### 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) |
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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 - Mar 1984 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Computational Mechanics
- Mechanics of Materials
- Mechanical Engineering
- Physics and Astronomy(all)
- Computer Science Applications

### Cite this

*Computer Methods in Applied Mechanics and Engineering*,

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