### Abstract

This paper presents analytic solutions of the uniaxial extension of an elasto-plastic rectangular plate problem; the solutions are for rate fields at the instance when the stress in the plate reaches yield stress. The solutions are obtained by solving an integral equation for a plastic loading parameter, which is equivalent with a boundary value problem for displacement rate. It is shown that the integral equation has multiple solutions when softening is assumed and that the solution that corresponds to a thin shear band is the most realizable among these solutions. The thickness of the shear band is explicitly computed. Although the problem setting of the plate problem is simple, these analytic solutions will serve as a reference to examine numerical analysis methods of elasto-plastic problems.

Original language | English |
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Pages (from-to) | 773-786 |

Number of pages | 14 |

Journal | Mechanics of Materials |

Volume | 39 |

Issue number | 8 |

DOIs | |

Publication status | Published - 2007 Aug |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mechanics of Materials

### Cite this

**On analytic solution of uniaxial extension of elasto-plastic rectangular plate.** / Hori, Muneo; Oguni, Kenji.

Research output: Contribution to journal › Article

*Mechanics of Materials*, vol. 39, no. 8, pp. 773-786. https://doi.org/10.1016/j.mechmat.2006.08.010

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TY - JOUR

T1 - On analytic solution of uniaxial extension of elasto-plastic rectangular plate

AU - Hori, Muneo

AU - Oguni, Kenji

PY - 2007/8

Y1 - 2007/8

N2 - This paper presents analytic solutions of the uniaxial extension of an elasto-plastic rectangular plate problem; the solutions are for rate fields at the instance when the stress in the plate reaches yield stress. The solutions are obtained by solving an integral equation for a plastic loading parameter, which is equivalent with a boundary value problem for displacement rate. It is shown that the integral equation has multiple solutions when softening is assumed and that the solution that corresponds to a thin shear band is the most realizable among these solutions. The thickness of the shear band is explicitly computed. Although the problem setting of the plate problem is simple, these analytic solutions will serve as a reference to examine numerical analysis methods of elasto-plastic problems.

AB - This paper presents analytic solutions of the uniaxial extension of an elasto-plastic rectangular plate problem; the solutions are for rate fields at the instance when the stress in the plate reaches yield stress. The solutions are obtained by solving an integral equation for a plastic loading parameter, which is equivalent with a boundary value problem for displacement rate. It is shown that the integral equation has multiple solutions when softening is assumed and that the solution that corresponds to a thin shear band is the most realizable among these solutions. The thickness of the shear band is explicitly computed. Although the problem setting of the plate problem is simple, these analytic solutions will serve as a reference to examine numerical analysis methods of elasto-plastic problems.

UR - http://www.scopus.com/inward/record.url?scp=34047103940&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34047103940&partnerID=8YFLogxK

U2 - 10.1016/j.mechmat.2006.08.010

DO - 10.1016/j.mechmat.2006.08.010

M3 - Article

AN - SCOPUS:34047103940

VL - 39

SP - 773

EP - 786

JO - Mechanics of Materials

JF - Mechanics of Materials

SN - 0167-6636

IS - 8

ER -