Nonlinear Elasticity and Hysteresis

The book provides the reader with the knowledge, tools, and methods to understand the phenomenon of hysteresis in porous materials.

As many challenges have been met only recently, the book summarizes the research results usually found only scattered in the literature, connecting knowledge from traditionally separated research fields to provide a better understanding of the physical phenomena of coupled elastic-fluid systems.

The result is an invaluable self-contained reference book for materials scientists, civil, mechanical and construction engineers concerned with development and maintenance of structures made of porous materials.

Preface XI

List of Contributors XV

1 Dynamic Pressure and Temperature Responses of Porous Sedimentary Rocks by Simultaneous Resonant Ultrasound Spectroscopy and Neutron Time-of-Flight Measurements 1
James A. TenCate, Timothy W. Darling, and Sven C. Vogel

1.1 Introduction and Background 1

1.2 Macroscopic Measurements 3

1.2.1 Stress-Strain Measurements 3

1.2.2 Temperature Variations 4

1.2.3 Moisture Content Variations 5

1.2.4 Vibrational Excitation Variations 6

1.3 Motivation for Neutron Scattering Measurements 7

1.4 SMARTS: Simultaneous Stress–Strain and Neutron Diffraction Measurements 9

1.5 HIPPO: Simultaneous Step-Temperature Modulus/Sound Speed and Neutron Diffraction Measurements 12

1.5.1 Sample 13

1.5.2 Sample Cell 14

1.5.3 Procedure 15

1.5.4 Results 16

1.5.5 Comparison/Reference Measurements 19

1.6 Discussion and Conclusions 21

Acknowledgments 23

References 23

2 Adsorption, Cavitation, and Elasticity in Mesoporous Materials 27
Annie Grosman and Camille Ortega

2.1 Experimental Evidence of Collective Effects During Evaporation 28

2.1.1 Porous Vycor Glass 28

2.1.2 Porous Silicon 30

2.1.3 SBA-15 Silica 31

2.2 Adsorption-Induced Strain 33

2.3 Thermodynamics of the Solid–Fluid Interface 34

2.3.1 The Solid–Vapor Interface 37

2.3.2 The Solid–Liquid Interface 40

2.4 Stress Effect on the Adsorption Process 43

2.4.1 Supported and Free Standing Porous Si Layers 43

2.4.2 Monitoring of the External Stress 45

2.5 Cavitation in Metastable Fluids Confined to Linear Mesopores 47

2.5.1 The Elemental Isotherms 47

2.5.2 Si/A/B and Si/B/A Configurations 48

2.5.2.1 Si/A/B Configuration 49

2.5.2.2 Si/B/A Configuration 50

2.5.3 Nature of the Nucleation Process 51

2.5.3.1 Homogeneous Nucleation 51

2.5.3.2 Heterogeneous Nucleation and Elastic Strain 52

References 55

3 Theoretical Modeling of Fluid–Solid Coupling in Porous Materials 57
Robert Alan Guyer and Hyunsun Alicia Kim

3.1 Introduction 57

3.2 Systems and Models 57

3.3 Problems 60

3.3.1 Systems of Interest 62

3.3.2 Quantities of Interest 62

3.4 Mechanical Response to Applied External Forces 63

3.5 Fluid in the Skeleton 66

3.6 Fluid in the Pore Space 73

3.7 Summary and Conclusion 76

References 79

4 Influence of Damage and Moisture on the Nonlinear Hysteretic Behavior of Quasi-Brittle Materials 81
Jan Carmeliet

4.1 Nonlinear, Hysteretic, and Damage Behavior of Quasi-Brittle Materials 81

4.2 Macroscopic Damage Model for Quasi-Brittle Materials 85

4.3 Preisach-Mayergoyz (PM) Model for Nonlinear Hysteretic Elastic Behavior 88

4.4 Coupling the Macroscopic Damage Model and Damage-Dependent PM Model: Algorithmic Aspects 93

4.5 Moisture Dependence of Hysteretic and Damage Behavior of Quasi-Brittle Materials 94

4.5.1 Moisture-Dependent Mechanical Experiments 96

4.5.2 Moisture-Dependent Damage and PM Model 99

Acknowledgment 102

References 102

5 Modeling the Poromechanical Behavior of Microporous and Mesoporous Solids: Application to Coal 105
Matthieu Vandamme, Patrick Dangla, Saeid Nikoosokhan, and Laurent Brochard

