Microstructural randomness and scaling in mechanics of materials
Author(s)
Bibliographic Information
Microstructural randomness and scaling in mechanics of materials
（Modern mechanics and mathematics）
Taylor & Francis, c2008
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Note
Includes bibliographical references and index
Description and Table of Contents
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. Random Processes and Fields. Planar Lattice Models: Periodic Topologies and Elastostatics. Lattice Models: Rigidity, Randomness, Dynamics, and Optimality. Two- versus Three-Dimensional Classical Elasticity. Two- versus Three-Dimensional Micropolar Elasticity. Mesoscale Bounds for Linear Elastic Microstructures. Random Field Models and Stochastic Finite Elements. Hierarchies of Mesoscale Bounds for Nonlinear and Inelastic Microstructures. Mesoscale Response in Thermomechanics of Random Media. Waves and Wavefronts in Random Media. Bibliography. Index.
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