Modeling and Simulation in Science, Engineering and Technology

Advances in Multifield Theories for Continua with Substructure

Editors: Capriz, Gianfranco, Mariano, Paolo Maria (Eds.)

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About this book

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

 

Reviews

"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

 


Table of contents (10 chapters)

  • Work Conditions and Energy Functions for Ideal Elastic-Plastic Materials

    Šilhavý, M.

    Pages 1-31

  • Generalized Elastic-Plastic Decomposition in Defective Crystals

    Parry, G. P.

    Pages 33-50

  • Cocycles, Compatibility, and Poisson Brackets for Complex Fluids

    Cendra, Hernán (et al.)

    Pages 51-73

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

    Naimark, O. B.

    Pages 75-114

  • Extended Thermodynamics: A Multifield Theory Par Exellence

    Müller, I.

    Pages 115-126

Buy this book

eBook $89.00
price for USA (gross)
  • ISBN 978-0-8176-8158-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $169.00
price for USA
  • ISBN 978-0-8176-4324-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $119.00
price for USA
  • ISBN 978-1-4612-6465-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Advances in Multifield Theories for Continua with Substructure
Editors
  • Gianfranco Capriz
  • Paolo Maria Mariano
Series Title
Modeling and Simulation in Science, Engineering and Technology
Copyright
2004
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-0-8176-8158-6
DOI
10.1007/978-0-8176-8158-6
Hardcover ISBN
978-0-8176-4324-9
Softcover ISBN
978-1-4612-6465-1
Series ISSN
2164-3679
Edition Number
1
Number of Pages
XI, 263
Topics