Material Instabilities In Solids

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.

This book offers a recipe for constructing the numerical models for representing the complex nonlinear behavior of structures and their components, represented as deformable solid bodies. Its appeal extends to those interested in linear problems of mechanics.

The proceedings of a Symposium Year on Material instabilities in continuum mechanics organized by the Department of Mathematics, Heriot-Watt University, Edinburgh, 1985-1986.

Addresses behaviour of materials under extreme mechanical conditions and of failure in terms of non-linear continuum mechanics and instability theory.