Books

  1. 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


    Errata

    Review in MathSciNet
    Review in Zentralblatt-Math

  2. Thermoelasticty with Finite Wave Speeds, with J. Ignaczak, Oxford Mathematical Monographs, Oxford University Press (2010)

    Review in MathSciNet
    Review in ZentralBlatt-Math