Microstructural Randomness and Scaling in Mechanics of Materials: 1st Edition (Hardback) book cover

Microstructural Randomness and Scaling in Mechanics of Materials

1st Edition

By Martin Ostoja-Starzewski

Chapman and Hall/CRC

497 pages | 135 B/W Illus.

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Hardback: 9781584884170
pub: 2007-08-13
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Description

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.

Table of Contents

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

About the Series

Modern Mechanics and Mathematics

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Subject Categories

BISAC Subject Codes/Headings:
MAT003000
MATHEMATICS / Applied
SCI041000
SCIENCE / Mechanics / General
SCI077000
SCIENCE / Solid State Physics