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Homogenization of coupled phenomena in heterogenous media [[electronic resource] /] / Jean-Louis Auriault, Claude Boutin, Christian Geindreau
Homogenization of coupled phenomena in heterogenous media [[electronic resource] /] / Jean-Louis Auriault, Claude Boutin, Christian Geindreau
Autore Auriault J.-L (Jean-Louis)
Pubbl/distr/stampa London, UK, : ISTE
Descrizione fisica 1 online resource (478 p.)
Disciplina 620.1/1015118
620.11015118
Altri autori (Persone) BoutinClaude
GeindreauChristian
Collana ISTE
Soggetto topico Inhomogeneous materials - Mathematical models
Coupled problems (Complex systems)
Homogenization (Differential equations)
ISBN 1-282-68632-1
9786612686320
0-470-61203-7
0-470-61044-1
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Homogenization 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
1.3.4.1. 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 βα 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
2.2. 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
2.4.4. 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
3.2.1. 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(ε2); 3.3.2.2. Steady state: Pl = O(ε3); 3.3.2.3. Non-homogenizable description: Pl = O(ε); 3.3.3. Comments on the different possible choices for spatial variables
3.4. Expressing problems within the formalism of multiple scales
Record Nr. UNINA-9910139470003321
Auriault J.-L (Jean-Louis)  
London, UK, : ISTE
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Homogenization of coupled phenomena in heterogenous media [[electronic resource] /] / Jean-Louis Auriault, Claude Boutin, Christian Geindreau
Homogenization of coupled phenomena in heterogenous media [[electronic resource] /] / Jean-Louis Auriault, Claude Boutin, Christian Geindreau
Autore Auriault J.-L (Jean-Louis)
Pubbl/distr/stampa London, UK, : ISTE
Descrizione fisica 1 online resource (478 p.)
Disciplina 620.1/1015118
620.11015118
Altri autori (Persone) BoutinClaude
GeindreauChristian
Collana ISTE
Soggetto topico Inhomogeneous materials - Mathematical models
Coupled problems (Complex systems)
Homogenization (Differential equations)
ISBN 1-282-68632-1
9786612686320
0-470-61203-7
0-470-61044-1
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Homogenization 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
1.3.4.1. 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 βα 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
2.2. 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
2.4.4. 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
3.2.1. 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(ε2); 3.3.2.2. Steady state: Pl = O(ε3); 3.3.2.3. Non-homogenizable description: Pl = O(ε); 3.3.3. Comments on the different possible choices for spatial variables
3.4. Expressing problems within the formalism of multiple scales
Record Nr. UNINA-9910830680803321
Auriault J.-L (Jean-Louis)  
London, UK, : ISTE
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Homogenization of coupled phenomena in heterogenous media / / Jean-Louis Auriault, Claude Boutin, Christian Geindreau
Homogenization of coupled phenomena in heterogenous media / / Jean-Louis Auriault, Claude Boutin, Christian Geindreau
Autore Auriault J.-L (Jean-Louis)
Pubbl/distr/stampa London, UK, : ISTE
Descrizione fisica 1 online resource (478 p.)
Disciplina 620.1/1015118
620.11015118
Altri autori (Persone) BoutinClaude
GeindreauChristian
Collana ISTE
Soggetto topico Inhomogeneous materials - Mathematical models
Coupled problems (Complex systems)
Homogenization (Differential equations)
ISBN 1-282-68632-1
9786612686320
0-470-61203-7
0-470-61044-1
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Homogenization 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
1.3.4.1. 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 βα 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
2.2. 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
2.4.4. 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
3.2.1. 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(ε2); 3.3.2.2. Steady state: Pl = O(ε3); 3.3.2.3. Non-homogenizable description: Pl = O(ε); 3.3.3. Comments on the different possible choices for spatial variables
3.4. Expressing problems within the formalism of multiple scales
Record Nr. UNINA-9910877482603321
Auriault J.-L (Jean-Louis)  
London, UK, : ISTE
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui