Some model problems of polycrystal plasticity with deficient basic crystals

Robert Kohn, Thomas D. Little

Research output: Contribution to journalArticle

Abstract

We consider the yield set of a (rigid-perfectly-plastic) polycrystal, where the basic crystal has very few slip systems. One would like to predict whether the effective behavior is ductile or rigid. We address this issue for some model problems of antiplane shear and plane stress. Our main tools are nonlinear homogenization, bounds via compensated compactness, and the elastic comparison method.

Original languageEnglish (US)
Pages (from-to)172-197
Number of pages26
JournalSIAM Journal on Applied Mathematics
Volume59
Issue number1
StatePublished - Sep 1998

Fingerprint

Polycrystal
Polycrystals
Plasticity
Crystal
Plastics
Compensated Compactness
Anti-plane Shear
Crystals
Comparison Method
Plane Stress
Shear Stress
Homogenization
Slip
Predict
Model

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Some model problems of polycrystal plasticity with deficient basic crystals. / Kohn, Robert; Little, Thomas D.

In: SIAM Journal on Applied Mathematics, Vol. 59, No. 1, 09.1998, p. 172-197.

Research output: Contribution to journalArticle

@article{661275301fb94713ad85dd7a211a131a,
title = "Some model problems of polycrystal plasticity with deficient basic crystals",
abstract = "We consider the yield set of a (rigid-perfectly-plastic) polycrystal, where the basic crystal has very few slip systems. One would like to predict whether the effective behavior is ductile or rigid. We address this issue for some model problems of antiplane shear and plane stress. Our main tools are nonlinear homogenization, bounds via compensated compactness, and the elastic comparison method.",
author = "Robert Kohn and Little, {Thomas D.}",
year = "1998",
month = "9",
language = "English (US)",
volume = "59",
pages = "172--197",
journal = "SIAM Journal on Applied Mathematics",
issn = "0036-1399",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "1",

}

TY - JOUR

T1 - Some model problems of polycrystal plasticity with deficient basic crystals

AU - Kohn, Robert

AU - Little, Thomas D.

PY - 1998/9

Y1 - 1998/9

N2 - We consider the yield set of a (rigid-perfectly-plastic) polycrystal, where the basic crystal has very few slip systems. One would like to predict whether the effective behavior is ductile or rigid. We address this issue for some model problems of antiplane shear and plane stress. Our main tools are nonlinear homogenization, bounds via compensated compactness, and the elastic comparison method.

AB - We consider the yield set of a (rigid-perfectly-plastic) polycrystal, where the basic crystal has very few slip systems. One would like to predict whether the effective behavior is ductile or rigid. We address this issue for some model problems of antiplane shear and plane stress. Our main tools are nonlinear homogenization, bounds via compensated compactness, and the elastic comparison method.

UR - http://www.scopus.com/inward/record.url?scp=0032153950&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032153950&partnerID=8YFLogxK

M3 - Article

VL - 59

SP - 172

EP - 197

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

SN - 0036-1399

IS - 1

ER -