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The purpose of this paper is to describe a theory of the propagation of elastic waves in hysteretic nonlinear elastic materials, e.g., rock. In the next section, we introduce the Priesach-Mayergoyz (P-M) model [6,7] of hysteretic systems and adapt it to describe the hysteretic mesoscopic elastic units (HMEU) determining the elastic properties of a rock. We combine the P-M model with effective medium theory (EMT) [8] to find the elastic response of a rock that has experienced a specified pressure history. Next, we consider elastic wave propagation in a hysteretic nonlinear elastic system governed by a history dependent equation of state. We consider one-dimensional propagation of compressional waves. The equation of motion for the longitudinal displacement field contains the same hysteretic nonlinear interactions that characterize the equation of state. We solve the equation of motion using the Green function technique developed by McCall [9]. This solution lets us identify the qualitative features in harmonic generation that are signatures of nonlinearity 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.
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.
The 'P-M Space' model of Guyer and McCall has some success in describing the large nonlinear effects ('slow dynamics') observed by Johnson et al. in rocks. The model uses elements which couple classical nonlinear elasticity with hysteretic components. The actual processes and scales corresponding to the model elements are not yet defined, however it is reasonable to seek energy scales by studying the low-temperature dependence of the elastic constants. We have measured qualitative elastic properties of basalt and Berea sandstone from room temperature down to 4 K using Resonant Ultrasound Spectroscopy (RUS). A simple elastic solid should show a monotonic increase in the elastic constants as temperature decreases. The basalt samples show this gross behavior but the sandstone shows a very unexpected anomalous regime between 40 K and 200 K where the elastic constants decrease with decreasing temperature. Both rocks show temperature-dependent structure in both the modulus and internal friction, and also significant hysteresis, indicating history and rate-dependent properties. This data provides insight into the time and energy scales of dynamical effects observed in sandstones.
Volume 1 covers: * Mathematical models * Differential equations * Stochastic aspects of hysteresis * Binary detection using hysteresis * Models of unemployment in economics Volume 2 covers: * Physical models of magnetic hysteresis * All aspects of magnetisation dynamics Volume 3 covers: * Hysteresis phenomena in materials * Over 2100 pages, rich with supporting illustrations, figures and equations * Contains contributions from an international list of authors, from a wide-range of disciplines * Covers all aspects of hysteresis - from differential equations, and binary detection, to models of unemployment and magnetisation dynamics.
Volume is indexed by Thomson Reuters CPCI-S (WoS). These 379 peer-reviewed papers, presented in a two-volume set, cover the latest advances in nanocrystalline materials, thin films and chemical vapor deposition, biocomposites, ceramics technology, MEMS, coatings, nanopowders, fuel cells, etc.; together with their practical application.
This multi-contributed volume provides a practical, applications-focused introduction to nonlinear acoustical techniques for nondestructive evaluation. Compared to linear techniques, nonlinear acoustical/ultrasonic techniques are much more sensitive to micro-cracks and other types of small distributed damages. Most materials and structures exhibit nonlinear behavior due to the formation of dislocation and micro-cracks from fatigue or other types of repetitive loadings well before detectable macro-cracks are formed. Nondestructive evaluation (NDE) tools that have been developed based on nonlinear acoustical techniques are capable of providing early warnings about the possibility of structural failure before detectable macro-cracks are formed. This book presents the full range of nonlinear acoustical techniques used today for NDE. The expert chapters cover both theoretical and experimental aspects, but always with an eye towards applications. Unlike other titles currently available, which treat nonlinearity as a physics problem and focus on different analytical derivations, the present volume emphasizes NDE applications over detailed analytical derivations. The introductory chapter presents the fundamentals in a manner accessible to anyone with an undergraduate degree in Engineering or Physics and equips the reader with all of the necessary background to understand the remaining chapters. This self-contained volume will be a valuable reference to graduate students through practising researchers in Engineering, Materials Science, and Physics. Represents the first book on nonlinear acoustical techniques for NDE applications Emphasizes applications of nonlinear acoustical techniques Presents the fundamental physics and mathematics behind nonlinear acoustical phenomenon in a simple, easily understood manner Covers a variety of popular NDE techniques based on nonlinear acoustics in a single volume
"This book seeks to advance cutting-edge research in the field, with a special focus on cross-disciplinary work involving recent advances in IT, enabling structural-health experts to wield groundbreaking new models of artificial intelligence as a diagnostic tool capable of identifying future problems before they even appear"--Provided by publisher.