo KONDO, Qizhi ZHU, Vincent MONCHIET and Jian-Fu SHAO ). 10.1. Introduction. 10.2. Anisotropic elastic damage model with unilateral effects. 10.3. A new model for ductile micro-cracked materials. 10.4. Conclusions. 10.5. Acknowledgement. 10.6. Appendix. 10.7. Bibliography. Chapter 11. Bifurcation in Granular Materials: A Multiscale Approach ( Francois NICOT, Luc SIBILLE and Felix DARVE ). 11.1. Introduction. 11.2. Microstructural origin of the vanishing of the second-order work. 11.3. Some remarks on the basic micro-macro relation for the second-order work. 11.4. Conclusion. 11.5. Bibliography. Chapter 12. Direct Scale Transition Approach for Highly-filled Viscohyperelastic Particulate Composites: Computational Study ( Carole NADOT-MARTIN, Marion TOUBOUL, Andre DRAGON and Alain FANGET ). 12.1. Morphological approach in the finite strain framework. 12.2. Evaluation involving FEM/MA confrontations. 12.3. Conclusions and prospects. 12.4. Bibliography. Chapter 13. A Modified Incremental Homogenization Approach for Non-linear Behaviors of Heterogenous Cohesive Geomaterials ( Ariane ABOU-CHAKRA GUERY, Fabrice CORMERY, Jian-Fu SHAO and Djimedo KONDO ). 13.1. Introduction. 13.2. Experimental observations on the Callovo-Oxfordian argillite behavior. 13.3. Incremental formulation of the homogenized constitutive relation. 13.4. Modifying of the local constituents'behaviors. 13.5. Implementation and numerical validation of the model. 13.6. Calibration and experimental validations of the modified incremental micromechanical model. 13.7. Conclusions. 13.8. Acknowledgement. 13.9. Bibliography. Chapter 14. Meso- to Macro-scale Probability Aspects for Size Effects and Heterogenous Materials Failure ( Jean-Baptiste COLLIAT, Martin HAUTEFEUILLE and Adnan IBRAHIMBEGOVIC ). 14.1. Introduction. 14.2. Meso-scale deterministic model. 14.3. Probability aspects of inelastic localized failure for heterogenous materials. 14.4. Results of the probabilistic characterization of the two phase material. 14.5. Size effect modeling. 14.6. Conclusion. 14.7. Acknowledgments. 14.8. Bibliography. Chapter 15. Damage and Permeability in Quasi-brittle Materials: from Diffuse to Localized Properties ( Gilles PIJAUDIER-CABOT, Frederic DUFOUR and Marta CHOINSKA ). 15.1. Introduction. 15.2. Mechanical problem - continuum damage modeling. 15.3. Permeability matching law. 15.4. Calculation of a crack opening in continuum damage calculations. 15.5. Structural simulations. 15.6. Conclusions. 15.7. Acknowledgement. 15.8. Bibliography. Chapter 16. A Multiscale Modeling of Granular Materials with Surface Energy Forces ( Pierre-Yves HICHER and Ching S. CHANG ). 16.1. Introduction. 16.2. Stress-strain model. 16.3. Results of numerical simulation without surface energy forces consideration. 16.4. Granular material with surface energy forces: the example of lunar soil. 16.5. Summary and conclusion. 16.6. Bibliography. Chapter 17. Length Scales in Mechanics of Granular Solids ( Farhang RADJAI ). 17.1. Introduction. 17.2. Model description. 17.3. Force chains. 17.4. Fluctuating particle displacements. 17.5. Friction mobilization. 17.6. Conclusion. 17.7. Acknowledgements. 17.8. Bibliography. List of Authors. Index.