1. Microstructural Randomness and Scaling in Mechanics of Materials, Modern Mechanics and Mathematics Series, Chapman & Hall/CRC/Taylor & Francis (2007). 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 from Statistical Volume Element (SVE) to Representative Volume Element (RVE) in conductivity, linear and finite elasticity/thermoelasticity, elasto-plasticity, permeability, electrostatics…
- 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
2. Thermoelasticty with Finite Wave Speeds, with J. Ignaczak, Oxford Mathematical Monographs, Oxford University Press (2009)
3. Tensor-Valued Random Fields for Continuum Physics, with A. Malyarenko, Cambridge Monographs on Mathematical Physics, Cambridge University Press, 2019.
4. Random Fields of Piezoelectricity and Piezomagnetism: Correlation Structures, with A. Malyarenko and A. Amiri-Hezaveh, SpringerBriefs in Applied Sciences and Technology and SpringerBriefs in Mathematical Methods, 2020.