5.1 Modeling of Saturated Porous Media 107

5.1.1 Macroporous Media 108

5.1.2 Generic (and Potentially Microporous) Media 110

5.1.3 Mesoporous Media 112

5.2 Application to Coal Seams 114

5.2.1 Modeling of a Representative Elementary Volume of a Coal Seam 116

5.2.2 A Source of Hysteresis: The Kinetics of Transfer Between Cleats and Coal Matrix 119

5.2.3 Simulating an Injection of Carbon dioxide in a Coal Seam 122

5.3 Conclusions and Perspectives 124

References 125

6 A Theoretical Approach to the Coupled Fluid–Solid Physical Response of Porous and Cellular Materials: Dynamics 127
Mark W. Schraad

6.1 Introduction 127

6.1.1 Traditional Modeling Approaches 128

6.1.2 A Unifying Theoretical Approach 130

6.2 Theoretical Approach 131

6.2.1 Single-Field Equations and the Ensemble Averaging Process 133

6.2.2 Multifield Equations 134

6.3 Closure Models 135

6.3.1 Reynold’s Stress and Body Forces 136

6.3.2 Material Stress Gradients 136

6.3.2.1 Momentum Exchange 137

6.3.2.2 Fluid-Field and Solid-Field Stresses 138

6.3.2.3 Solid Matrix Constitutive Models 139

6.4 Demonstration Simulations 139

6.5 Concluding Remarks 149

References 150

7 Swelling ofWood Tissue: Interactions at the Cellular Scale 153
Dominique Derome, Jan Carmeliet, Ahmad Rafsanjani, Alessandra Patera, and Robert Alan Guyer

7.1 Introduction 153

7.2 Description of Wood 154

7.3 Absorption of Moisture in Wood 155

7.4 Swelling of Wood Tissue – Investigations by Phase Contrast Synchrotron X-Ray Tomographic Microscopy 156

7.4.1 Behavior of Homogeneous Tissues 158

7.5 Parametric Investigation of Swelling of Honeycombs – Investigation by Hygroelastic Modeling 161

7.5.1 Simulation Methodology 162

7.5.2 Layered Cell Wall 163

7.5.3 Effects of Geometric Variations 165

7.6 Beyond Recoverable Swelling and Shrinkage: Moisture-Induced Shape Memory 167

7.7 Discussion 168

7.7.1 On the Origin of Hysteresis of Sorption as a Function of Relative Humidity 168

7.7.2 On the Effects on Moisture Sorption 168

Acknowledgment 169

References 169

8 Hydro-Actuated Plant Devices 171
Khashayar Razghandi, Sebastien Turcaud, and Ingo Burgert

8.1 Introduction 171

8.2 General Aspects of Plant Material–Water Interactions 173

8.2.1 Principle Mechanics: Stress and Strain 173

8.2.2 Water as an Engine 174

8.2.2.1 Inflation 174

8.2.2.2 Swelling 176

8.2.3 Plant Cell Walls 177

8.2.4 Cell Wall–Water Interaction 179

8.2.4.1 Swelling/Shrinkage of Wood 180

8.2.5 Principles of Anisotropic Deformation 181

8.3 Systems Based on Inner Cell Pressure – Living Turgorized Cells 182

8.3.1 Cell Growth – Turgor: Plastic Deformation of the Cell Wall 182

8.3.2 Movement via Elastic Deformation of the Cell Wall 182

8.3.2.1 Stomatal Movement 183

8.3.2.2 Venus Flytrap: A Turgor-Based Rapid Movement 184

8.4 Systems Based on Water Uptake of Cell Walls 185

8.4.1 Bilayered Structures for Bending 185

8.4.1.1 Passive Hydro-Actuation in Pine Cones 186

8.4.1.2 Wheat Awns Hydro-Actuated Swimming Movement 187

8.4.2 Bilayered Structures for Twisting Movements 188

8.4.2.1 Curling of Erodium Awns 188

8.5 Systems Based on a Differential Swelling of Cell Wall Layer 190

8.5.1 Tension Wood Fibers 190

8.5.2 Contractile Roots 191

8.5.3 Ice Plant Seed Capsule 192

8.5.3.1 Ice Plant Capsule Opening as a Case Study for the Capacity of Water as a Plant Movement Actuator 194

8.6 Biomimetic Potential 195

Acknowledgments 197

References 197

Index 201

Preface

DYNAMIC PRESSURE AND TEMPERATURE RESPONSES OF POROUS SEDIMENTARY ROCKS BY SIMULTANEOUS RESONANT ULTRASOUND SPECTROSCOPY AND NEUTRON TIME-OF-FLIGHT MEASUREMENTS
Introduction and Background
Macroscopic Measurements
Motivation for Neutron Scattering Measurements
SMARTS: Simultaneous Stress-Strain and Neutron Diffraction Measurements
HIPPO: Simultaneous Step-Temperature Modulus/Sound Speed and Neutron Diffraction Measurements
Discussion and Conclusions

