Ostoja-Starzewski Microstructural Randomness and Scaling in Mechanics of Materials

Erscheinungsjahr 2010
ISBN: 978-1-4200-1027-5
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 497 Seiten

Reihe: Modern Mechanics and Mathematics

An area at the intersection of solid mechanics, materials science, and stochastic mathematics, mechanics of materials often necessitates a stochastic approach to grasp the effects of spatial randomness. Using this approach, Microstructural Randomness and Scaling in Mechanics of Materials explores numerous stochastic models and methods used in the mechanics of random media and illustrates these in a variety of applications.

The book first offers a refresher in several tools used in stochastic mechanics, followed by two chapters that outline periodic and disordered planar lattice (spring) networks. Subsequent chapters discuss stress invariance in classical planar and micropolar elasticity and cover several topics not yet collected in book form, including the passage of a microstructure to an effective micropolar continuum.

After forming this foundation in various methods of stochastic mechanics, the book focuses on problems of microstructural randomness and scaling. It examines both representative and statistical volume elements (RVEs/SVEs) as well as micromechanically based stochastic finite elements (SFEs). The author also studies nonlinear elastic and inelastic materials, the stochastic formulation of thermomechanics with internal variables, and wave propagation in random media.

The concepts discussed in this comprehensive book can be applied to many situations, from micro and nanoelectromechanical systems (MEMS/NEMS) to geophysics.

Zielgruppe

Mechanical, aerospace, civil, and environmental engineers, applied mathematicians, physicists, and geophysicists.

Autoren/Hrsg.

Ostoja-Starzewski, Martin

Fachgebiete

• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde

Inhaltsverzeichnis

PREFACE

BASIC RANDOM MEDIA MODELS
Probability Measure of Geometric Objects
Basic Point Fields
Directional Data
Random Fibers, Random Line Fields, Tessellations
Basic Concepts and Definitions of Random Microstructures

RANDOM PROCESSES AND FIELDS
Elements of One-Dimensional Random Fields
Mechanics Problems on One-Dimensional Random Fields
Elements of Two- and Three-Dimensional Random Fields
Mechanics Problems on Two- and Three-Dimensional Random Fields
Ergodicity
The Maximum Entropy Method

PLANAR LATTICE MODELS: PERIODIC TOPOLOGIES AND ELASTOSTATICS
One-Dimensional Lattices
Planar Lattices: Classical Continua
Applications in Mechanics of Composites
Planar Lattices: Nonclassical Continua
Extension-Twist Coupling in a Helix

LATTICE MODELS: RIGIDITY, RANDOMNESS, DYNAMICS, AND OPTIMALITY
Rigidity of Networks
Spring Network Models for Disordered Topologies
Particle Models
Michell Trusses: Optimal Use of Material

TWO- VERSUS THREE-DIMENSIONAL CLASSICAL ELASTICITY
Basic Relations
The CLM Result and Stress Invariance
Poroelasticity

TWO- VERSUS THREE-DIMENSIONAL MICROPOLAR ELASTICITY
Micropolar Elastic Continua
Classical vis-à-vis Nonclassical (Elasticity) Models
Planar Cosserat Elasticity
The CLM Result and Stress Invariance
Effective Micropolar Moduli and Characteristic Lengths of Composites

MESOSCALE BOUNDS FOR LINEAR ELASTIC MICROSTRUCTURES
Micro-, Meso-, and Macroscales
Volume Averaging
Spatial Randomness
Hierarchies of Mesoscale Bounds
Examples of Hierarchies of Mesoscale Bounds
Moduli of Trabecular Bone

RANDOM FIELD MODELS AND STOCHASTIC FINITE ELEMENTS
Mesoscale Random Fields
Second-Order Properties of Mesoscale Random Fields
Does There Exist a Locally Isotropic, Smooth Elastic Material?
Stochastic Finite Elements for Elastic Media
Method of Slip-Lines for Inhomogeneous Plastic Media
Michell Trusses in the Presence of Random Microstructure

HIERARCHIES OF MESOSCALE BOUNDS FOR NONLINEAR AND INELASTIC MICROSTRUCTURES
Physically Nonlinear Elastic Microstructures
Finite Elasticity of Random Composites
Elastic-Plastic Microstructures
Rigid-Perfectly Plastic Microstructures
Viscoelastic Microstructures
Stokes Flow in Porous Media
Thermoelastic Microstructures
Scaling and Stochastic Evolution in Damage Phenomena
Comparison of Scaling Trends

MESOSCALE RESPONSE IN THERMOMECHANICS OF RANDOM MEDIA
From Statistical Mechanics to Continuum Thermodynamics
Extensions of the Hill Condition
Legendre Transformations in (Thermo)Elasticity
Thermodynamic Orthogonality on the Mesoscale
Complex versus Compound Processes: The Scaling Viewpoint
Toward Continuum Mechanics of Fractal Media

WAVES AND WAVEFRONTS IN RANDOM MEDIA
Basic Methods in Stochastic Wave Propagation
Toward Spectral Finite Elements for Random Media
Waves in Random 1D Composites
Transient Waves in Heterogeneous Nonlinear Media
Acceleration Wavefronts in Nonlinear Media

BIBLIOGRAPHY
INDEX