Dr. Dawn Lott-Crumpler Department of Mathematics University of Maryland College Park, MD 20742-0001
This material appeared in print in Modelling and Simulation of Materials Science and Engineering.
Shear bands, localized regions of high strain, form in ductile materials as a result of severe plastic flow. The formation of shear bands occurs in a variety of materials; i.e., polycrystalline structural metals, rocks, ductile single crystals, polymers and other solids. These shear bands, triggered by inhomogeneities in the material, signify the possibility of further deformation and are often the precursor to failure. Shear bands may denote weak areas or areas of plastic flow and are accompanied by strain rates which are orders of magnitude higher than strain rates found in the undeformed portion of the material.
We employ an adaptive Chebyshev pseudo-spectral method for the numerical computation of shear bands in one and two dimensions. The method allows very high resolution of the spatial structure of the band and is used to study both the dynamics of band formation and its spatial structure with special emphasis on the role of imperfections.