### Abstract

The finite deformation, elasto-viscoplastic response of beams is considered from a numerical point of view in this paper. Formulations in terms of stress resultants are discussed and extended to include viscoplastic material response by introducing rate equations for the evolution of the finite inelastic deformations. Special attention is given to the objectivity of the rates and to the form of the plastic flow potential. An alternative one-dimensional formulation, obtained by introducing a kinematic constraint and numerically integrating over the cross section of the beam, is also presented. Both formulations account for the effect of warping, which arises as a result of shear deformation. A numerical algorithm for the time-dependent problem is presented in which the numerically integrated nonlinear rate equations are 'exactly' satisfied at each iteration of the Newton-Raphson scheme. The implications of the formulations discussed in this paper are illustrated through a set of numerical examples.

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

Pages (from-to) | 301-330 |

Number of pages | 30 |

Journal | Computer Methods in Applied Mechanics and Engineering |

Volume | 42 |

Issue number | 3 |

DOIs | |

State | Published - 1984 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Computer Science Applications
- Computational Mechanics

### Cite this

*Computer Methods in Applied Mechanics and Engineering*,

*42*(3), 301-330. https://doi.org/10.1016/0045-7825(84)90011-2

**Numerical formulations of elasto-viscoplastic response of beams accounting for the effect of shear.** / Simo, Juan C.; Hjelmstad, Keith; Taylor, Robert L.

Research output: Contribution to journal › Article

*Computer Methods in Applied Mechanics and Engineering*, vol. 42, no. 3, pp. 301-330. https://doi.org/10.1016/0045-7825(84)90011-2

}

TY - JOUR

T1 - Numerical formulations of elasto-viscoplastic response of beams accounting for the effect of shear

AU - Simo, Juan C.

AU - Hjelmstad, Keith

AU - Taylor, Robert L.

PY - 1984

Y1 - 1984

N2 - The finite deformation, elasto-viscoplastic response of beams is considered from a numerical point of view in this paper. Formulations in terms of stress resultants are discussed and extended to include viscoplastic material response by introducing rate equations for the evolution of the finite inelastic deformations. Special attention is given to the objectivity of the rates and to the form of the plastic flow potential. An alternative one-dimensional formulation, obtained by introducing a kinematic constraint and numerically integrating over the cross section of the beam, is also presented. Both formulations account for the effect of warping, which arises as a result of shear deformation. A numerical algorithm for the time-dependent problem is presented in which the numerically integrated nonlinear rate equations are 'exactly' satisfied at each iteration of the Newton-Raphson scheme. The implications of the formulations discussed in this paper are illustrated through a set of numerical examples.

AB - The finite deformation, elasto-viscoplastic response of beams is considered from a numerical point of view in this paper. Formulations in terms of stress resultants are discussed and extended to include viscoplastic material response by introducing rate equations for the evolution of the finite inelastic deformations. Special attention is given to the objectivity of the rates and to the form of the plastic flow potential. An alternative one-dimensional formulation, obtained by introducing a kinematic constraint and numerically integrating over the cross section of the beam, is also presented. Both formulations account for the effect of warping, which arises as a result of shear deformation. A numerical algorithm for the time-dependent problem is presented in which the numerically integrated nonlinear rate equations are 'exactly' satisfied at each iteration of the Newton-Raphson scheme. The implications of the formulations discussed in this paper are illustrated through a set of numerical examples.

UR - http://www.scopus.com/inward/record.url?scp=0021386697&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0021386697&partnerID=8YFLogxK

U2 - 10.1016/0045-7825(84)90011-2

DO - 10.1016/0045-7825(84)90011-2

M3 - Article

VL - 42

SP - 301

EP - 330

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0374-2830

IS - 3

ER -