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TECHNICAL PAPERS

# Stabilized Mixed Finite Elements With Embedded Strong Discontinuities for Shear Band Modeling

[+] Author and Article Information
P. J. Sánchez

Centro Internacional de Métodos Computacionales en Ingeniería, INTEC-UNL-CONICET, Güemes 3450, S3000 GLN Santa Fe, Argentinapsanchez@intec.unl.edu.ar

V. Sonzogni

Centro Internacional de Métodos Computacionales en Ingeniería, INTEC-UNL-CONICET, Güemes 3450, S3000 GLN Santa Fe, Argentina

A. E. Huespe, J. Oliver

Technical University of Catalonia, Campus Nord, Modul C1, c/Jordi Girona 1-3, 08034 Barcelona, Spain

J. Appl. Mech 73(6), 995-1004 (Feb 13, 2006) (10 pages) doi:10.1115/1.2190233 History: Received July 01, 2005; Revised February 13, 2006

## Abstract

A stabilized mixed finite element with elemental embedded strong discontinuities for shear band modeling is presented. The discrete constitutive model, representing the cohesive forces acting across the shear band, is derived from a rate-independent $J2$ plastic continuum material model with strain softening, by using a projection-type procedure determined by the Continuum-Strong Discontinuity Approach. The numerical examples emphasize the increase of the numerical solution accuracy obtained with the present strategy as compared with alternative procedures using linear triangles.

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## Figures

Figure 1

Strong discontinuity problem

Figure 2

Stress tensor structure in S

Figure 3

Figure 6

Slope stability problem: Finite element discretizations

Figure 7

Slope stability problem: Evolution of plastic loading states using the PGPSD-N element (M3)

Figure 8

Slope stability problem. PGPSD-N elements in post-bifurcation condition at the end of the analysis: (a) Mesh M1. (b) Mesh M2. (c) Mesh M3.

Figure 9

Slope stability problem. Deformed configuration at point “C” in the equilibrium path: (a) PGP Formulation; (b) PGPSD-N Formulation; (c) Comparison of the Load-Displacement (δu) curves for both strategies.

Figure 10

Slope stability problem. Load-displacement (δu) curves: (a) PGPSD-N Convergence. (b) Comparison of elements.

Figure 11

Slope stability problem. Relative errors vs element size: (a) Load-displacement response (in terms of L2-norm). (b) Ultimate load Pu.

Figure 12

2D cracked panel: (a) Geometry and boundary conditions. (b) Mesh M1: 1301 elements (h≈4[mm]). (c) Mesh M2: 5252 elements (h≈2[mm]).

Figure 13

2D cracked panel: (a) Load-displacement equilibrium paths. (b) Deformed configuration PGPSD-N (M2).

Figure 4

Displacement field interpolation: (a) Element d.o.f.’s, (b) φe(x) function, (c) Heaviside’s step function HSe(x), (d) Elemental unit jump function MSe(x)

Figure 5

Slope stability problem: Geometry and boundary condition

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