LEADER 05475nam 2200721Ia 450 001 9910816450503321 005 20240404153200.0 010 $a1-86094-961-4 035 $a(CKB)1000000000399195 035 $a(EBL)1681508 035 $a(OCoLC)879074395 035 $a(SSID)ssj0000107020 035 $a(PQKBManifestationID)11133719 035 $a(PQKBTitleCode)TC0000107020 035 $a(PQKBWorkID)10012325 035 $a(PQKB)11540850 035 $a(MiAaPQ)EBC1681508 035 $a(WSP)0000P258 035 $a(Au-PeEL)EBL1681508 035 $a(CaPaEBR)ebr10201305 035 $a(CaONFJC)MIL505351 035 $a(EXLCZ)991000000000399195 100 $a20030910d2002 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aAsymptotic models of fields in dilute and densely packed composites /$fA.B. Movchan, N.V. Movchan, C.G. Poulton 205 $a1st ed. 210 $aLondon $cImperial College Press ;$aRiver Edge, NJ $cWorld Scientific Pub. [distributor]$dc2002 215 $a1 online resource (204 p.) 300 $aDescription based upon print version of record. 311 $a1-86094-318-7 320 $aIncludes bibliographical references (p. 185-188) and index. 327 $aContents ; 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 327 $a1.1.2.2 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 327 $a1.1.4 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 327 $a1.2.2 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 327 $a1.3.2.1 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 327 $a1.4.4 Square array of circular inclusions 330 $a 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 606 $aBoundary value problems$xAsymptotic theory 606 $aComposite materials$xDefects$xMathematical models 606 $aDifferential equations, Partial$xAsymptotic theory 606 $aElasticity 606 $aElectromagnetism 615 0$aBoundary value problems$xAsymptotic theory. 615 0$aComposite materials$xDefects$xMathematical models. 615 0$aDifferential equations, Partial$xAsymptotic theory. 615 0$aElasticity. 615 0$aElectromagnetism. 676 $a620.118 700 $aMovchan$b A. B$g(Alexander B.)$058644 701 $aMovchan$b N. V$g(Nataliya V.)$01441467 701 $aPoulton$b C. G$g(Chris G.)$01696336 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910816450503321 996 $aAsymptotic models of fields in dilute and densely packed composites$94076233 997 $aUNINA