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Nonlinear Mesoscopic Elasticity: The Complex Behaviour of Rocks, Soil, Concrete

Nonlinear Mesoscopic Elasticity: The Complex Behaviour of Rocks, Soil, Concrete

Robert A. Guyer, Paul A. Johnson

ISBN: 978-3-527-62827-8

Aug 2009

410 pages



This handbook brings together a great deal of new data on the static and dynamic elastic properties of granular and other composite material. The authors are at the very center of today's research and present new and imported theoretical tools that have enabled our current understanding of the complex behavior of rocks.
There are three central themes running throughout the presentation:
· Rocks as the prototypical material for defining a class of materials
· The PM space model as a useful theoretical construct for developing a phenomenology
· A sequence of refined analysis methods.
This suite of new methods for both recording and analyzing data is more than a single framework for interpretation, it is also a toolbox for the experimenter. A comprehensive and systematic book of utmost interest to anybody involved in non-destructive testing, civil engineering, and geophysics.


1 Introduction.

1.1 Systems.

1.2 Examples of Phenomena.

1.3 The Domain of Exploration.

1.4 Outline.


2 Microscopic/Macroscopic Formulation of the Traditional Theory of Linear and Nonlinear Elasticity.

2.1 Prefatory Remarks.

2.2 From Microscopic to Continuum.

2.3 Continuum Elasticity and Macroscopic Phenomenology.

2.4 Thermodynamics.

2.5 Energy Scales.


3 Traditional Theory of Nonlinear Elasticity, Results.

3.1 Quasistatic Response; Linear and Nonlinear.

3.2 Dynamic Response; Linear.

3.3 Quasistatic/Dynamic Response; Nonlinear.

3.4 Dynamic Response; Nonlinear.

3.5 Exotic Response; Nonlinear.

3.6 Green Functions.


4 Mesoscopic Elastic Elements and Macroscopic Equations of State.

4.1 Background.

4.2 Elastic Elements.

4.3 Effective Medium Theory.

4.4 Equations of State; Examples.


5 Auxiliary Fields.

5.1 Temperature.

5.2 Saturation.

5.3 The Conditioning Field, X.


6 Hysteretic Elastic Elements.

6.1 Finite Displacement Elastic Elements; Quasistatic Response.

6.2 Finite Displacement Elastic Elements: Inversion.

6.3 Finite Displacement Elastic Elements: Dynamic Response.

6.4 Models with Hysteresis.

6.5 Summary.

6.6 Models with Hysteresis, Detail.


7 The Dynamics of Elastic Systems; Fast and Slow.

7.1 Fast/Slow Linear Dynamics.

7.2 Fast Nonlinear Dynamics.

7.3 Auxiliary Fields and Slow Dynamics.

7.4 Summary.


8 Q and Issues of Data Modeling/Analysis.

8.1 Attenuation in Linear Elastic Systems.

8.2 Nonlinear Attenuation.

8.3 Why Measure Q?

8.4 How to Measure Q.

8.5 Resonant Bar Revisited.


9 Elastic State Spectroscopies and Elastic State Tomographies.

9.1 Spectroscopies.

9.2 Tomographies, Linear, Inhomogeneous.

9.3 Tomographies, Nonlinear, Inhomogeneous.


10 Quasistatic Measurements.

10.1 Some Basic Observations.

10.2 Quasistatic Stress-Strain Data; Hysteresis.

10.3 Coupling to Auxiliary Fields.

10.4 Inversion.


11 Dynamic Measurements.

11.1 Quasistatic-Dynamic.

11.2 Dynamic–Dynamic.

11.3 Examples of Systems.


12 Field Observations.

12.1 Active Probes.

12.2 Passive Probes.


13 Nonlinear Elasticity and Nondestructive Evaluation and Imaging.

13.1 Overview.

13.2 Historical Context.

13.3 Simple Conceptual Model of a Crack in an Otherwise Elastically Linear Solid.

13.4 Nonlinear Elastic Wave Spectroscopy in Nondestructive Evaluation (NEWS).

13.5 Progressive Mechanical Damage Probed by NEWS Techniques.

13.6 Mechanical Damage Location and Imaging.

13.7 Other Methods for Extracting the Elastic Nonlinearity.

13.8 Summary.


Color Plates.