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

Juan C. Simo, Keith D. Hjelmstad, Robert L. Taylor

Research output: Contribution to journalArticlepeer-review

70 Scopus citations


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 languageEnglish (US)
Pages (from-to)301-330
Number of pages30
JournalComputer Methods in Applied Mechanics and Engineering
Issue number3
StatePublished - Mar 1984
Externally publishedYes

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • General Physics and Astronomy
  • Computer Science Applications


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