ADSORPTION, CAVITATION, AND ELASTICITY IN MESOPOROUS MATERIALS
Experimental Evidence of Collective Effects During Evaporation
Adsorption-Induced Strain
Thermodynamics of the Solid-Fluid Interface
Stress Effect on the Adsorption Process
Cavitation in Metastable Fluids Confined to Linear Mesopores

THEORETICAL MODELING OF FLUID-SOLID COUPLING IN POROUS MATERIALS
Introduction
Sytems and Models
Problems
Mechanical Response to Applied External Forces
Fluid in the Skeleton
Fluid in the Pore Space
Summary and Conclusion

INFLUENCE OF DAMAGE AND MOISTURE ON THE NONLINEAR HYSTERETIC BEHAVIOR OF QUASI-BRITTLE MATERIALS
Nonlinear, Hysteretic, and Damage Behavior of Quasi-Brittle Materials
Macroscopic Damage Model for Quasi-Brittle Materials
Preisach-Mayergoyz (PM) Model for Nonlinear Hysteretic Elastic Behavior
Coupling the Macroscopic Damage Model and Damage-Dependent PM Model: Algorithmic Aspects
Moisture Dependence of Hysteretic and Damage Behavior of Quasi-Brittle Materials

MODELING THE POROMECHANICAL BEHAVIOR OF MICROPOROUS AND MESOPOROUS SOLIDS: APPLICATION TO COAL
Modeling of Saturated Porous Media
Application to Coal Seams
Conclusions and Perspectives

A THEORETICAL APPROACH TO THE COUPLED FLUID-SOLID PHYSICAL RESPONSE OF POROUS AND CELLULAR MATERIALS: DYNAMICS
Introduction
Theoretical Approach
Closure Models
Demonstration Simulations
Concluding Remarks

SWELLING OF WOOD TISSUE: INTERACTIONS AT THE CELLULAR SCALE
Introduction
Description of Wood
Absorption of Moisture in Wood
Swelling of Wood Tissue -
Investigations by Phase Contrast
Pharametric Investigation of Swelling of Honeycombs -
Investigation by Hydroelastic Modeling
Beyond Recoverable Swelling and Shrinkage: Moisture-Induced Shape Memory
Discussion

HYDRO-ACTUATED PLANT DEVICES
Introduction
General Aspects of Plant Material -
Water Interactions
Systems Based on Inner Cell Pressure -
Living Turgorized Cells
Systems Based on Water Uptake of Cell Walls
Systems Based on a Differential Swelling of Cell Wall Layer
Biomimetic Potential

Index Dr H. Alicia Kim is Senior Lecturer in the Department of Mechanical Engineering, University of Bath, UK and an affiliate at the Earth and Environmental Sciences Division, Los Alamos National Laboratory. She received her PhD degree in Aeronautical Engineering, University of Sydney, Australia in 2001. Her research expertise includes numerical methods of finite element formulation and their applications in nonlinear hysteretic materials and optimisation of aerospace structures. She has authored more than 12 international publications.

Professor Robert Guyer received his PhD degree from Cornell University in 1966. He is the author of more than 200 refereed journal articles. His area of expertise includes transport in disordered systems, quantum crystals, nonlinear elasticity, granular media as well as time reversal methods in geophysics. In addition to his career at the University of Massachusetts (Amherst) he has had appointments at Research Center Julich, Harvard, U of Toronto, U of Florida, Cornell, Los Alamos National Laboratory, and in several industrial research labs.
Even such seemingly different materials like wood and sandstone share similarities: both are porous and exhibit hysteretic behavior upon water uptake and evaporation, i.e., their properties depend not only on the current state of the materials, but on the history of state changes. Both materials are examples for strongly-coupled elastic-fluid systems which are ruled by the interplay between the moisture content and the mechanical stress field. Porous materials which exhibit hysteresis are becoming increasingly important for carbon sequestration, multifunctional materials design and mechanical control of surface catalysis.
The book contains experimental investigations which cover diverse coupled elastic-fluid systems on the micro-meso and on the macro scale. This is complemented by modelling studies to foster the understanding of the experimentally observed phenomena. The book benefits both experimentalists and theoreticians alike and connects knowledge from research areas across traditional discipline boundaries.