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**A finite element model for strain localization analysis of strongly discontinuous fields based on standard Galerkin approximation.**
*(English)*
Zbl 1003.74074

Summary: This paper presents a finite element model for strain localization analysis of elastoplastic solids subjected to discontinuous displacement fields based on standard Galerkin approximation. Strain enhancements via jumps in the displacement field 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 rate-independent 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 flow, as well as plane strain compression of dilatant cohesive/frictional materials, are presented to demonstrate absolute objectivity with respect to mesh refinement and insensitivity to mesh alignment of finite element solutions.

### MSC:

74S05 | Finite element methods applied to problems in solid mechanics |

74R20 | Anelastic fracture and damage |

### Keywords:

frictional materials; finite element model; strain localization; elastoplastic solids; discontinuous displacement; Galerkin approximation; shear band; yield condition; rate-independent strain-softening Drucker-Prager model; slip line; stress-point integration algorithm; deviatoric plastic flow
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\textit{R. I. Borja}, Comput. Methods Appl. Mech. Eng. 190, No. 11--12, 1529--1549 (2000; Zbl 1003.74074)

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