Phase Transformations and Material Instabilities in Solids (Publication of the Mathematics Research Center, the Univ of Wisconsin--madiSon, No 52)

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. Content: Front Matter , Page iii Copyright , Page iv CONTRIBUTORS , Pages vii-viii PREFACE , Page ix , MORTON E. GURTIN MATERIAL INSTABILITIES AND THE CALCULUS OF VARIATIONS , Pages 1-19 , J.M. Ball MECHANICAL ANALOGS OF COEXISTENT PHASES , Pages 21-36 , E. Chater, J.W. Hutchinson ADAPTIVE FINITE ELEMENT METHODS AND THE NUMERICAL SOLUTION OF SHEAR BAND PROBLEMS , Pages 37-60 , D.A. Drew, J.E. Flaherty THE CAUCHY AND BORN HYPOTHESES FOR CRYSTALS , Pages 61-77 , J.L. Ericksen THE ARRANGEMENT OF COHERENT PHASES IN A LOADED BODY , Pages 79-98 , R.D. James THE GRADIENT THEORY OF PHASE TRANSITIONS ON A FINITE INTERVAL , Pages 99-112 , M.E. Gurtin ONE-DIMENSIONAL SHOCK LAYERS IN KORTEWEG FLUIDS , Pages 113-127 , R. Hagan, J. Serrin DYNAMICS OF DENDRITIC PATTERN FORMATION , Pages 129-146 , J.S. Langer MORPHOLOGICAL INSTABILITIES DURING PHASE TRANSFORMATIONS , Pages 147-162 , R.F. Sekerha DYNAMICS OF FIRST ORDER PHASE TRANSITIONS , Pages 163-203 , M. Slemrod EQUILIBRIUM SHAPES OF SURFACES AND GRAIN BOUNDARIES , Pages 205-213 , J.E. Taylor INDEX , Pages 215-217