| Description |
1 online resource (298 p.) |
| Contents |
Cover -- Half Title -- Series Page -- Title Page -- Copyright Page -- Contents -- Preface -- Chapter 1: Introductory Remarks -- 1.1. Some functional spaces -- 1.1.1. Periodic functions -- 1.1.2. Lax-Milgram Theorem -- 1.2. Variational formulation -- 1.3. Geometry of the two-phase composite -- 1.4. Two-scale convergence method -- 1.5. The concept of a homogenized equation -- 1.6. Two-scale convergence with time dependence -- 1.7. Potential and solenoidal fields -- Chapter 2: The Homogenization Technique Applied to Soft Tissue -- 2.1. Homogenization of soft tissue |
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2.2. Galerkin approximations -- 2.3. Derivation of the effective equation of u0 -- Chapter 3: Acoustics in Porous Media -- 3.1. Introduction -- 3.2. diphasic macroscopic behavior -- 3.2.1. Derivation of the effective equations for u0 -- 3.3. Well-posedness for problems (3.2.48) and (3.2.55) -- 3.4. The slightly compressible diphasic behavior -- Chapter 4: Wet Ionic, Piezoelectric Bone -- 4.1. introduction -- 4.2. Wet bone with ionic interaction -- 4.2.1. Nondimentionalized equations -- 4.2.2. Fluid equations with slight compressibility -- 4.2.3. Nernst-Plank equations |
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4.3. Homogenization using formal power series -- 4.4. Wet bone without ionic interaction -- 4.4.1. Reuss bound on the energy -- 4.4.2. Fluid displacement -- 4.4.3. Kinetic energy -- 4.4.4. Constitutive equations -- 4.5. Electrodynamics -- 4.5.1. Electrically isotropic solid -- 4.5.2. Electromagnetism in the fluid -- 4.5.3. Effective electromagnetic -- Chapter 5: Viscoelasticity, and Contact Friction between the Phases -- 5.1. Kelvin-Voigt Material -- 5.1.1.Two-scale convergence approach -- 5.2. Rigid particles in a visco-elastic medium -- 5.3. Equations of motion and contact conditions |
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5.3.1. Boundary conditions -- 5.3.2. Approximation of the contact conditions -- 5.3.3. Microscale equations -- 5.4. Two-scale expansions and formal homogenization -- 5.5. Model case I: Linear contact conditions -- 5.5.1. Cell problems -- 5.5.2. Averaged equations for Model I -- 5.6. Model II: Quadratic contact conditions -- 5.6.1. Averaged equation for Model II -- 5.7. Model III: Power type contact condition -- 5.7.1. Contact conditions, ansatz and cell problems -- 5.7.2. The relation between x 1 and x 0 -- 5.7.3. Effective stress -- 5.7.4. Effective drag force |
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Chapter 6: Acoustics in a Random Microstructure -- 6.1. Introduction -- 6.2. Stochastic two-scale limits -- 6.3. Periodic approximation -- Chapter 7: Non-Newtonian Interstitial Fluid -- 7.1. The slightly compressible polymer: Microscale problem -- 7.2. A priori estimates -- 7.3. Two-scale system -- 7.4. Description of the effective stress -- 7.5. Effective equations -- Chapter 8: Multiscale FEM for the Modeling of Cancellous Bone -- 8.1. Concept of the multiscale FEM -- 8.2. Microscale: The RVE proposal and effective properties -- 8.2.1. Modeling of the RVE for cancellous bone |
| Notes |
Description based upon print version of record |
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8.2.2. Modeling of the solid phase |
| Form |
Electronic book
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| Author |
Vasilic, Ana
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Klinge, Sandra
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Panchenko, Alex
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Hackl, Klaus
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| ISBN |
9780429533242 |
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0429533241 |
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