Title: Randomness and Scaling in Mechanics of Materials

Speaker: Martin Ostoja-Starzewski, University of Illinois, Urbana-Champaign

Date/Time: Thursday, April 22, 2010, 2:30 – 3:30 pm       

Location: CSRI Building/Room 90 (Sandia NM)

Brief Abstract: Microstructural randomness is present in most solid materials. When dominant (e.g. macroscopic) length scales are large relative to microscale ones, one can safely work within classical, deterministic solid mechanics. However, when the separation of scales does not hold - as is typically the case with many randomly structured (composite, polycrystalline, geological, biological, ...) materials - various concepts of continuum solid 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). Indeed, the RVE is set up in terms of two hierarchies of bounds stemming, respectively, from Dirichlet and Neumann boundary value problems set up on the SVE. We discuss the trends to approach the RVE in: planar conductivity, linear elasticity, physically nonlinear elasticity, plasticity, Darcy permeability, and thermoelasticity. This methodology then forms a logical basis for continuum random fields and stochastic finite element methods. Time permitting we will allude to other stochastic mechanics problems lacking separation of scales: fracture, shape optimization, and fractal geometries.

CSRI POC: Paul Demmie, (505) 844-7400