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Atomistic and Continuum Modeling of Nanocrystalline Materials develops a complete and rigorous state-of-the-art analysis of the modeling of the mechanical behavior of nanocrystalline (NC) materials. Among other key topics the material focuses on the novel techniques used to predict the behavior of nanocrystalline materials. Particular attention is given to recent theoretical and computational frameworks combining atomistic and continuum approaches. Also, the most relevant deformation mechanisms governing the response of nanocrystalline materials are addressed and discussed in correlation with available experimental data. Drawing upon years of practical and academic experience and using numerous examples, authors Mohammed Cherkaoui and Laurent Capolungo cover a wide spectrum of material, including: New modeling techniques and their potential applications and possible extensions, such as molecular dynamics, strain gradient based finite element simulations, and novel micromechanical schemes Novel models describing plastic deformation processes occurring in nanocrystalline materials including grain boundary dislocation emission How to construct and use a molecular dynamics code for practical use in the modeling of NC materials Atomistic and Continuum Modeling of Nanocrystalline Materials is a must have book for researchers as well as graduate students who are either entering these fields for the first time, or those already conducting research in this area and intending to extend their knowledge of nanocrystalline materials.

Continuum mechanics -- Mathematical models. --- Nanocrystals. --- Nanostructured materials. --- Nanostructured materials --- Nanocrystals --- Continuum mechanics --- Manufactured Materials --- Nanostructures --- Nanoparticles --- Technology, Industry, and Agriculture --- Technology, Industry, Agriculture --- Chemical & Materials Engineering --- Materials Science --- Engineering & Applied Sciences --- Mathematical models --- Mathematical models. --- Mechanics of continua --- Nanosized crystals --- Nanomaterials --- Nanometer materials --- Nanophase materials --- Nanostructure controlled materials --- Nanostructure materials --- Ultra-fine microstructure materials --- Elasticity --- Mechanics, Analytic --- Field theory (Physics) --- Crystals --- Microstructure --- Nanotechnology

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This book offers a broad overview of the potential of continuum mechanics to describe a wide range of macroscopic phenomena in real-world problems. Building on the fundamentals presented in the authors’ previous book, Continuum Mechanics using Mathematica®, this new work explores interesting models of continuum mechanics, with an emphasis on exploring the flexibility of their applications in a wide variety of fields. Specific topics, which have been chosen to show the power of continuum mechanics to characterize the experimental behavior of real phenomena, include: * various aspects of nonlinear elasticity, including equilibrium equations and their variational formulation, nonlinear constitutive equations, existence and uniqueness theorems of Van Buren and Stoppelli, and Signorini's method with some extensions to live loads and acceleration waves * continua with directors * a model of a continuum with a nonmaterial moving interface * mixture theory: The Gibbs Rule in a binary mixture * interaction between electric or magnetic fields with matter * micromagnetism * continua in special relativity and relativistic interactions between matter and electromagnetic fields Appendices are included to provide background information on topics such as surface geometry, first-order PDEs, and weak solutions to models. Mathematica® notebooks also accompanying the text are available for download at http://www.birkhauser.com/978-0-8176-4869-5. Aimed at advanced graduate students, applied mathematicians, mathematical physicists, and engineers, the work will be an excellent self-study reference or supplementary textbook in graduate-level courses focusing on advanced topics and research trends in continuum mechanics.

Continuum mechanics -- Mathematical models. --- Continuum mechanics. --- Mathematics. --- Continuum mechanics --- Engineering & Applied Sciences --- Applied Mathematics --- Mathematical models --- Mechanics of continua --- Engineering. --- Applied mathematics. --- Engineering mathematics. --- Mathematical models. --- Physics. --- Continuum physics. --- Mechanics. --- Continuum Mechanics and Mechanics of Materials. --- Classical Continuum Physics. --- Theoretical, Mathematical and Computational Physics. --- Mathematical Modeling and Industrial Mathematics. --- Applications of Mathematics. --- Elasticity --- Mechanics, Analytic --- Field theory (Physics) --- Mechanics, Applied. --- Solid Mechanics. --- Classical and Continuum Physics. --- Classical Mechanics. --- Math --- Science --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Mathematical physics. --- Engineering --- Engineering analysis --- Mathematical analysis --- Models, Mathematical --- Simulation methods --- Physical mathematics --- Classical field theory --- Continuum physics --- Mathematics