Instabilities modeling in geomechanics /
Coordinated by Ioannis Stefanou, Jean Sulem.
- London : Hoboken, NJ : ISTE, Ltd. ; Wiley, 2021.
- 1 online resource (361 p.)
- Mechanics, Geomechanics .
- Mechanics--computational mechanics. Geomechanics. .
4.7. References.
Includes bibliographical references and index.
Cover -- Half-Title Page -- Title Page -- Copyright Page -- Contents -- Introduction -- 1. Multiphysics Role in Instabilities in Geomaterials: a Review -- 1.1. Introduction -- 1.2. General remarks -- 1.3. Solid phase material criteria -- 1.4. Material sample stability: experimental -- 1.5. Boundary value problems: uniqueness and stability at the field scale -- 1.5.1. Landslides -- 1.5.2. Thermal pressurization problem -- 1.5.3. Localization during drying of geomaterials -- 1.6. Conclusion -- 1.7. References -- 2. Fundamentals of Bifurcation Theory and Stability Analysis -- 2.1. Introduction 2.2. Bifurcation and stability of dynamical systems -- 2.2.1. Definition of stability -- 2.2.2. Linear systems of ODEs -- 2.2.3. Nonlinear systems of ODEs -- 2.2.4. An example of LSA -- 2.3. Stability of two-dimensional linear dynamical systems -- 2.3.1. Classification of fixed points -- 2.3.2. Love mechanics: Romeo and Juliet -- 2.4. Commmon types of bifurcations -- 2.4.1. Saddle-node bifurcation -- 2.4.2. Transcritical bifurcation -- 2.4.3. Supercritical and subcritical pitchfork bifurcation -- 2.4.4. From one to two dimensions -- limit cycles 2.4.5. Bifurcations in two dimensions -- supercritical and subcritical Hopf bifurcation -- 2.4.6. Mathematical bifurcations in PDEs -- 2.5. From ODEs to PDEs -- 2.5.1. Deformation bands and the acoustic tensor -- 2.5.2. Deformation bands as an instability problem -- 2.6. Summary -- 2.7. Appendix -- 2.8. References -- 3. Material Instability and Strain Localization Analysis -- 3.1. Introduction -- 3.2. Shear band model -- 3.2.1. Strain localization criterion -- 3.2.2. Strain localization, loss of ellipticity and vanishing speed of acceleration waves 3.3. Shear band formation in element tests on rocks -- 3.3.1. Drucker-Prager model -- 3.3.2. Non-coaxial plasticity -- 3.3.3. Cataclastic shear banding -- 3.3.4. Postlocalization behavior -- 3.4. Strain localization in fluid-saturated porous media -- 3.4.1. Strain localization criterion in fluid-saturated porous media -- 3.4.2. Stability analysis of undrained shear on a saturated layer -- 3.5. Conclusion -- 3.6. References -- 4. Experimental Investigation of the Emergence of Strain Localization in Geomaterials -- 4.1. Introduction -- 4.2. Methods -- 4.2.1. Digital image correlation 4.2.2. X-ray computed tomography -- 4.2.3. Experimental devices for in situ full-field measurements -- 4.3. Selected materials -- 4.3.1. Hostun sand -- 4.3.2. Caicos ooids sand -- 4.3.3. Vosges sandstone -- 4.3.4. Callovo-Oxfordian clayey rock -- 4.4. Strain localization in sands -- 4.4.1. Plane strain compression by FRS -- 4.4.2. Triaxial compression by X-ray CT and DIC -- 4.4.3. Triaxial compression by X-ray CT, the critical void ratio -- 4.5. Strain localization in porous rocks -- 4.5.1. Strain localization in Vosges sandstone -- 4.5.2. Strain localization in a clayey rock -- 4.6. Conclusion