Nonlinear Elasticity and Hysteresis E-Book

• Herausgeber: Wiley-VCH
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 370

Veröffentlichungsjahr: 2014

Beschreibung

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.

Leseprobe

Table of Contents

Cover

Related Titles

Title Page

Copyright

Preface

Acknowledgment

List of Contributors

Chapter 1: Dynamic Pressure and Temperature Responses of Porous Sedimentary Rocks by Simultaneous Resonant Ultrasound Spectroscopy and Neutron Time-of-Flight Measurements

1.1 Introduction and Background

1.2 Macroscopic Measurements

1.3 Motivation for Neutron Scattering Measurements

1.4 SMARTS: Simultaneous Stress–Strain and Neutron Diffraction Measurements

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

1.6 Discussion and Conclusions

Acknowledgments

References

Chapter 2: Adsorption, Cavitation, and Elasticity in Mesoporous Materials

2.1 Experimental Evidence of Collective Effects During Evaporation

2.2 Adsorption-Induced Strain

2.3 Thermodynamics of the Solid–Fluid Interface

2.4 Stress Effect on the Adsorption Process

2.5 Cavitation in Metastable Fluids Confined to Linear Mesopores

References

Chapter 3: Theoretical Modeling of Fluid–Solid Couplingin Porous Materials

3.1 Introduction

3.2 Systems and Models

3.3 Problems

3.4 Mechanical Response to Applied External Forces

3.5 Fluid in the Skeleton

3.6 Fluid in the Pore Space

3.7 Summary and Conclusion

References

Chapter 4: Influence of Damage and Moisture on the Nonlinear Hysteretic Behavior of Quasi-Brittle Materials

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

4.2 Macroscopic Damage Model for Quasi-Brittle Materials

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

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

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

Acknowledgment

References

Chapter 5: Modeling the Poromechanical Behavior of Microporousand Mesoporous Solids: Application to Coal

5.1 Modeling of Saturated Porous Media

5.2 Application to Coal Seams

5.3 Conclusions and Perspectives

References

Chapter 6: A Theoretical Approach to the Coupled Fluid–Solid Physical Response of Porous and Cellular Materials: Dynamics

6.1 Introduction

6.2 Theoretical Approach

6.3 Closure Models

6.4 Demonstration Simulations

6.5 Concluding Remarks

References

Chapter 7: Swelling of Wood Tissue: Interactions at the Cellular Scale

7.1 Introduction

7.2 Description of Wood

7.3 Absorption of Moisture in Wood

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

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

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

7.7 Discussion

Acknowledgment

References

Chapter 8: Hydro-Actuated Plant Devices

8.1 Introduction

8.2 General Aspects of Plant Material–Water Interactions

8.3 Systems Based on Inner Cell Pressure – Living Turgorized Cells

8.4 Systems Based on Water Uptake of Cell Walls

8.5 Systems Based on a Differential Swelling of Cell Wall Layer

8.6 Biomimetic Potential

Acknowledgments

References

Index

EULA

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Guide

Cover

Table of Contents

Preface

Chapter 1: Dynamic Pressure and Temperature Responses of Porous Sedimentary Rocks by Simultaneous Resonant Ultrasound Spectroscopy and Neutron Time-of-Flight Measurements

