Desiccation Cracks and Their Patterns : Formation and Modelling in Science and Nature.
- 1st ed.
- 1 online resource (370 pages)
- Statistical Physics of Fracture and Breakdown Series .
- Statistical Physics of Fracture and Breakdown Series .
Cover -- Contents -- Preface -- List of Symbols -- Chapter 1 Introduction -- 1.1 Why Study Drying Mud? -- 1.2 Objectives and Organization of the Book -- 1.3 Approach and Scope -- References -- Chapter 2 Elasticity -- 2.1 On Springs -- 2.2 Deformation, Displacement and Strain -- 2.3 Transformations of Strains, Principal Strains and Volumetric Strain -- 2.4 Stress -- 2.5 Thermodynamics and the Work of Deformation -- 2.6 Linear Elasticity -- 2.7 Different Formulations of Linear Elasticity -- 2.8 Plane Elasticity -- 2.8.1 Plane Strain and Plane Stress -- 2.8.2 Airy Stress Function -- 2.9 Summary -- 2.10 Further Reading -- References -- Chapter 3 Fracture Mechanics -- 3.1 Griffith and Fracture Energy -- 3.2 Stress Concentration -- 3.3 Stress Intensity Factors -- 3.4 Fracture Toughness and the Relationship Between K and G -- 3.5 Summary of the Critical Conditions for Fracture -- 3.6 An Example: Thin-Film Fracture -- 3.7 Nonlinear and Dissipative Effects of Fracture -- 3.7.1 A Plastic Zone Model of Fracture -- 3.7.2 A Mesoscopic View - The Path-Independent J-integral -- 3.7.3 Dynamic Elasticity and Dynamic Fracture -- 3.8 Crack Path Selection -- 3.9 Summary and Further Reading -- References -- Chapter 4 Poroelasticity -- 4.1 Pressure and Stress in a Two-component System -- 4.1.1 Fick's Laws -- 4.1.2 Darcy's Law -- 4.1.3 Network and Total Stress -- 4.2 Linear Poroelasticity -- 4.2.1 Poroelastic Energy Density -- 4.2.2 Poroelastic Constitutive Relations -- 4.2.3 Different Formulations of Poroelasticity -- 4.3 Relationship Between Poroelasticity and Thermoelasticity -- 4.4 Worked Examples of Poroelastic Deformation -- 4.5 Poroelasticity and a Driving Force for Fracture -- 4.6 Summary and Further Reading -- References -- Chapter 5 Colloids and Clays -- 5.1 DLVO Theory -- 5.1.1 van der Waals Potential -- 5.1.2 Electrostatic Potential. 5.1.3 DLVO Theory and its Limitations -- 5.2 Clays -- 5.3 Summary and Further Reading -- References -- Chapter 6 Desiccation -- 6.1 Surface Tension and Capillary Pressure -- 6.1.1 Contact Lines and Capillary Rise -- 6.2 Solidification Through Evaporation -- 6.2.1 Skin Formation -- 6.2.2 Crystals and Cages -- 6.2.3 Aggregation -- 6.3 Pore-Scale Processes -- 6.3.1 Structure of a Drying Soil -- 6.3.2 Dynamics of a Drying Soil -- 6.4 Continuum Models of Drying -- 6.4.1 Surface Drying -- 6.4.2 Internal Transport: Carman-Kozeny -- 6.5 Further Reading -- References -- Chapter 7 Patterns of Crack Networks in Homogeneous Media -- 7.1 Introduction -- 7.2 Experimental Observations -- 7.2.1 Sequential Fragmentation and Length Scale Selection -- 7.2.2 Scaling of Crack Width -- 7.2.3 Distribution of Angles Between Cracks -- 7.3 Directional Drying -- 7.4 Characterizing the Crack Pattern: 2D View -- 7.4.1 Scale Invariance in Crack Patterns: Self-Similar and Self-Affine Structures -- 7.4.1.1 Scale Invariant Crack Width Distribution -- 7.4.1.2 Fractal Dimension of the Crack Edge -- 7.4.1.3 Self-Affinity of the Fracture Surface -- 7.4.1.4 Fractal Fracture Mechanics -- 7.4.2 Topology and Connectivity of the Crack Network -- 7.4.2.1 Minkowski Numbers and Densities -- 7.4.2.2 Network Theory Approach: Mapping onto an Equivalent Network -- 7.4.3 Percolation -- 7.5 Instabilities: Spirals and Wavy Cracks, En Echelon/En Passant Cracks, Star Cracks, and Wing Cracks -- 7.5.1 En Echelon Cracks -- 7.5.2 En Passant Cracks -- 7.5.3 Spiral Cracks -- 7.5.4 Wavy Cracks -- 7.5.5 Star Bursts and More Patterns -- 7.6 Crack Dynamics and Branching Cracks -- 7.7 Transition Between Different Modes of Instability and Fracture -- 7.7.1 Dendrite to Fracture -- 7.7.2 Viscous Fingering to Fracture -- 7.7.3 Invasion Percolation to Fracture. 