Advances in Multifield Theories for Continua with Substructure (eBook, PDF)

Redaktion: Capriz, Gianfranco; Mariano, Paolo Maria

• Format: PDF

Produktbeschreibung

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

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Produktdetails

• Verlag: Birkhäuser Boston
• Seitenzahl: 263
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9780817681586
• Artikelnr.: 44203771

Inhaltsangabe

Preface.- 1. Work Conditions and Energy Functions for Ideal Elastic-Plastic Materials.- 2. Generalized Elastic-Plastic Decomposition in Defective Crystals.- 3. Cocycles, Compatibility, and Poisson Brackets for Complex Fluids.- 4. Defect-Induced Transitions as Mechanisms of Plasticity and Failure in Multifield Continua.- 5. Extended Thermodynamics: A Multifield Theory Par Excellence.- 6. Microstructure and Turbulence in Dilute Polymer Solutions.- 7. Fluxes and Flux-Conjugate Stresses.- 8. Algebra, Geometry, and Computations of Exact Relations for Effective Moduli of Composites.- 9. A Multifield Theory for the Modeling of the Macroscopic Behavior of Shape Memory Materials.- 10. Balance at a Junction among Coherent Interfaces in Materials with Substructure.

Rezensionen

"As an outgrowth of a symposium held in Taormina, Italy, in 2001, ten invited papers on multifield theories for continua with substructure are presented here. Multifield theories aim to bridge the area between materials science and continuum mechanics. From the standpoint of material constituents, the simplest model is considered in the contribution of I. Müller: a monatomic gas.... Other contributions deal with the interaction of polymer chains and the turbulent state of a fluid...with topological properties of defects, of shape memory and others. The perhaps most theoretical article is by Cendra, Marsden and Ratiu on...extended...Poisson brackets with cocycles. The articles, though dealing with nontrivial matters, are quite readable and informative even for the nonspecialist."

-Monatshefte für Mathematik

"...This compendium is extremely diverse ...The individual contributions in this compendium are certainly quite interesting and worth reading."

-Rezensionen