List of Illustrations

Figure 1

Figure 2

Figure 3

Figure 1.1

Figure 1.2

Figure 1.3

Figure 1.4

Figure 1.5

Figure 1.6

Figure 1.7

Figure 1.8

Figure 1.9

Figure 1.10

Figure 1.11

Figure 1.12

Figure 1.13

Figure 1.14

Figure 1.15

Figure 1.16

Figure 2.1

Figure 2.2

Figure 2.3

Figure 2.4

Figure 2.5

Figure 2.20

Figure 2.6

Figure 2.7

Figure 2.8

Figure 2.9

Figure 2.10

Figure 2.11

Figure 2.12

Figure 2.13

Figure 2.14

Figure 2.15

Figure 2.16

Figure 2.17

Figure 2.18

Figure 2.19

Figure 3.1

Figure 3.2

Figure 3.3

Figure 3.4

Figure 3.5

Figure 3.6

Figure 3.7

Figure 3.8

Figure 3.9

Figure 3.10

Figure 3.11

Figure 3.17

Figure 3.11

Figure 3.12

Figure 3.13

Figure 3.14

Figure 3.15

Figure 4.1

Figure 4.2

Figure 4.3

Figure 4.4

Figure 4.5

Figure 4.6

Figure 4.7

Figure 4.8

Figure 4.9

Figure 4.10

Figure 4.11

Figure 4.12

Figure 5.1

Figure 5.2

Figure 5.3

Figure 5.4

Figure 5.5

Figure 5.6

Figure 5.7

Figure 5.8

Figure 6.1

Figure 6.2

Figure 6.3

Figure 6.4

Figure 6.5

Figure 6.6

Figure 6.7

Figure 6.8

Figure 6.9

Figure 7.1

Figure 7.2

Figure 7.3

Figure 7.4

Figure 7.5

Figure 7.6

Figure 7.7

Figure 7.8

Figure 7.9

Figure 7.10

Figure 8.1

Figure 8.2

Figure 8.3

Figure 8.4

Figure 8.5

Figure 8.6

Figure 8.7

Figure 8.8

Figure 8.9

Figure 8.10

Figure 8.11

Figure 8.12

Figure 8.13

Figure 8.14

Figure 8.15

Figure 8.16

Figure 8.17

Figure 8.18

List of Tables

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Murray, E.J., Sivakumar, V., Murray, E.J.

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2010

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Öchsner, A., Murch, G.E., de Lemos, M.J. (eds.)

Cellular and Porous Materials

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Zhao, D., Wan, Y., Zhou, W.

Ordered Mesoporous Materials

2012

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Edited by H. Alicia Kimand Robert A. Guyer

Nonlinear Elasticity and Hysteresis

Fluid-Solid Coupling in Porous Media

The Editors

Dr. H. Alicia Kim

University of Bath

Dept. of Mech. Engineering

BA2 7AY Bath

United Kingdom

Robert A. Guyer

Los Alamos National Laboratory

Los Alamos

NM 87545

USA

and

University of Nevada

Department of Physics

1664 N. Virginia Street

Reno

NV 89557-0220

USA

Cover

The image was kindly supplied by Schreiber N., Gierlinger N., Putz N., Fratzl P., Neinhuis C., Burgert I. (2010) The Plant Journal. 61:854 – 861. Copyright by Blackwell Publishing Ltd.

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Preface

The subject matter of this book is the description of the behavior of porous materials in the presence of fluids. Porous materials are many, for example, soil or a sandstone, designed material such as a Nuclepore filter or MCM-41, wood fiber, or the cellular solid in the keel of an ice plant. Fluids often occupy the pore spaces in these materials and can alter the geometry/mechanical properties of the porous materials. It is this fluid–solid coupling that is discussed in the chapters herein.

We identify two important components of the fluid–solid interaction at the interface of solid and pore space. One relates to the phase change of fluid and the other relates to change of the mechanical state of solid. These changes depend on the thermodynamic state defined by (P, σ, T), that is, the fluid is at pressure P, the solid is at stress σ, and both are at temperature T. The pressure P is the pressure of the fluid that is far from the pore walls. At low fluid pressure, the pore space is filled with unsaturated vapor (Figure 1a). As the fluid pressure increases (moving up the dotted line in Figure 1a), the fluid on approaching the pore walls is inhomogeneous, evolving from gas to gas–liquid coexistence and eventually to liquid, because of forces exerted by the solid on the fluid. On further increase in the fluid pressure, the liquid near the pore wall solidifies. This evolution is depicted in the one-dimensional pore space of Figure 2. The x-axis indicates a physical pore space discretized for illustrative purposes in layers. The fluid pressure increases from Figure 2a–d, and the fluid near the pore wall undergoes phase changes. At fluid pressure equal to the saturated vapor pressure, Figure 2d, the fluid far from the pore wall is bulk liquid and the fluid close to the wall, which has not become solid, is at an effective pressure greater than the saturated vapor pressure. The fluid at the pore wall has become solid at an effective pressure, which is much greater than the saturated vapor pressure. While this evolution of the fluid in response to the fluid pressure is taking place, the solid, at stress σ, is almost unchanged.

Figure 1 (a, b) Phase diagrams of the material in a porous media system. The fluid is in principle at (P, T) and the solid, able to be addressed independently of the fluid, is in principle at (σ, T).

Figure 2 Fluid configuration in a pore space near a wall as pressure increases from (a) to (d). (a) Pressure is far from the saturated vapor pressure; (b) pressure is increasing; (c) pressure is approaching the saturated vapor pressure; and (d) pressure is at saturated vapor pressure.

The second component of the fluid–solid interaction is the development of a mechanical force system in the solid. At the pore wall, the solid pulls on the fluid, causing the inhomogeneous fluid arrangements in Figure 2a–d. In reaction, the fluid pulls on the solid causing a stain field in the solid. This is illustrated in Figure 3, a pore space in one dimension (for simplicity) bounded by solid on either side. As pressure approaches Psat, phase changes occur that are shown in Figure 2. The solid phase of the fluid appears on the pore wall due to densification as a result of forces exerted by the pore wall system. Concomitantly, the fluid pulls the pore walls into the pore space. A strain develops in the solid. This strain, often assumed to be small and able to be neglected, is driven by the fluid and can be a complex function of the history of the fluid configurations.

