Microstructural Randomness and Scaling in Mechanics of Materials

Martin Ostoja-Starzewski

August 13, 2007 by Chapman and Hall/CRC
Reference - 497 Pages - 135 B/W Illustrations
ISBN 9781584884170 - CAT# C4174
Series: Modern Mechanics and Mathematics


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  • Presents basic coverage of random geometry and continuum random fields for readers unacquainted with this area
  • Reviews truss-type and beam-type lattices as well as the construction of the corresponding classical and nonclassical continua
  • Explores-for the first time in book form-scaling to the RVE in conductivity, linear or finite elasticity and thermoelasticity, elasto-plasticity, and flow in porous media
  • Provides methods for problems below the RVE via SFEs
  • Studies effects of microscale material randomness on wavefronts in (in)elastic/nonlinear media
  • Includes a number of applications from engineering and science to promote active research in the field
  • Contains numerous problems at the end of the first six chapters
  • Summary

    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.