A finite element model for strain localization analysis of strongly discontinuous fields based on standard Galerkin approximation
✍ Scribed by Ronaldo I. Borja
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 1015 KB
- Volume
- 190
- Category
- Article
- ISSN
- 0045-7825
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✦ Synopsis
This paper presents a ®nite element model for strain localization analysis of elastoplastic solids subjected to discontinuous displacement ®elds based on standard Galerkin approximation. Strain enhancements via jumps in the displacement ®eld are captured and condensed on the material level, leading to a formulation that does not require static condensation to be performed on the element level. The mathematical formulation revolves around the dual response of a macroscopic point cut by a shear band, which requires the satisfaction of the yield condition on the band as the same stress point unloads elastically just outside the band. Precise conditions for the appearance of slip lines, including their initiation and evolution, are outlined for a rateindependent, strain-softening Drucker±Prager model, and explicit analytical expressions are used to describe the orientation of the slip line in a plane strain setting. At post-localization the stress-point integration algorithm along the band is exact and amenable to consistent linearization. Numerical examples involving simple shearing of elastoplastic solids with deviatoric plastic ¯ow, as well as plane strain compression of dilatant cohesive/frictional materials, are presented to demonstrate absolute objectivity with respect to mesh re®nement and insensitivity to mesh alignment of ®nite element solutions.