Figure 3 Fluid configuration in a pore wall system. The phase changes within the fluid and the strain induced in the pore wall are illustrated. The fluid pressure increases from (a) very low to (c) the saturated vapor pressure.

The solid could be under no stresses except that caused by forces from the fluid. However, it is, in principle, possible to have a stress field in the solid that is set independent of the forces from the fluid. This possibility, illustrated in Figure 1b, is the domain of Biot theory. For the most part, this subject area is not developed in this book. An exception is the paper by Vandamme et al. in Chapter 5.

The interaction of fluid and solid in porous materials at local scale manifests itself as complex nonlinear phenomena at global scale. One interesting nonlinear phenomenon that this book draws attention to is hysteresis. Hysteresis can be in the response to mechanical probes such as the stress–strain curve of a dry Berea sandstone, discussed in Chapter 1. The mechanical state of a typical sandstone evolves slowly over time following finite frequency excitation. Chapter 1 presents the mechanical experiments that interrogate the internal strain of the grains using a neutron beam and reveals important features of the behavior of rocks, that is, consolidated granular media.

There are also many systems in which the coupling between fluid and solid brings about the complex behavior, and some hysteresis can arise only as a result of the coupling. Chapter 2 is an experimental and theoretical study of mesoporous silicon material and presents a thermodynamic model at the fluid–solid interface. It reports adsorption-induced strain in the solids and the reciprocal stress effect on the adsorption process. Chapter 3 develops a theory to describe the fluid–solid coupling at the local scale. The manifestation of this interaction is described and investigated using a finite element model. The inhomogeneous system composed of fluid and solid elements can accommodate a variety of circumstances such as bulk fluid in the pore space of a rock, fluid in the wall fabric of wood or a cellular solid, and fluid in the polymeric filling of a cellular solid framework. Chapter 4 continues to present a theoretical study that formulates a model for stress–strain behavior of dry quasi-brittle materials allowing damage to be created. The Preisach model is used to model the damages at microscale, and this is translated as density to the macroscopic elastic elements to interpret the macroscopic behavior in terms of evolving populating of microscopic elements. The dry quasi-brittle material model is then modified to include moisture by allowing fluid–solid coupling in the form of an effective internal stress. Chapter 5 focuses on coal that serves as a valuable model of saturated porous material. The particularly interesting feature of coal is the range of length scales of the pores from macroscopic to mesoscopic, cleats, and matrix pores. This is modeled combining thermodynamic description of two pore systems, the macroscopic cleat system and the mesoscopic matrix system, which are coupled by a Darcy flow that is driven by a pressure gradient. Chapter 6 brings an alternative perspective on mechanics of porous materials by developing a multifield model and applying it to a series of foams. The particular interest here is the behavior of coupled fluid–solid systems under dynamic loading.

Chapter 7 examines the fluid–solid coupling in the context of wood swelling. The experimental observations are obtained by the modern X-ray tomography technique at a micrometer scale, and strains at multiple scales of hierarchical wood tissues are studied as a function of moisture content. This is accompanied by a parallel modeling study that explores the role of materials' structure as moisture content changes. The final chapter, Chapter 8, also investigates biological cellular materials, that is, plants. The authors employ this coupling in numerous ways from the analog of “blowing up a balloon” to a “mechanical” thermostat. Systems that exhibit this wide range of behaviors are described, for example, systems based on inner cell pressure, systems based on water uptake into the cell wall, systems based on a differential swelling of cell wall layers, and systems that illustrate the capacity of water as a plant movement actuator.

Acknowledgment

We would like to thank the following people and organisations for their support in publishing this book: The authors of the chapters for their contributions, The anonymous reviewers for the chapters for their insightful and helpful comments, J Machta, R Hallock, R Lilly and A Wootters in a long intermittent conversation that informed our understanding, and Institute of Geophysics and Planetary Physics and EES-17 at Los Alamos National Laboratory, the University of Nevada, Reno, USA and the University of Bath, UK.

List of Contributors

Laurent Brochard

Université Paris-Est

Laboratoire Navier (UMR 8205)

CNRS, ENPC, IFSTTAR

Marne-la-Vallée

France

Ingo Burgert

ETH Zurich - Swiss Federal Institute of Technology

Institute for Building Materials (IfB)

HIF E 23.2, Stefano-Franscini-Platz 3

Zurich

Switzerland

and

Empa, Swiss Federal Laboratory for Materials Science and Technology

Applied Wood Research Laboratory

Ueberlandstrasse 129

Dubendorf

Switzerland

Jan Carmeliet

ETH Zürich, Institute of Technology in Architecture

Chair of Building Physics

Stefano-Franscini-Platz 5

Zurich

Switzerland

and

Empa, Swiss Federal Laboratory for Materials Science and Technology

Laboratory of Building Science and Technology

Uberlandstrasse 129

Dubendorf

Switzerland

Patrick Dangla

Université Paris-Est

Laboratoire Navier (UMR 8205)

