Fx. Garaizar et J. Trangenstein, ADAPTIVE MESH REFINEMENT AND FRONT-TRACKING FOR SHEAR BANDS IN AN ANTIPLANE SHEAR MODEL, SIAM journal on scientific computing (Print), 20(2), 1999, pp. 750-779
In this paper we describe a numerical algorithm for the study of shear
-band formation and growth in a two-dimensional antiplane shear of gra
nular materials. The algorithm combines front-tracking techniques and
adaptive mesh refinement. Tracking provides a more careful evolution o
f the band when coupled with special techniques to advance the ends of
the shear band in the presence of a loss of hyperbolicity. The adapti
ve mesh refinement allows the computational effort to be concentrated
in important areas of the deformation, such as the shear band and the
elastic relief wave. The main challenges are the problems related to s
hear bands that extend across several grid patches and the effects tha
t a nonhyperbolic growth rate of the shear bands has in the refinement
process. We give examples of the success of the algorithm for various
levels of refinement.