### Abstract

A special theory of elastic-plastic response is considered in which the internal energy density, free energy density, entropy density, and Cauchy stress are taken to be functions of elastic deformation gradient, plastic deformation gradient, and temperature. The minimum symmetries of the elastic response are evaluated. It is shown that the minimum symmetries of the elastic response can be obtained from the material's initial symmetries and the value of the plastic deformation gradient. It is also shown that symmetries of the elastic response can not be reduced by plastic deformation in non-thermodynamic theories which take the stress to only be a function of elastic deformation gradient and temperature, or for thermodynamic theories for which the free energy is assumed to only be a function of elastic deformation gradient and temperature. Therefore, in these special cases, if a material is initially isotropic, its elastic response will remain isotropic; if the material is initially transversely isotropic, its elastic response will remain transversely isotropic; etc.

Original language | English (US) |
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Title of host publication | Anisotropy and Inhomogeneity in Elasticity and Plasticity |

Editors | M.W. Hyer |

Publisher | Publ by ASME |

Pages | 19-23 |

Number of pages | 5 |

ISBN (Print) | 0791811379 |

State | Published - Jan 1 1993 |

Event | 1st Joint Mechanics Meeting of ASME/ASCE/SES - MEET'N'93 - Charlottesville, VA, USA Duration: Jun 6 1993 → Jun 9 1993 |

### Publication series

Name | American Society of Mechanical Engineers, Applied Mechanics Division, AMD |
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Volume | 158 |

ISSN (Print) | 0160-8835 |

### Other

Other | 1st Joint Mechanics Meeting of ASME/ASCE/SES - MEET'N'93 |
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City | Charlottesville, VA, USA |

Period | 6/6/93 → 6/9/93 |

### Fingerprint

### ASJC Scopus subject areas

- Mechanical Engineering

### Cite this

*Anisotropy and Inhomogeneity in Elasticity and Plasticity*(pp. 19-23). (American Society of Mechanical Engineers, Applied Mechanics Division, AMD; Vol. 158). Publ by ASME.

**Evolution of material symmetry in the elastic response of a fully strain space theory of plasticity.** / Negahban, Mehrdad; Wineman, Alan S.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Anisotropy and Inhomogeneity in Elasticity and Plasticity.*American Society of Mechanical Engineers, Applied Mechanics Division, AMD, vol. 158, Publ by ASME, pp. 19-23, 1st Joint Mechanics Meeting of ASME/ASCE/SES - MEET'N'93, Charlottesville, VA, USA, 6/6/93.

}

TY - GEN

T1 - Evolution of material symmetry in the elastic response of a fully strain space theory of plasticity

AU - Negahban, Mehrdad

AU - Wineman, Alan S.

PY - 1993/1/1

Y1 - 1993/1/1

N2 - A special theory of elastic-plastic response is considered in which the internal energy density, free energy density, entropy density, and Cauchy stress are taken to be functions of elastic deformation gradient, plastic deformation gradient, and temperature. The minimum symmetries of the elastic response are evaluated. It is shown that the minimum symmetries of the elastic response can be obtained from the material's initial symmetries and the value of the plastic deformation gradient. It is also shown that symmetries of the elastic response can not be reduced by plastic deformation in non-thermodynamic theories which take the stress to only be a function of elastic deformation gradient and temperature, or for thermodynamic theories for which the free energy is assumed to only be a function of elastic deformation gradient and temperature. Therefore, in these special cases, if a material is initially isotropic, its elastic response will remain isotropic; if the material is initially transversely isotropic, its elastic response will remain transversely isotropic; etc.

AB - A special theory of elastic-plastic response is considered in which the internal energy density, free energy density, entropy density, and Cauchy stress are taken to be functions of elastic deformation gradient, plastic deformation gradient, and temperature. The minimum symmetries of the elastic response are evaluated. It is shown that the minimum symmetries of the elastic response can be obtained from the material's initial symmetries and the value of the plastic deformation gradient. It is also shown that symmetries of the elastic response can not be reduced by plastic deformation in non-thermodynamic theories which take the stress to only be a function of elastic deformation gradient and temperature, or for thermodynamic theories for which the free energy is assumed to only be a function of elastic deformation gradient and temperature. Therefore, in these special cases, if a material is initially isotropic, its elastic response will remain isotropic; if the material is initially transversely isotropic, its elastic response will remain transversely isotropic; etc.

UR - http://www.scopus.com/inward/record.url?scp=0027187677&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0027187677&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0027187677

SN - 0791811379

T3 - American Society of Mechanical Engineers, Applied Mechanics Division, AMD

SP - 19

EP - 23

BT - Anisotropy and Inhomogeneity in Elasticity and Plasticity

A2 - Hyer, M.W.

PB - Publ by ASME

ER -