Advances in Multifield Theories of Continua With Substructure

by Capriz, Gianfranco; Mariano, Paolo Maria

• ISBN13: 9780817643249
• ISBN10: 0817643249
• Format: Hardcover
• Copyright: 2004-03-01
• Publisher: Birkhauser

Summary

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

Table of Contents

Preface

Work Conditions and Energy

Functions for Ideal Elastic-Plastic Materials

Generalized Elastic-Plastic Decomposition in Defective Crystals

Cocycles, Compatibility, and Poisson Brackets for Complex Fluids

Defect-Induced Transitions as Mechanisms of Plasticity and Failure in Multifield Continua

Extended Thermodynamics: A Multifield Theory Par Excellence

Muller Microstructure and Turbulence in Dilute Polymer Solutions

Fluxes and Flux-Conjugate Stresses

Geometry, and Computations of Exact Relations for Effective Moduli of Composites

A Multifield Theory for the Macroscopic Modeling of Shape Memory Materials

Balance at a Junction among Coherent Interfaces in Materials with Substructure

G. Capriz

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