**Colloquium: Thursday, December 8, 4:10 PM, Lewis Lab 316**

**Randomness in Mechanics of Materials**

**Martin Ostoja-Starzewski**

Department of Mechanical Science and Engineering

University of Illinois at Urbana-Champaign

Microstructural randomness is present in just about all solid materials. When dominant (macroscopic) length scales are large relative to microscales, one can safely work within classical, deterministic solid mechanics. However, when the separation of scales does not hold, various concepts of continuum mechanics need to be re-examined and new methods developed. In this talk we focus on scaling from a Statistical Volume Element (SVE) to a Representative Volume Element (RVE). Starting from the Hill-Mandel homogeneity condition, without assuming any spatial periodicity, the RVE is approached in terms of two hierarchies of bounds stemming, respectively, from uniform kinematic and static boundary value problems set up on the SVE. This is illustrated in various settings: conductivity, linear or finite (thermo)elasticity, plasticity, viscoelasticity, and Darcy permeability. In the latter case, should the pores’ sizes be comparable to nanoscales, one may have to account for violations of the second law of thermodynamics. The entire methodology can also be extended to homogenization of random media by micropolar (Cosserat) rather than by classical (Cauchy) continua. This methodology also forms a systematic basis for setting up of random fields with continuous realizations and stochastic finite element methods.

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Physics and Astronomy Colloquia are usually scheduled for Thursdays at 4:10 PM in Lewis Lab room 316. Refreshments and snacks are available in the nearby coffee room at 3:45 PM.

**Physics Colloquium Schedule for FALL 2016**

**Click on Title below for past or upcoming Announcements (where available), and Speaker name for website. ** ** **