### Abstract

Effects of spatial random fluctuations in the yield condition of rigid-perfectly plastic continuous media are analyzed in cases of a Cauchy boundary value problem and a characteristic boundary value problem. Plastic material is assumed to be isotropic and hence it is described by a random field of plastic limit k, which is taken as space-homogeneous, ergodic, and having a high signal-to-noise ratio. The solution method is based on a stochastic generalization of the method of slip-lines, whose significant feature is that the deterministic characteristics are replaced by the forward evolution cones. Comparisons of response of this random medium and a deterministic homogeneous medium with a plastic limit equal to the average of k are carried out in specific examples of the two boundary value problems under study. It is found that the weak material randomness always leads to a relatively much stronger scatter in the position and field variables. In cases of inhomogeneous boundary data the sensitivity of field quantities to the strength of randomness of plastic limit k is very high and amplifies the differences between the average solution of a stochastic problem and the solution of the homogeneous medium problem.

Original language | English (US) |
---|---|

Pages (from-to) | 149-158 |

Number of pages | 10 |

Journal | American Society of Mechanical Engineers, Applied Mechanics Division, AMD |

Volume | 135 |

State | Published - Jan 1 1992 |

Externally published | Yes |

Event | ASME Summer Mechanics and Materials Conferences - Tempe, AZ, USA Duration: Apr 28 1992 → May 1 1992 |

### Fingerprint

### ASJC Scopus subject areas

- Mechanical Engineering

### Cite this

**Boundary value problems in plastic flow of random media.** / Ostoja-Starzewski, Martin.

Research output: Contribution to journal › Conference article

}

TY - JOUR

T1 - Boundary value problems in plastic flow of random media

AU - Ostoja-Starzewski, Martin

PY - 1992/1/1

Y1 - 1992/1/1

N2 - Effects of spatial random fluctuations in the yield condition of rigid-perfectly plastic continuous media are analyzed in cases of a Cauchy boundary value problem and a characteristic boundary value problem. Plastic material is assumed to be isotropic and hence it is described by a random field of plastic limit k, which is taken as space-homogeneous, ergodic, and having a high signal-to-noise ratio. The solution method is based on a stochastic generalization of the method of slip-lines, whose significant feature is that the deterministic characteristics are replaced by the forward evolution cones. Comparisons of response of this random medium and a deterministic homogeneous medium with a plastic limit equal to the average of k are carried out in specific examples of the two boundary value problems under study. It is found that the weak material randomness always leads to a relatively much stronger scatter in the position and field variables. In cases of inhomogeneous boundary data the sensitivity of field quantities to the strength of randomness of plastic limit k is very high and amplifies the differences between the average solution of a stochastic problem and the solution of the homogeneous medium problem.

AB - Effects of spatial random fluctuations in the yield condition of rigid-perfectly plastic continuous media are analyzed in cases of a Cauchy boundary value problem and a characteristic boundary value problem. Plastic material is assumed to be isotropic and hence it is described by a random field of plastic limit k, which is taken as space-homogeneous, ergodic, and having a high signal-to-noise ratio. The solution method is based on a stochastic generalization of the method of slip-lines, whose significant feature is that the deterministic characteristics are replaced by the forward evolution cones. Comparisons of response of this random medium and a deterministic homogeneous medium with a plastic limit equal to the average of k are carried out in specific examples of the two boundary value problems under study. It is found that the weak material randomness always leads to a relatively much stronger scatter in the position and field variables. In cases of inhomogeneous boundary data the sensitivity of field quantities to the strength of randomness of plastic limit k is very high and amplifies the differences between the average solution of a stochastic problem and the solution of the homogeneous medium problem.

UR - http://www.scopus.com/inward/record.url?scp=0026484481&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0026484481&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:0026484481

VL - 135

SP - 149

EP - 158

JO - American Society of Mechanical Engineers, Applied Mechanics Division, AMD

JF - American Society of Mechanical Engineers, Applied Mechanics Division, AMD

SN - 0160-8835

ER -