LEADER 05156nam 2200601 a 450 001 9910810941503321 005 20240516083404.0 010 $a1-283-14381-X 010 $a9786613143815 010 $a981-4282-45-6 035 $a(CKB)3360000000001325 035 $a(EBL)731217 035 $a(OCoLC)740444832 035 $a(SSID)ssj0000523212 035 $a(PQKBManifestationID)12178625 035 $a(PQKBTitleCode)TC0000523212 035 $a(PQKBWorkID)10557445 035 $a(PQKB)10412759 035 $a(MiAaPQ)EBC731217 035 $a(WSP)00007427 035 $a(Au-PeEL)EBL731217 035 $a(CaPaEBR)ebr10480003 035 $a(CaONFJC)MIL314381 035 $a(EXLCZ)993360000000001325 100 $a20110401d2010 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aHomogenization methods for multiscale mechanics /$fChiang C. Mei, Bogdan Vernescu 205 $a1st ed. 210 $aHackensack, N.J. $cWorld Scientific$d2010 215 $a1 online resource (350 p.) 300 $aDescription based upon print version of record. 311 $a981-4282-44-8 320 $aIncludes bibliographical references and index. 327 $aIntroductory examples of homogenization method. Long waves in a layered elastic medium ; Short waves in a weakly stratified elastic medium ; Dispersion of passive solute in pipe flow ; Typical procedure of homogenization analysis -- Diffusion in a composite. Basic equations for two components in perfect contact ; Effective equation on the macroscale ; Effective boundary condition ; Symmetry and positiveness of effective conductivity ; Laminated composites ; Bounds for effective conductivity ; Hashin-Shtrikman bounds ; Other approximate results for dilute inclusions ; Thermal resistance at the interface ; Laminated composites with thermal resistance ; Bounds for the effective conductivity ; Chemical transport in aggregated soil ; Appendix 2A : heat transfer in a two-slab system -- Seepage in rigid porous media. Equations for seepage flow and Darcy's law ; Uniqueness of the cell boundary-value problem ; Symmetry and positiveness of hydraulic conductivity ; Numerical computation of the permeability tensor ; Seepage of a compressible fluid ; Two-dimensional flow through a three-dimensional matrix ; Porous media with three scales ; Brinkman's modification of Darcy's law ; Effects of weak fluid intertia ; Appendix 3A : spatial averaging theorem -- Dispersion in periodic media or flows. Passive solute in a two-scale seepage flow ; Macrodispersion in a three-scale porous medium ; Dispersion and transport in a wave boundary layer above the seabed ; Appendix 4A : derivation of convection-dispersion equation ; Appendix 4B : an alternate form of macrodispersion tensor -- Heterogeneous elastic materials. effective equations on the macroscale ; The effective elastic coefficients ; Application to fiber-reinforced composite ; Elastic panels with periodic microstructure ; Variational principles and bounds for the elastic moduli ; Hashin-Shtrikman bounds ; Partially cohesive composites ; Appendix 5A : properties of a tensor of fourth rank -- Deformable porous media. Basic equations for fluid and solid phases ; Scale estimates ; Multiple-scale expansions ; Averaged total momentum of the composite ; Averaged mass conservation of fluid phase ; Averaged fluid momentum ; Time-Harmonic motion ; Properties of the effective coefficients ; Computed elastic coefficients ; Boundary-layer approximation for macroscale problems ; Appendix 6A : properties of the compliance tensor ; Appendix 6B : variational principle for the elastostatic problem in a cell -- Wave propagation in inhomogeneous media. Long wave through a compact cylinder array ; Bragg scattering of short waves by a cylinder array ; Sound propagation in a bubbly liquid ; One-dimensional sound through a weakly random medium ; Weakly nonlinear dispersive waves in a random medium ; Harmonic generation in random media. 330 $aIn many physical problems several scales present either in space or in time, caused by either inhomogeneity of the medium or complexity of the mechanical process. A fundamental approach is to first construct micro-scale models, and then deduce the macro-scale laws and the constitutive relations by properly averaging over the micro-scale. The perturbation method of multiple scales can be used to derive averaged equations for a much larger scale from considerations of the small scales. In the mechanics of multiscale media, the analytical scheme of upscaling is known as the Theory of Homogenizati 606 $aHomogenization (Differential equations) 606 $aMathematical physics 615 0$aHomogenization (Differential equations) 615 0$aMathematical physics. 676 $a515.3/53 700 $aMei$b Chiang C$030497 701 $aVernescu$b Bogdan$01718326 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910810941503321 996 $aHomogenization methods for multiscale mechanics$94115182 997 $aUNINA