Fractals and Randomness in Mechanics of Materials

摘要: These notes provide an introduction to two aspects of mechanics materials: (i) effects randomness on scaling effective constitutive responses and (ii) fractal geometries. The first aspect is relevant when the separation scales does not hold [i.e. dominant (macroscopic) length are large relative microscale ones]. Then, various concepts continuum solid need be re-examined new methods developed. Thus, we focus from a Statistical Volume Element (SVE) Representative (RVE). Using micromechanics, RVE approached in terms hierarchies bounds stemming, respectively, Dirichlet Neumann boundary value problems set up SVE. While linear conductive elastic microstructures were treated (Ostoja-Starzewski, 2001), here review this (non)linear (thermo)elasticity, elasto-plasticity, viscoelasticity. We also signal concept function as well touch scale stochastic damage mechanics.