عنوان مقاله [English]
A shear band is a narrow zone of intense shearing strain within a largely
unsheared matrix. During the shear band formation, relative tangential
displacement of blocks of material on two sides of the band occurs. Width of
this region varies from a few to hundreds of microns. Despite the infinitesimal
width of the band, its relative tangential deformation may extend to several
centimeters and may even lead to exertion of macroscopic influence on the
medium.In this paper, a new method for modeling of shear band is presented. A
bifurcation analysis is used to detect the onset of localization in an element
to determine the geometry of the localized deformation modes. Therefore, a
computational procedure is discussed for detecting the onset of localization
and determining the localization directions and the shear band path. A zero
thickness element is utilized to simulate the slip surface in the shear band.
Plane strain condition is assumed in numerical simulations, and elasto-plastic
finite element method is used in analysis.When the onset of localization is detected, the zero thickness element is added to the shear band path, which closely reproduces the shear band response. The proposed methodology is applied to two numerical examples, and the results are compared with the other existing methods which demonstrate the ability of the method to resolve the geometry of localized failure modes and reproduce the shear band response.
The first example is a simple shear problem that includes a rectangular solid
with fixed supports in its bottom, subjected to uniform shear deformation on
the upper boundary. The second example is a slope failure problem, which
includes a downward displacement applied to the middle of a rigid block on the
top of a slope. The shear band path and the force-displacement curves are
plotted for both examples and have good agreement with the reported results.