LEADER 05624nam 2200697Ia 450 001 9910830680803321 005 20170815145117.0 010 $a1-282-68632-1 010 $a9786612686320 010 $a0-470-61203-7 010 $a0-470-61044-1 035 $a(CKB)2550000000005836 035 $a(EBL)477624 035 $a(OCoLC)609853534 035 $a(SSID)ssj0000354325 035 $a(PQKBManifestationID)11259049 035 $a(PQKBTitleCode)TC0000354325 035 $a(PQKBWorkID)10313162 035 $a(PQKB)10022305 035 $a(MiAaPQ)EBC477624 035 $a(PPN)153401478 035 $a(EXLCZ)992550000000005836 100 $a20090504d2009 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aHomogenization of coupled phenomena in heterogenous media$b[electronic resource] /$fJean-Louis Auriault, Claude Boutin, Christian Geindreau 210 $aLondon, UK $cISTE ;$aHoboken, NJ $cJ. Wiley$d2009 215 $a1 online resource (478 p.) 225 1 $aISTE ;$vv.149 300 $aDescription based upon print version of record. 311 $a1-84821-161-9 320 $aIncludes bibliographical references and index. 327 $aHomogenization of Coupled Phenomena in Heterogenous Media; Contents; Main notations; Introduction; Part one. Upscaling Methods; Chapter 1. An Introduction to Upscaling Methods; 1.1. Introduction; 1.2. Heat transfer in a periodic bilaminate composite; 1.2.1. Transfer parallel to the layers; 1.2.2. Transfer perpendicular to the layers; 1.2.3. Comments; 1.2.4. Characteristic macroscopic length; 1.3. Bounds on the effective coefficients; 1.3.1. Theorem of virtual powers; 1.3.2. Minima in the complementary power and potential power; 1.3.3. Hill principle; 1.3.4. Voigt and Reuss bounds 327 $a1.3.4.1. Upper bound: Voigt1.3.4.2. Lower bound: Reuss; 1.3.5. Comments; 1.3.6. Hashin and Shtrikman's bounds; 1.3.7. Higher-order bounds; 1.4. Self-consistent method; 1.4.1. Boundary-value problem; 1.4.2. Self-consistent hypothesis; 1.4.3. Self-consistent method with simple inclusions; 1.4.3.1. Determination of ?? for a homogenous spherical inclusion; 1.4.3.2. Self-consistent estimate; 1.4.3.3. Implicit morphological constraints; 1.4.4. Comments; Chapter 2. Heterogenous Medium: Is an Equivalent Macroscopic Description Possible?; 2.1. Introduction 327 $a2.2. Comments on techniques for micro-macro upscaling2.2.1. Homogenization techniques for separated length scales; 2.2.2. The ideal homogenization method; 2.3. Statistical modeling; 2.4. Method of multiple scale expansions; 2.4.1. Formulation of multiple scale problems; 2.4.1.1. Homogenizability conditions; 2.4.1.2. Double spatial variable; 2.4.1.3. Stationarity, asymptotic expansions; 2.4.2. Methodology; 2.4.3. Parallels between macroscopic models for materials with periodic and random structures; 2.4.3.1. Periodic materials; 2.4.3.2. Random materials with a REV 327 $a2.4.4. Hill macro-homogenity and separation of scales2.5. Comments on multiple scale methods and statistical methods; 2.5.1. On the periodicity, the stationarity and the concept of the REV; 2.5.2. On the absence of, or need for macroscopic prerequisites; 2.5.3. On the homogenizability and consistency of the macroscopic description; 2.5.4. On the treatment of problems with several small parameters; Chapter 3. Homogenization by Multiple Scale Asymptotic Expansions; 3.1. Introduction; 3.2. Separation of scales: intuitive approach and experimental visualization 327 $a3.2.1. Intuitive approach to the separation of scales3.2.2. Experimental visualization of fields with two length scales; 3.2.2.1. Investigation of a flexible net; 3.2.2.2. Photoelastic investigation of a perforated plate; 3.3. One-dimensional example; 3.3.1. Elasto-statics; 3.3.1.1. Equivalent macroscopic description; 3.3.1.2. Comments; 3.3.2. Elasto-dynamics; 3.3.2.1. Macroscopic dynamics: Pl = O(?2); 3.3.2.2. Steady state: Pl = O(?3); 3.3.2.3. Non-homogenizable description: Pl = O(?); 3.3.3. Comments on the different possible choices for spatial variables 327 $a3.4. Expressing problems within the formalism of multiple scales 330 $aBoth naturally-occurring and man-made materials are often heterogeneous materials formed of various constituents with different properties and behaviours. Studies are usually carried out on volumes of materials that contain a large number of heterogeneities. Describing these media by using appropriate mathematical models to describe each constituent turns out to be an intractable problem. Instead they are generally investigated by using an equivalent macroscopic description - relative to the microscopic heterogeneity scale - which describes the overall behaviour of the media. Fundamental que 410 0$aISTE 606 $aInhomogeneous materials$xMathematical models 606 $aCoupled problems (Complex systems) 606 $aHomogenization (Differential equations) 615 0$aInhomogeneous materials$xMathematical models. 615 0$aCoupled problems (Complex systems) 615 0$aHomogenization (Differential equations) 676 $a620.1/1015118 676 $a620.11015118 700 $aAuriault$b J.-L$g(Jean-Louis)$01604346 701 $aBoutin$b Claude$01604347 701 $aGeindreau$b Christian$01604348 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910830680803321 996 $aHomogenization of coupled phenomena in heterogenous media$93929132 997 $aUNINA