Multiscale Theory of Composites and Random Media

This is the first book to introduce Green-function-based multiscale theory and the corresponding finite element method, which are readily applicable to composites and random media. The methodology is considered to be the one that most effectively tackles the uncertainty of stress propagation in complex heterogeneities of random media, and which presents multiscale theory from distinctive scale separation and scale-coupling viewpoints. Deliberately taking a multiscale perspective, it covers scale separation and then scale coupling. Both micromechanics and novel scale-coupling mechanics are described in relation to variational principles and bounds, as well as in the emerging topics on percolation and scale-coupling computation. It gives detail on the different bounds encountered, covering classical second and third order, new fourth order, and innovative ellipsoidal variations. Green-function-based multiscale theory is addressed to applications in solid mechanics and transport of complex media ranging from micro- and nano-composites, polycrystals, soils, rocks, cementitious materials, to biological materials. It is useful as a graduate textbook in civil and mechanical engineering and as a reference.

Author Biography: Xi Frank Xu is a professor in civil engineering at Beijing Jiaotong University, and was formerly an assistant professor at Stevens Institute of Technology, USA. He received the 2010 K.J. Bathe Award for the Best Paper by a Young Researcher in the Field of Computational Engineering.

Prelims. Introduction: Emerging Scale-Coupling Mechanics. Random Morphology and Correlation Functions. Part I. Analytical Homogenization of Scale Separation Problems. Green-Function-Based Variational Principles. Nth-Order Variational Bounds. Ellipsoidal Bound. Prediction of Percolation Threshold. PART II - Computational Analysis of Scale Coupling Problems. Green-Function-Based Variational Principles for Scale-Coupling Problems. Multiscale Stochastic Finite Element Method and Multiphase Composites. Multiscale Stochastic Finite Element Method and Continuous Random Media. References. Index.