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REVIEW ARTICLES: Theoretical

Plastic Flow of Random Media: Micromechanics, Markov Property and Slip-Lines

[+] Author and Article Information
Martin Ostoja-Starzewski

Department of Metallurgy, Mechanics and Materials Science, Michigan State University, East Lansing, MI 48824-1226, USA

Appl. Mech. Rev 45(3S), S75-S81 (Mar 01, 1992) doi:10.1115/1.3121394 History: Online April 30, 2009

Abstract

The classical method of slip-lines (characteristics) of planar flow of perfectly-plastic media is generalized to a stochastic setting. The media are charaterized by space-homogeneous statistics of the yield limit k, whose derivation is outlined on the basis of micromechanics. The field equations of the random continuum approximation lead to a stochastic hyperbolic system. This system, when stated in a finite difference form, displays a Markov property for the forward evolution. On that basis, two methods of solution of boundary value problems - an exact one and a mean-field one - are outlined through an example of a Cauchy problem. The principal observation is that even for a weak material randomness the stochastic solution may differ qualitatively from that of a homogeneous deterministic medium and have a strong scatter.

Copyright © 1992 by American Society of Mechanical Engineers
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