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Phase Transformations and Material Instabilities in Solids contains the proceedings of an interdisciplinary conference on phase transitions and material instabilities in solids, conducted by the Mathematics Research Center of the University of Wisconsin-Madison on October 11-13, 1983 in Madison, Wisconsin. The papers explore phase transformations and material instabilities in solids and cover topics ranging from equilibrium shapes of surfaces to morphological instabilities and dendrite formation. Shock-induced phase transitions are also considered. Comprised of 11 chapters, this book begins with a discussion on material instabilities and the calculus of variations, followed by an analysis of mechanical analogs of coexistent phases. A model for the formation of shear bands in simple shear that involves the description of irreversible mechanical shear and the resulting heat release is then presented. Subsequent chapters focus on the Cauchy and Born hypotheses for crystals; the arrangement of coherent phases in a loaded body; one-dimensional shock layers in Korteweg fluids; and dynamics of first-order phase transitions. The final chapter deals with equilibrium shapes of surfaces and grain boundaries. This monograph will be of interest to students, practitioners, and researchers in mathematics and statistical physics.
Modern, powerful computational methods, combined with major improvements in experimental techniques, have resulted in significant advances in the study of material instabilities. This book presents the latest research in the field of material instabilities in solid materials (soils, concrete, rocks, ceramics, metals, polymers and composites) and associated phenomena, such as strain localisation, fracture and failure in general. Collected within this volume are the cutting edge contributions from the prestigious IUTAM Symposium of 1997. A broad spectrum of materials is covered, with the emphasis on common aspects of failure, and a full range of experimental, analytical and numerical methods are addressed. In addition, the state-of-the-art, and recent advances covered in the book are summarised in the introductory chapter. No other treatise is available which is so up to date and compiled by such a broad spectrum of leading researchers. This book will find a wide appeal amongst practising engineers, researchers and students in civil, mechanical and aerospace engineering, and researchers and students in materials science.
This book collects recent theoretical developments in the area of material instability in elastic and plastic solids along with related analytical and numerical methods and applications. The existing different approaches to instability phenomena in metal single crystals, polycristals and in geomaterials are presented with the emphasis laid on mutual relations and on unifying concepts, including elliptictly loss and the energy criterion. Quasi-static bifurcation, initiation of single or multiple shear bands and post-critical strain localization are examined along with dynamic phenomena as wave propagation, moving shocks, internal snap-through and instability of flutter type. This gives an overview of a variety of material instability problems, methods and applications.
Addresses behaviour of materials under extreme mechanical conditions and of failure in terms of non-linear continuum mechanics and instability theory.
The past three decades have been a period where useful current and voltage instabilities in solids have progressed from exciting research problems to a wide variety of commercially available devices. Materials and electronics research has led to devices such as the tunnel (Esaki) diode, transferred electron (Gunn) diode, avalanche diodes, real-space transfer devices, and the like. These structures have proven to be very important in the generation, amplification, switching, and processing of microwave signals up to frequencies exceeding 100 GHz. In this treatise we focus on a detailed theoretical understanding of devices of the kind that can be made unstable against circuit oscillations, large amplitude switching events, and in some cases, internal rearrangement of the electric field or current density distribution. The book is aimed at the semiconductor device physicist, engineer, and graduate student. A knowledge of solid state physics on an elementary or introductory level is assumed. Furthermore, we have geared the book to device engineers and physicists desirous of obtaining an understanding substantially deeper than that associated with a small signal equivalent circuit approach. We focus on both analytical and numerical treatment of specific device problems, concerning ourselves with the mechanism that determines the constitutive relation governing the device, the boundary conditions (contact effects), and the effect of the local circuit environment.
Understanding the origin of spatio-temporal order in open systems far from thermal equilibrium and the selection mechanisms of spatial struc tures and their symmetries is a major theme of present day research into the structures of continuous matter. The development of methods for pro ducing spatially ordered microstructures in solids by non-equilibrium methods opens the door to many technological applications. It is also be lieved that the key to laminar/turbulence transitions in fluids lies in the achievement of spatio-temporal order. Let us also emphasize the fact that the idea of self-organization in it self is at the origin of a reconceptualisation of science. Indeed, the appear ance of order which usually has been associated with equilibrium phase transitions appears to be characteristic of systems far from thermal equi librium. This phenomenon which was considered exceptional at first now the rule in driven systems. The chemical oscillations obtained appears to be in the Belousov-Zhabotinskii reaction were initially considered to be ther modynamically impossible and were rejected by a large number of chemists. Now these oscillations and related phenomena (waves, chaos, etc. ) are the subject of intensive research and new classes of chemical oscil lators have been recently discovered. Even living organisms have long been considered as the result of chance rather than necessity. Such points of view are now abandoned under the overwhelming influence of spatio-tem poral organization phenomena in various domains ranging from physics to biology via chemistry, nonlinear optics, and materials science .
The proceedings of a Symposium Year on Material instabilities in continuum mechanics organized by the Department of Mathematics, Heriot-Watt University, Edinburgh, 1985-1986.