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Produktbild: Applications of Homogenization Theory to the Study of Mineralized Tissue

Applications of Homogenization Theory to the Study of Mineralized Tissue Tissu

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Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

01.12.2022

Abbildungen

schwarz-weiss Illustrationen, Tabellen, schwarz-weiss

Verlag

Taylor & Francis

Seitenzahl

283

Maße (L/B/H)

23,4/15,6/1,6 cm

Gewicht

453 g

Sprache

Englisch

ISBN

978-0-367-71372-0

Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

01.12.2022

Abbildungen

schwarz-weiss Illustrationen, Tabellen, schwarz-weiss

Verlag

Taylor & Francis

Seitenzahl

283

Maße (L/B/H)

23,4/15,6/1,6 cm

Gewicht

453 g

Sprache

Englisch

ISBN

978-0-367-71372-0

Herstelleradresse

Libri GmbH
Europaallee 1
36244 Bad Hersfeld
DE

Email: gpsr@libri.de

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  • Produktbild: Applications of Homogenization Theory to the Study of Mineralized Tissue

  • Introductory Remarks

    Some Functional Spaces

    Variational Formulation

    Geometry of Two Phase Composite

    Two-scale Convergence Method

    The Concept of a Homogenized Equation

    Two-Scale convergence with time dependence

    Potential and Solenoidal Fields

    The Homogenization Technique Applied to Soft Tissue

    Homogenization of Soft Tissue

    Galerkin approximations

    Derivation of the effective equation of U0

    Acoustics in Porous Media

    Introduction

    Diphasic Macroscopic Behavior

    Well-posedness for problem (3.2.49 and 3.2.55)

    The slightly compressible di-phasic behavior

    Wet Ionic, Piezo-electric Bone

    Introduction

    Wet bone with ionic interaction

    Homogenization using Formal Power Series

    Wet bone without ionic interaction

    Electrodynamics

    Visco-elasticity and Contact Friction Between the Phases

    Kelvin-Voigt Material

    Rigid Particles in a Visco-elastic Medium

    Equations of motion and contact conditions

    Two-scale expansions and formal homogenization

    Model case I: Linear contract conditions

    Model case II: Quadratic contract conditions

    Model case III: Power type contact condition

    Acoustics in a Random Microstructure

    Introduction

    Stochastic Two-scale limits

    Periodic Approximation

    Non-Newtonian Interstitial Fluid

    The Slightly Compressible Polymer. Microscale Problem

    A Priori Estimates

    Two-Scale System

    Description of the effective stress

    Effective equations

    Multiscale FEM for the modeling of cancellous bone

    Concept of the multiscale FEM

    Microscale: Modeling of the RVE and calculation of the effective material properties

    Macroscale: Simulation of the ultrasonic test

    Simplified version of the RVE and comparison with the experimental results

    Anisotropy of cancellous bone

    Investigation of the influence of reflection on the attenuation of cancellous bone

    Determination of the geometry of the RVE for cancellous bone by using the effective complex shear modulus

    G-convergence and Homogenization of Viscoelastic Flows

    Introduction

    Main definitions. Corrector operators for G-convergence

    A scalar elliptic equation in divergence form

    Homogenization of two-phase visco-elastic flows with time-varying interface

    Main theorem and outline of the proof

    Corrector operators and oscillating test functions

    Inertial terms in the momentum balance equation

    Effective deviatoric stress. Proof of the main theorem

    Fluid-structure interaction

    Biot Type Models for Bone Mechanics

    Bone Rigidity

    Anisotropic Biot Systems

    The Case of a non-Newtonian Interstitial Fluid

    Some Time-Dependent Solutions to the Biot System

    Creation of RVE for Bone Microstructure

    The RVE Model

    Reformulation as a Graves-like scheme

    Absorbring boundary condition-perfectly matched layer

    Discretized systems

    Bone Growth and Adaptive Elasticity

    The Model

    Scalings of Unknowns

    Asymptotic Solutions

    Further Reading