TY - JOUR
T1 - Numerical formulations of elasto-viscoplastic response of beams accounting for the effect of shear
AU - Simo, Juan C.
AU - Hjelmstad, Keith D.
AU - Taylor, Robert L.
N1 - Funding Information:
The authors thank Professor J.M. Kelly for advice offered during the execution of this research. Support for the second author was provided by Professor E.P. Popov under a grant from the NationaE Science Foundation (Grant No. CEE 81-07217). This support is gratefully acknowledged. The opinions expressed in this paper are those of the authors and do not necessarily reflect the views of NSF.
PY - 1984/3
Y1 - 1984/3
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.
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U2 - 10.1016/0045-7825(84)90011-2
DO - 10.1016/0045-7825(84)90011-2
M3 - Article
AN - SCOPUS:0021386697
SN - 0045-7825
VL - 42
SP - 301
EP - 330
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
IS - 3
ER -