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Instabilities and Self-Organization in MaterialsVolume I: Fundamentals of Nanoscience, Volume II: Applications in Materials Design and Nanotechnology$
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Nasr Ghoniem and Daniel Walgraef

Print publication date: 2008

Print ISBN-13: 9780199298686

Published to Oxford Scholarship Online: May 2008

DOI: 10.1093/acprof:oso/9780199298686.001.0001

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Instabilities and Self-Organization in Materials

Nasr M. Ghoniem

Daniel D. Walgraef

Oxford University Press

This chapter discusses the main elements of continuum theory, which will be utilized further in later sections dealing with a variety of applications. First, a basic review of vector and tensor operations is presented, followed by descriptions of stress and strain tensors, and their relationships through thermodynamic functions. The special conditions of anisotropic crystals are also discussed. Green's tensor functions are derived for the displacement field of a material in response to a point force, for both isotropic and anisotropic crystals. Then, the methods of Eshelby for inclusions and inhomogeneities are presented, with analytical solutions to special problems of a second phase within a perfect crystals. This is followed by a presentation of the basic elements of crystal plasticity, and its connection with dislocation (or incompatibility) fields. The elastic fields of complex dislocation loop ensembles are finally given for both isotropic and anisotropic crystals.

Keywords:   continuum theory, isotropic crystals, anisotropic crystals, vector calculus, tensor calculus, thermodynanics, deformation, Green's tensor functions, Eshelby

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