- Microstructural Randomness and Scaling in Mechanics of Materials, Modern Mechanics and Mathematics Series, Chapman & Hall/CRC/Taylor & Francis (2008)
The book develops and reviews a number of stochastic models and methods useful in mechanics of random media, a field at the intersection of solid mechanics, materials science, stochastic mathematics and statistical physics. The first six of 11 chapters include problems, so that the book may be used for a graduate course. Among the book's unique features are:
- basic coverage of random geometry and continuum random fields
- review of truss-type and beam-type lattices, and construction of corresponding classical and non-classical continua
- theory and consequences of stress invariance in planar classical and micropolar elasticity
- introduction to statistical continuum theories
- scaling to Representative Volume Element (RVE) in conductivity, linear and finite elasticity/thermoelasticity, elasto-plasticity, flow in porous media, ...
- methods for problems with resolution below the RVE via e.g. stochastic finite elements
- a study of effects of microscale material randomness on waves in (in)elastic/non-linear media, with focus on wavefronts
- Thermoelasticty with Finite Wave Speeds, with J. Ignaczak, Oxford Mathematical Monographs, Oxford University Press (2009)