### Abstract

This paper focuses on the application of statistical continuum mechanics to the prediction of mechanical response of polycrystalline materials and microstructure evolution under large plastic deformations. A statistical continuum mechanics formulation is developed by applying a Green's function solution to the equations of stress equilibrium in an infinite domain. The distribution and morphology of grains (crystals) in polycrystalline materials is represented by a set of correlation functions that are described by the corresponding probability functions. The elastic deformation is neglected and a viscoplastic power law is employed for crystallographic slip in single crystals. In this formulation, two- and three-point probability functions are used. A secant modulus-based formulation is used. The statistical analysis is applied to simulate homogeneous deformation processes under uniaxial tension, uniaxial compression and plane strain compression of an FCC polycrystal. The results are compared to the well-known Taylor upper bound model and discussed in comparison to experimental observations.

Original language | English |
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Pages (from-to) | 589-607 |

Number of pages | 19 |

Journal | Journal of the Mechanics and Physics of Solids |

Volume | 49 |

Issue number | 3 |

DOIs | |

Publication status | Published - Mar 2001 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mechanical Engineering
- Mechanics of Materials
- Condensed Matter Physics

### Cite this

*Journal of the Mechanics and Physics of Solids*,

*49*(3), 589-607. https://doi.org/10.1016/S0022-5096(00)00040-5

**Statistical continuum theory for large plastic deformation of polycrystalline materials.** / Garmestani, H.; Lin, S.; Adams, B. L.; Ahzi, Said.

Research output: Contribution to journal › Article

*Journal of the Mechanics and Physics of Solids*, vol. 49, no. 3, pp. 589-607. https://doi.org/10.1016/S0022-5096(00)00040-5

}

TY - JOUR

T1 - Statistical continuum theory for large plastic deformation of polycrystalline materials

AU - Garmestani, H.

AU - Lin, S.

AU - Adams, B. L.

AU - Ahzi, Said

PY - 2001/3

Y1 - 2001/3

N2 - This paper focuses on the application of statistical continuum mechanics to the prediction of mechanical response of polycrystalline materials and microstructure evolution under large plastic deformations. A statistical continuum mechanics formulation is developed by applying a Green's function solution to the equations of stress equilibrium in an infinite domain. The distribution and morphology of grains (crystals) in polycrystalline materials is represented by a set of correlation functions that are described by the corresponding probability functions. The elastic deformation is neglected and a viscoplastic power law is employed for crystallographic slip in single crystals. In this formulation, two- and three-point probability functions are used. A secant modulus-based formulation is used. The statistical analysis is applied to simulate homogeneous deformation processes under uniaxial tension, uniaxial compression and plane strain compression of an FCC polycrystal. The results are compared to the well-known Taylor upper bound model and discussed in comparison to experimental observations.

AB - This paper focuses on the application of statistical continuum mechanics to the prediction of mechanical response of polycrystalline materials and microstructure evolution under large plastic deformations. A statistical continuum mechanics formulation is developed by applying a Green's function solution to the equations of stress equilibrium in an infinite domain. The distribution and morphology of grains (crystals) in polycrystalline materials is represented by a set of correlation functions that are described by the corresponding probability functions. The elastic deformation is neglected and a viscoplastic power law is employed for crystallographic slip in single crystals. In this formulation, two- and three-point probability functions are used. A secant modulus-based formulation is used. The statistical analysis is applied to simulate homogeneous deformation processes under uniaxial tension, uniaxial compression and plane strain compression of an FCC polycrystal. The results are compared to the well-known Taylor upper bound model and discussed in comparison to experimental observations.

UR - http://www.scopus.com/inward/record.url?scp=0034826312&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034826312&partnerID=8YFLogxK

U2 - 10.1016/S0022-5096(00)00040-5

DO - 10.1016/S0022-5096(00)00040-5

M3 - Article

AN - SCOPUS:0034826312

VL - 49

SP - 589

EP - 607

JO - Journal of the Mechanics and Physics of Solids

JF - Journal of the Mechanics and Physics of Solids

SN - 0022-5096

IS - 3

ER -