Microstructural Randomness and Scaling in Mechanics of Materials

ISBN-13: 9781584884170 / Angielski / Twarda / 2007 / 497 str.

Martin Ostoja-Starzewski

Opis

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.

Spis treści

PREFACEBASIC RANDOM MEDIA MODELSProbability Measure of Geometric ObjectsBasic Point FieldsDirectional Data Random Fibers, Random Line Fields, TessellationsBasic Concepts and Definitions of Random MicrostructuresRANDOM PROCESSES AND FIELDSElements of One-Dimensional Random FieldsMechanics Problems on One-Dimensional Random FieldsElements of Two- and Three-Dimensional Random FieldsMechanics Problems on Two- and Three-Dimensional Random FieldsErgodicity The Maximum Entropy MethodPLANAR LATTICE MODELS: PERIODIC TOPOLOGIES AND ELASTOSTATICS One-Dimensional Lattices Planar Lattices: Classical ContinuaApplications in Mechanics of Composites Planar Lattices: Nonclassical ContinuaExtension-Twist Coupling in a HelixLATTICE MODELS: RIGIDITY, RANDOMNESS, DYNAMICS, AND OPTIMALITY Rigidity of NetworksSpring Network Models for Disordered TopologiesParticle ModelsMichell Trusses: Optimal Use of MaterialTWO- VERSUS THREE-DIMENSIONAL CLASSICAL ELASTICITY Basic Relations The CLM Result and Stress InvariancePoroelasticityTWO- VERSUS THREE-DIMENSIONAL MICROPOLAR ELASTICITY Micropolar Elastic Continua Classical vis-à-vis Nonclassical (Elasticity) ModelsPlanar Cosserat Elasticity The CLM Result and Stress InvarianceEffective Micropolar Moduli and Characteristic Lengths of CompositesMESOSCALE BOUNDS FOR LINEAR ELASTIC MICROSTRUCTURESMicro-, Meso-, and MacroscalesVolume AveragingSpatial Randomness Hierarchies of Mesoscale Bounds Examples of Hierarchies of Mesoscale BoundsModuli of Trabecular BoneRANDOM 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 MediaMethod of Slip-Lines for Inhomogeneous Plastic Media Michell Trusses in the Presence of Random MicrostructureHIERARCHIES OF MESOSCALE BOUNDS FOR NONLINEAR AND INELASTIC MICROSTRUCTURESPhysically Nonlinear Elastic Microstructures Finite Elasticity of Random CompositesElastic-Plastic MicrostructuresRigid-Perfectly Plastic MicrostructuresViscoelastic Microstructures Stokes Flow in Porous MediaThermoelastic MicrostructuresScaling and Stochastic Evolution in Damage PhenomenaComparison of Scaling TrendsMESOSCALE RESPONSE IN THERMOMECHANICS OF RANDOM MEDIAFrom Statistical Mechanics to Continuum ThermodynamicsExtensions of the Hill Condition Legendre Transformations in (Thermo)ElasticityThermodynamic Orthogonality on the MesoscaleComplex versus Compound Processes: The Scaling ViewpointToward Continuum Mechanics of Fractal MediaWAVES AND WAVEFRONTS IN RANDOM MEDIABasic Methods in Stochastic Wave PropagationToward Spectral Finite Elements for Random MediaWaves in Random 1D CompositesTransient Waves in Heterogeneous Nonlinear MediaAcceleration Wavefronts in Nonlinear MediaBIBLIOGRAPHYINDEX

O autorze

Martin Ostoja-Starzewski