7.8 Towards Three Dimensions: Geological Formations, Drying Soil and Peeling -- 7.8.1 Obreimoff's Experiment -- 7.8.2 Natural Mud Cracks in Quasi-2D -- 7.9 Simulation of Quasi-2D Patterns -- 7.9.1 2D Modelling of Fracture: The Fibre Bundle Model -- 7.9.2 Random Fuse Model -- 7.9.3 Spring Network Model -- 7.9.4 Other Models -- 7.10 Summary -- 7.11 Further Reading -- References -- Chapter 8 The Effects of Plasticity on Crack Formation -- 8.1 Introduction to Rheology -- 8.1.1 Elastic Material and Fluid -- 8.1.2 Linear Viscoelasticity -- 8.1.3 Bingham Model -- 8.2 Elastoplasticity for Slow Deformation Processes -- 8.2.1 Decomposition of Elastic and Plastic Deformation -- 8.2.2 Thermodynamics of Elastoplasticity -- 8.2.3 Yield Conditions and the Normality Law -- 8.2.4 Yield Conditions of Paste-Like Materials -- 8.3 Crack Propagation in a Layer of Wet Paste -- 8.3.1 Plumose Structure in Crack Surfaces -- 8.3.2 Microscopic Observation of Plastic Deformation -- 8.3.3 Measurements of the Speed of Crack Growth in a Uniform Paste Layer -- 8.4 Theoretical Approaches for Crack Velocities -- 8.4.1 Viscoelastic Effect on Crack Propagation: 1D Lattice Model of Rheological Elements -- 8.4.2 Competition of Global Plastic Relaxation and Crack Growth -- 8.5 Memory Effect of Paste Due to Its Plasticity -- 8.5.1 Memory of Vibration and Its Visualization as Desiccation Crack Pattern -- 8.5.1.1 Memory of Vibration and Lamellar Crack Pattern -- 8.5.1.2 Plasticity of Paste -- 8.5.1.3 Condition for the Memory Effect of Vibration: Experimental Results -- 8.5.2 Residual Tension Theory to Explain Memory Effect of Vibration -- 8.5.2.1 Quasi-linear Analysis -- 8.5.2.2 Governing Equations for Non-linear Analysis -- 8.5.2.3 Non-linear Analysis -- 8.5.2.4 Condition for the Memory Effect of Vibration: Theoretical Explanation. 8.5.3 Position Control of Cracks by Memory Effect and Faraday Waves -- 8.5.4 Memory of Flow and a Role of Interaction Between Colloidal Particles -- Further Reading -- References -- Chapter 9 Special Topics -- 9.1 Tailoring Crack Patterns -- 9.1.1 Effect of Electric Fields on Desiccation Cracks -- 9.1.1.1 Effects of a Direct Field (DC) -- 9.1.1.2 Effect of an Alternating Field (AC) -- 9.1.1.3 DC Field Effect in Drying Droplets -- 9.1.2 Effect of a Magnetic Field on Desiccation Cracks -- 9.1.3 Patterning Cracks Through Micro-Technology -- 9.2 Designing Crack-Resistant Materials and Composites -- 9.2.1 Composites of Soft and Hard Particles -- 9.2.1.1 Employing Heterogeneous Material -- 9.2.2 Crack Reduction with 'Liquid Particles' -- 9.3 Crack Patterns in Drying Droplets of Biofluids -- 9.3.1 Human Blood Droplets and Drying Dynamics -- 9.3.2 Effect of Relative Humidity on Drying Droplets -- 9.3.3 Substrate Effect on Drying Droplets of Blood -- 9.4 Evolving Crack Networks -- 9.4.1 Columnar Joints -- 9.4.2 Evolving Mud Cracks -- 9.4.3 Other Crack Patterns -- 9.5 Further Reading -- References -- Appendix A: A Primer on Vectors and Tensors -- A.1 Tensor Notation -- A.2 Tensor Multiplication -- A.3 Tensor Transformations -- A.4 Tensor Differentiation -- Appendix B: Fractals: Self-Similar and Self-Affine Systems -- B.1 Self-Similarity and Fractal Dimension -- B.2 Self-Affine Systems -- B.3 Further Reading -- References -- Appendix C: Formulation of Elastoplasticity Based on Dissipation Functions -- References -- Appendix D: Steady Propagating Solution of Langer Model -- Appendix E: Stress Expression in Finite Deformation Theory -- References -- Index -- EULA.