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Physics of elasticity and crystal defects

Author: Adrian P Sutton
Publisher: Oxford New York, NY Oxford University Press 2020 ©2020
Series: Oxford series on materials modelling, 6.
Edition/Format:   eBook : Document : English : First editionView all editions and formats
Summary:
Although linear elasticity of defects in solids is well established, this textbook introduces the subject in a novel way by comparing key concepts at the atomic scale and at the usual continuum scale, and it explores the relationships between these treatments. There are exercises to work through, with solutions for instructors from the OUP website
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Genre/Form: Electronic books
Additional Physical Format: Print version
Sutton, Adrian P.
Physics of Elasticity and Crystal Defects
Oxford : Oxford University Press USA - OSO,c2020
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Adrian P Sutton
ISBN: 9780192605184 0192605186 9780191893001 0191893005
OCLC Number: 1163183665
Notes: 6.12 The stress field of an edge dislocation in isotropic elasticity
Description: 1 online resource illustrations
Contents: Cover --
Series page --
Physics of elasticity and crystal defects --
Copyright --
Foreword --
Contents --
Preface --
1: Strain --
1.1 The continuum approximation --
1.2 What is deformation? --
1.3 The displacement vector and the strain tensor --
1.3.1 Normal strain and shear strain --
1.4 Closing remarks --
1.5 Problem set 1 --
2: Stress --
2.1 What is stress? --
2.2 Cauchy's stress tensor in a continuum --
2.3 Normal stresses and shear stresses --
2.4 Stress at the atomic scale --
2.5 Invariants of the stress tensor --
2.5 Invariants of the stress tensor 2.6 Shear stress on a plane and the von Mises stress invarian --
2.7 Mechanical equilibrium --
2.8 Adiabatic and isothermal stress --
2.9 Problem set 2 --
3: Hooke's law and elastic constants --
3.1 Generalised Hooke's law: elastic constants and compliances --
3.2 The maximum number of independent elastic constants in a crystal --
3.2.1 The elastic energy density --
3.2.2 Matrix notation --
3.3 Transformation of the elastic constant tensorunder a rotation --
3.3.1 Neumann's principle --
3.4 Isotropic materials --
3.5 Anisotropic materials --
3.5.1 Cubic crystals 3.5.2 The directional dependence of the elastic constants in anisotropic media --
3.6 Further restrictions on the elastic constants --
3.7 Elastic constants and atomic interactions --
3.8 Isothermal and adiabatic elastic moduli --
3.9 Problem set 3 --
4: The Green's function in linear elasticity --
4.1 Differential equation for the displacement field` --
4.1.1 Navier's equation --
4.2 The physical meaning of the elastic Green's function --
4.2.1 Definition of the Green's function in linear elasticity --
4.2.2 The equation for the Green's function in an infinite medium 4.2.3 Solving elastic boundary value problems with the Green's function --
4.3 A general formula for the Green's function in anisotropic elastic media --
4.4 The Green's function in an isotropic elastic medium --
4.5 The multipole expansion --
4.6 Relation between the Green's functions for an elastic continuum and a crystal lattice --
4.7 Eshelby's ellipsoidal inclusion --
4.8 The equation of motion and elastic waves --
4.8.1 Elastic waves --
4.9 The elastodynamic Green's function --
4.10 Problem set 4 --
5: Point defects --
5.1 Introduction --
5.2 The misfitting sphere model of a point defect 5.3 Interaction energies --
5.4 The -tensor --
5.5 Problem set 5 --
6: Dislocations --
6.1 Introduction --
6.2 Dislocations as the agents of plastic deformation --
6.3 Characterisation of dislocations: the Burgers circuit --
6.4 Glide, climb and cross-slip --
6.5 The interaction energy between a dislocation and another source of stress --
6.6 The Peach-Koehler force on a dislocation --
6.7 Volterra's formula --
6.8 The infinitesimal loop --
6.9 The dipole tensor of an infinitesimal loop --
6.10 The infinitesimal loop in isotropic elasticity --
6.11 Mura's formula
Series Title: Oxford series on materials modelling, 6.
Responsibility: Adrian P. Sutton

Abstract:

Although linear elasticity of defects in solids is well established, this textbook introduces the subject in a novel way by comparing key concepts at the atomic scale and at the usual continuum scale, and it explores the relationships between these treatments. There are exercises to work through, with solutions for instructors from the OUP website

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