The current use of complex materials in nanotechnology and industrial engineering has led to a number of intricate problems in mechanics. The macroscopic behavior of such materials often depends critically on their substructures. Multifield theories in continuum mechanics provide the tools for modeling and describing these material substructures, as is emphasized in this book. Indeed multifield theories are an active area of research because of the numerous theoretical and numerical problems emerging in the field.

Written by leading mathematicians and engineers, the chapters feature a broad range of topics that offer both experimental results and clear, detailed answers to fundamental questions about the general formulation of multifield theories. Amid a rich collection of open problems, selected subjects treated include:

• Energetic and geometric properties of elastic-plastic materials

• Poisson structures for complex fluids

• Drag reduction in turbulence due to polymeric substructures

• Topological properties of stresses and defects

• Exact relations for the effective behavior of composites

• Multifield macroscopic modeling of shape memory effects and extended thermodynamics

• Properties of junctions and interfaces

  Applied mathematicians, mechanical and structural engineers, material scientists, graduate students, and researchers in the above areas will benefit from this work.

  Contributors:

  D. Bernardini, G. Capriz, C. M. Casciola, H. Cendra, E. DeAngelis, Y. Grabovsky, P. M. Mariano, J. Marsden, I. Müller, O. B. Naimark, G. Parry, T. J. Pence, R. Piva, T. S. Ratiu, R. Segev, M. Silhavy

  Klappentext

  Toachieve design, implementation,and servicing ofcomplex systems and struc­ tures in an efficient and cost-effective way,a deeper knowledge and understanding of the subtle cast and detailed evolution of materials is needed. The analysis in demand borders with the molecular and atomic one, spanning all the way down from classical continua. The study of the behavior of complex materials in sophisticated devices also opens intricate questions about the applicability of primary axioms ofcontinuum mechanics such as the ultimate nature of the material element itselfand the possibility ofidentifying itperfectly. So it is necessary to develop tools that allow usto formulate both theoretical models and methods of numerical approximation for the analysis of material substructures. Multifield theories in continuum mechanics, which bridge classical materials science and modern continuum mechanics, provide precisely these tools. Multifield theories not only address problems of material substructures, but also encompass well-recognized approaches to the study of soft condensed matter and allow one to model disparate conditions in various states ofmatter. However, research inmultifield theories is vast, and there is little in the way of a comprehensive distillation of the subject from an engineer's perspective. Therefore, the papers in the present volume, 1 which grew out of our experience as editors for an engineeringjournal, tackle some fundamental questions,suggest solutions of concrete problems, and strive to interpret a host of experimental evidence. In this spirit, each of the authors has contributed original results having in mind their wider applicability.

  Inhalt

  Preface Work Conditions and Energy Functions for Ideal Elastic-Plastic Materials / M. Silhavy Generalized Elastic-Plastic Decomposition in Defective Crystals / G.P. Parry Cocycles, Compatibility, and Poisson Brackets for Complex Fluids / H. Cendra, J. Marsden, T.S. Ratiu Defect-Induced Transitions as Mechanisms of Plasticity and Failure in Multifield Continua / O.B. Naimark Extended Thermodynamics: A Multifield Theory Par Excellence / I. Müller Microstructure and Turbulence in Dilute Polymer Solutions / E. De Angelis, C.M. Casciola, P.M. Mariano, R. Piva Fluxes and Flux-Conjugate Stresses / R. Segev Algebra, Geometry, and Computations of Exact Relations for Effective Moduli of Composites / Y. Grabovsky A Multifield Theory for the Macroscopic Modeling of Shape Memory Materials / D. Bernardini, T.J. Pence Balance at a Junction among Coherent Interfaces in Materials with Substructure / G. Capriz, P.M. Mariano