Asymptotic models of fields in dilute and densely packed composites / A.B. Movchan, N.V. Movchan, C.G. Poulton.

Format:

Book

Author/Creator:

Movchan, A. B. (Alexander B.)

Contributor:

Movchan, N. V. (Nataliya V.)

Poulton, C. G. (Chris G.)

Language:

English

Subjects (All):

Boundary value problems--Asymptotic theory.

Boundary value problems.

Composite materials--Defects--Mathematical models.

Composite materials.

Differential equations, Partial--Asymptotic theory.

Differential equations, Partial.

Elasticity.

Electromagnetism.

Physical Description:

1 online resource (204 p.)

Edition:

1st ed.

Place of Publication:

London : Imperial College Press ; River Edge, NJ : World Scientific Pub. [distributor], c2002.

Language Note:

English

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 me

Contents:

Contents ; Preface ; 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 1.1.5 Dipole matrices for inclusions ; 1.1.6 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 ; 1.4 Close-range contact between elastic inclusions ; 1.4.1 Governing equations ; 1.4.2 Complex potentials ; 1.4.3 Analysis for two circular elastic inclusions

1.4.4 Square array of circular inclusions

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 185-188) and index.

ISBN:

9781860949616

1860949614

OCLC:

879074395