| Description |
1 online resource (xi, 190 pages) : illustrations |
| Contents |
Preface; Contents; Chapter 1 Long and close range interaction within elastic structures; 1.1 Dilute composite structures. Scalar problems; 1.1.1 An elementary example. Motivation; 1.1.2 Asymptotic algorithm involving a boundary layer; 1.1.2.1 Formulation of the problem; 1.1.2.2 The leading-order approximation; 1.1.2.3 Asymptotic formula for the energy; 1.1.3 The dipole matrix; 1.1.3.1 Definition of the dipole matrix; 1.1.3.2 Symmetry of the dipole matrix; 1.1.3.3 The energy asymptotics for a body with a small void; 1.1.4 Dipole matrix for a 2D void in an infinite plane |
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1.1.5 Dipole matrices for inclusions1.1.6 A note on homogenization of dilute periodic structures; 1.2 Dipole fields in vector problems of linear elasticity; 1.2.1 Definitions and governing equations; 1.2.2 Physical interpretation; 1.2.3 Evaluation of the elements of the dipole matrix; 1.2.4 Examples; 1.2.5 The energy equivalent voids; 1.3 Circular elastic inclusions; 1.3.1 Inclusions with perfect bonding at the interface; 1.3.2 Dipole tensors for imperfectly bonded inclusions; 1.3.2.1 Derivation of transmission conditions at the zero-thickness interface; 1.3.2.2 Neutral coated inclusions |
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1.4 Close-range contact between elastic inclusions1.4.1 Governing equations; 1.4.2 Complex potentials; 1.4.3 Analysis for two circular elastic inclusions; 1.4.4 Square array of circular inclusions; 1.4.5 Integral approximation for the multipole coefficients. Inclusions close to touching; 1.4.5.1 Scalar problem; 1.4.5.2 Vector problem; 1.5 Discrete lattice approximations; 1.5.1 Illustrative one-dimensional example; 1.5.2 Two-dimensional array of obstacles; Chapter 2 Dipole tensors in spectral problems of elasticity; 2.1 Asymptotic behaviour of fields near the vertex of a thin conical inclusion |
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2.1.1 Spectral problem on a unit sphere2.1.2 Boundary layer solution; 2.1.2.1 The leading term; 2.1.2.2 Problem for w(2); 2.1.3 Stress singularity exponent A2; 2.2 Imperfect interface. ""Coated"" conical inclusion; 2.2.1 Formulation of the problem; 2.2.2 Boundary layer solution; 2.2.2.1 Change of coordinates for the ""coating"" layer; 2.2.2.2 Problem for w(1); 2.2.2.3 Problem for w(2); 2.2.2.4 Asymptotic behaviour of w(2) at infinity; 2.2.3 Stress singularity exponent A2; 2.2.4 Some examples. Discussion and conclusions; Chapter 3 Multipole methods and homogenisation in two-dimensions |
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3.1 The method of Rayleigh for static problems3.1.1 The multipole expansion and effective properties; 3.1.2 Solution to the static problem; 3.2 The spectral problem; 3.2.1 Formulation and Bloch waves; 3.2.2 The dynamic multipole method; 3.2.3 The dynamic lattice sums; 3.2.4 The integral equation and the Rayleigh identity; 3.2.5 The dipole approximation; 3.3 The singularly perturbed problem and non-commuting limits; 3.3.1 The Neumann problem and non-commuting limits; 3.3.2 The Dirichlet problem and source neutrality; 3.4 Non-commuting limits for the effective properties |
| Summary |
This monograph provides a systematic study of asymptotic models of continuum mechanics for composite structures, which are either dilute (for example, two-phase composite structures with small inclusions) or densely packed (in this case inclusions may be close to touching). It is based on the results of recent research and includes a comprehensive analysis of dipole and multipole fields associated with defects in solids. The text covers static problems of elasticity in dilute composites as well as spectral problems. Applications of the mathematical models included in the book are in damage mec |
| Bibliography |
Includes bibliographical references (pages 185-188) and index |
| Notes |
Print version record |
| Subject |
Boundary value problems -- Asymptotic theory.
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Composite materials -- Defects -- Mathematical models
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Differential equations, Partial -- Asymptotic theory.
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Elasticity.
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Electromagnetism.
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Elasticity
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electromagnetism.
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MATHEMATICS -- Differential Equations -- Partial.
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Boundary value problems -- Asymptotic theory
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Differential equations, Partial -- Asymptotic theory
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Elasticity
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Electromagnetism
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| Form |
Electronic book
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| Author |
Movchan, N. V. (Nataliya V.)
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Poulton, C. G. (Chris G.)
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| LC no. |
2004272773 |
| ISBN |
9781860949616 |
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1860949614 |
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