CNRS, ENPC, IFSTTAR

Marne-la-Vallée

France

Timothy W. Darling

Los Alamos National Laboratory

Los Alamos, NM 87545

USA

and

University of Nevada

Physics Department

N. Virginia St.

Reno, NV 89557-0220

USA

Dominique Derome

Empa

Swiss Federal Laboratory for Materials Science and Technology

Laboratory of Building Science and Technology

Uberlandstrasse 129

Dubendorf

Switzerland

Annie Grosman

Institut des Nanosciences de Paris (INSP)

Universite's Paris 6

UMR-CNRS 75-88

Campus Boucicaut

rue de Lourmel

Paris

France

Robert A. Guyer

Los Alamos National Laboratory

Los Alamos, NM 87545

USA

and

University of Nevada

Department of Physics

N. Virginia Street

Reno, NV 89557-0220

USA

H. Alicia Kim

University of Bath

Department of Mechanical Engineering

Bath

BA2 7AY

UK

Saeid Nikoosokhan

Université Paris-Est

Laboratoire Navier (UMR 8205)

CNRS, ENPC, IFSTTAR

Marne-la-Vallée

France

Camille Ortega

Institut des Nanosciences de Paris (INSP)

Universite's Paris 6

UMR-CNRS 75 – 88

Campus Boucicaut

rue de Lourmel

Paris

France

Alessandra Patera

Empa

Swiss Federal Laboratory for Materials Science and Technology

Laboratory of Building Science and Technology

Uberlandstrasse 129

Dubendorf

Switzerland

and

Paul Scherrer Institute

Swiss Light Source

Villigen

Switzerland

Ahmad Rafsanjani

McGill University

Mechanical Engineering Department

Sherbrooke Street West

Montreal Quebec H3A OC3

Canada

Khashayar Razghandi

Max-Planck-Institute of Colloids and Interfaces

Department of Biomaterials

Am Mühlenberg 1

Potsdam

Germany

Mark W. Schraad

Fluid Dynamics and Solid Mechanics Group (T-3)

Theoretical Division

Los Alamos National Laboratory

Mail Stop B216, P.O. Box 1663

Los Alamos, NM 87545

USA

James A. TenCate

Los Alamos National Laboratory

Los Alamos, NM 87545

USA

Sebastien Turcaud

Max-Planck-Institute of Colloids and Interfaces

Department of Biomaterials

Am Mühlenberg 1

Potsdam

Germany

Matthieu Vandamme

Université Paris-Est

Laboratoire Navier (UMR 8205)

CNRS, ENPC, IFSTTAR

Marne la Vallée

France

Sven C. Vogel

Los Alamos National Laboratory

Los Alamos, NM 87545

USA

1Dynamic Pressure and Temperature Responses of Porous Sedimentary Rocks by Simultaneous Resonant Ultrasound Spectroscopy and Neutron Time-of-Flight Measurements

James A. TenCate, Timothy W. Darling, and Sven C. Vogel

1.1 Introduction and Background

Rocks are everywhere, yet there are still surprising puzzles about their peculiar dynamic elastic properties, especially their hysteresis, non-Hookean response, and rate-dependent behavior. Since before recorded history, mankind has been making dwellings, hammering out monuments, and even constructing huge buildings out of rock, for example, the famous Strasbourg Cathedral built in the Middle Ages is made almost entirely from Vosges sandstone. Nowadays, one extracts oil and gas from rocks, explores ways to store excess CO2 in them, and tries to mimic their resilience and durability with concrete. The imperfect way in which mineral grains end up cemented into rocks dictates how fluids move in oil or gas reservoirs or in aquifers. Indeed, these very fluids are often a key mechanism for that cementation. The diagenesis of rocks, their formation, and cementation history are of great geological interest as well. Hence, the dynamic elastic properties of rocks have been a topic of continuing scientific study for well over a century.

To narrow the focus of this chapter, the subject is primarily the behavior of rocks that have commercial interest. These rocks may contain oil and gas, or might be considered as a reservoir for CO2 storage. These rocks are primarily sedimentary, and the focus of this chapter will sharpen even more, dealing exclusively with sandstones. A sandstone is an imperfectly cemented collection of quartz grains, which is porous and permeable to fluids (which often play a key role in the cementation) and may contain significant amounts of clays and other materials. In the experiments described here, the rocks studied will be extremely pure and clean sandstones, 99+% pure SiO formed from quartz (prehistoric, 77 MYBP) Aeolian beach sand, known as . Such rocks are simply composed of the grains and cementation.