Plastic flow of random media. Micromechanics, Markov property and slip-lines

Research output: Contribution to journalConference articlepeer-review


The classical method of slip-lines (characteristics) of planar flow of perfectly-plastic media is generalized to a stochastic setting. The media are characterized 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.

Original languageEnglish (US)
Pages (from-to)S73-S81
JournalApplied Mechanics Reviews
Issue number3 pt 2
StatePublished - Mar 1992
Externally publishedYes
EventSymposium on Material Instabilities in conjunction with the 22nd Midwestern Mechanics Conference - Rolla, MS, USA
Duration: Oct 1 1991Oct 1 1991

ASJC Scopus subject areas

  • Mechanical Engineering


Dive into the research topics of 'Plastic flow of random media. Micromechanics, Markov property and slip-lines'. Together they form a unique fingerprint.

Cite this