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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.
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
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