Nonlinear Mesoscopic Elasticity: The Complex Behaviour of Granular Media Including Rocks and Soil

Preface . Acknowledgements . 1 Introduction . 1.1 Systems . 1.2 Examples of Phenomena . 1.3 The Domain of Exploration . 1.4 Outline . References . 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 . References . 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 . References . 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 . References . 5 Auxiliary Fields . 5.1 Temperature . 5.2 Saturation . 5.3 The Conditioning Field, X . References . 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 . References . 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 . References . 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 . References . 9 Elastic State Spectroscopies and Elastic State Tomographies . 9.1 Spectroscopies . 9.2 Tomographies, Linear, Inhomogeneous . 9.3 Tomographies, Nonlinear, Inhomogeneous . References . 10 Quasistatic Measurements . 10.1 Some Basic Observations . 10.2 Quasistatic Stress-Strain Data Hysteresis . 10.3 Coupling to Auxiliary Fields . 10.4 Inversion . References . 11 Dynamic Measurements . 11.1 Quasistatic-Dynamic . 11.2 Dynamic-Dynamic . 11.3 Examples of Systems . References . 12 Field Observations . 12.1 Active Probes . 12.2 Passive Probes . References . 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 . References . Color Plates . Index .