Theory vs. experiment for finite strain viscoplastic, lagrangian constitutive model

Document Type

Article

Publication Date

1-1-1991

Abstract

The work outlined in this research demonstrates the applicability and effectiveness of the viscoplastic model presented by the authors (Voyiadjis & Mohammad [1987, 1988]) in solving complex (i.e., any shape and any deformation) finite strain problems. The use of the Lagrangian formulation in this work eliminates the controversy regarding the choice of the appropriate corotational stress rate, and provides a more convenient theory than the more common spatial formulation. Commercially pure aluminum is used in this work as it closely displays the properties outlined by the proposed constitutive equations (Voyiadjis & Mohammad) [1987, 1988]). The problem of analysis of displacements, stresses, and strains in elements made of this material subject to arbitrarily large deformations under the conditions of plane strain or axisymmetric stress distribution is formulated in terms of the finite element method. Two integration algorithms are developed applying the procedures outlined by Kanchi et al. [1978]; Hughes and Taylor [1978]; Simo and Ortiz [1985]; and Ortiz and Simo [1986]. These numerical procedures can be categorized into the visco-plastic tangent stiffness approach followed by the radial return and the operator-splitting approach. The algorithms are used to solve the thick plate bending problem subjected to finite deformations. Experimental verification for the bending of the plate problem is provided. Creep and relaxation behavior of the material is also investigated in this work. © 1991.

Publication Source (Journal or Book title)

International Journal of Plasticity

First Page

329

Last Page

350

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