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材料微观组织的随机性及其尺度效应对材料力学性能的影响（英文版）
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Microstructural Randomness and Scaling in Mechanics of Materials 简介： 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. 目录： Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii About the Author. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xxv 1 Basic Random Media Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Probability Measure of Geometric Objects . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1 Definitions of Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.2 Probabilities on Countable and Euclidean Sample Spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.1.2.1 is a Countable Set: = {ω1, ω2, . . .} . . . . . . . . . . . .4 1.1.2.2 is a 1D Euclidean Space: = R. . . . . . . . . . . . . . . .7 1.1.2.3 is a 2D Euclidean Space: = R2 . . . . . . . . . . . . . . .8 1.1.3 Random Points, Lines, and Planes. . . . . . . . . . . . . . . . . . . . . . .11 1.1.3.1 Random Lines in Two Dimensions. . . . . . . . . . . . . .11 1.1.3.2 Planes in Three Dimensions . . . . . . . . . . . . . . . . . . . . 14 1.1.3.3 Straight Lines in Three Dimensions. . . . . . . . . . . . . 14 1.2 Basic Point Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.2.1 Bernoulli Trials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.2.2 Example—Model of a Fiber Structure of Paper . . . . . . . . . . 15 1.2.3 Generalization to Many Types of Outcomes . . . . . . . . . . . . . 17 1.2.4 Binomial and Multinomial Point Fields . . . . . . . . . . . . . . . . . 17 1.2.4.1 Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.2.4.2 Simulation of a Binomial Point Field with n Points. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18 1.2.4.3 Generalization to a Multinomial Point Field . . . . 20 1.2.5 Bernoulli Lattice Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.2.6 Poisson Point Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 1.2.6.1 Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 1.2.6.2 Simulation of a Poisson Point Field . . . . . . . . . . . . . 22 1.2.6.3 Inhomogeneous Poisson Point Field . . . . . . . . . . . . 22 1.2.6.4 Inhibition and Hard-Core Processes . . . . . . . . . . . . 23 1.3 Directional Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.3.1 Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.3.2 Circular Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 1.4 Random Fibers, Random Line Fields, Tessellations . . . . . . . . . . . . . 27 1.4.1 Poisson Random Lines in Plane . . . . . . . . . . . . . . . . . . . . . . . . . 27 1.4.2 Finite Fiber Field in Plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 1.4.3 Random Tessellations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .30 1.4.3.1 Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 1.4.3.2 Planar (Poisson-)Voronoi Tessellations and Delaunay Triangulations . . . . . . . . . . . . . . . . . . .31 1.4.3.3 Modifications of Voronoi Tessellations . . . . . . . . . . 31 1.4.3.4 Random Crack Model . . . . . . . . . . . . . . . . . . . . . . . . . . 34 1.5 Basic Concepts and Definitions of Random Microstructures . . . . 35 1.5.1 General. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .35 1.5.1.1 Germ-Grain and Boolean Models. . . . . . . . . . . . . . . 35 1.5.1.2 Flocs as Continua . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 1.5.2 Toward Mathematical Morphology . . . . . . . . . . . . . . . . . . . . . 38 2 Random Processes and Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 2.1 Elements of One-Dimensional Random Fields. . . . . . . . . . . . . . . . . .45 2.1.1 Scalar Random Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 2.1.1.1 Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 2.1.1.2 Homogeneity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 2.1.2 Vector Random Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 2.2 Mechanics Problems on One-Dimensional Random Fields . . . . . .55 2.2.1 Propagation of Surface Waves along Random Boundaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 2.2.2 Fracture of Brittle Microbeams . . . . . . . . . . . . . . . . . . . . . . . . . . 57 2.2.2.1 Randomness of Microbeams. . . . . . . . . . . . . . . . . . . .57 2.2.2.2 Strain Energy Release Rate in Random Microbeams. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .58 2.2.2.3 Stochastic Crack Stability . . . . . . . . . . . . . . . . . . . . . . .61 2.3 Elements of Two- and Three-Dimensional Random Fields . . . . . . 62 2.3.1 Scalar and Vector Fields. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .62 2.3.1.1 Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 2.3.1.2 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 2.3.1.3 Properties of the Correlation Function Anisotropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 2.3.2 Random Tensor Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 2.3.2.1 Second-Rank Tensor Fields . . . . . . . . . . . . . . . . . . . . . 69 2.3.2.2 Fourth-Rank Tensor Fields . . . . . . . . . . . . . . . . . . . . . 71 2.4 Mechanics Problems on Two- and Three-Dimensional Random Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 2.4.1 Mean Field Equations of Random Materials . . . . . . . . . . . . . 72 2.4.2 Mean Field Equations of Turbulent Media. . . . . . . . . . . . . . .73 2.5 Ergodicity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 2.5.1 Basic Considerations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .75 2.5.2 Computation of (2.146) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 2.5.3 Conditions for (2.146) to Hold . . . . . . . . . . . . . . . . . . . . . . . . . . 76 2.5.4 Existence of the Limit in (2.146) . . . . . . . . . . . . . . . . . . . . . . . . . 76 ………………………………………………………………………………目录太多，中间的省略，需要的下载下来看看吧……………… 11.2.2 Spectral Finite Element for Flexural Waves. . . . . . . . . . .398 11.2.2.1 Deterministic Case. . . . . . . . . . . . . . . . . . . . . . . . .398 11.2.2.2 Random Case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .400 11.2.3 Observations and Related Work . . . . . . . . . . . . . . . . . . . . . 402 11.3 Waves in Random 1D Composites . . . . . . . . . . . . . . . . . . . . . . . . . . . 403 11.3.1 Motion in an Imperfectly Periodic Composite . . . . . . . . 403 11.3.1.1 Random Evolutions. . . . . . . . . . . . . . . . . . . . . . . .403 11.3.1.2 Effects of Imperfections on Floquet Waves. . . . . . . . . . . . . . . . . . . . . . . . . . . . .404 11.3.2 Waves in Randomly Segmented Elastic Bars . . . . . . . . . 407 11.4 TransientWaves in Heterogeneous Nonlinear Media . . . . . . . . . 408 11.4.1 A Class of Models of Random Media . . . . . . . . . . . . . . . . 408 11.4.2 Pulse Propagation in a Linear Elastic Microstructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 410 11.4.3 Pulse Propagation in Nonlinear Microstructures . . . . . 414 11.4.3.1 Bilinear Elastic Microstructures . . . . . . . . . . . . 414 11.4.3.2 Nonlinear Elastic Microstructures . . . . . . . . . . 417 11.4.3.3 Hysteretic Microstructures . . . . . . . . . . . . . . . . . 419 11.5 AccelerationWavefronts in Nonlinear Media . . . . . . . . . . . . . . . . 422 11.5.1 Microscale Heterogeneity versus Wavefront Thickness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422 11.5.1.1 Basic Considerations. . . . . . . . . . . . . . . . . . . . . . .422 11.5.1.2 Mesoscale Response . . . . . . . . . . . . . . . . . . . . . . . 425 11.5.2 Wavefront Dynamics in Random Microstructures . . . . 427 11.5.2.1 Model with One White Noise . . . . . . . . . . . . . . 427 11.5.2.2 Model with Two Correlated Gaussian Noises . . . . . . . . . . . . . . . . . . . . . . . . . . . 429 11.5.2.3 Model with Four Correlated Noises . . . . . . . . 432 |
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