Shear and compaction band formation on an elliptic yield cap

[1] Conditions for shear and compaction localization are examined for stress states on an elliptic yield cap in the space of Mises equivalent shear stress (tau) over bar and mean normal compressive stress sigma. Localization is predicted to occur when the slope of the hydrostatic stress versus inelastic volume strain curve falls to a critical value k(crit). When applied to the standard triaxial test, the analysis reveals a transition from compaction localization to shear localization as lateral confining stress sigma(c) decreases below a particular value. This value also corresponds to the largest value of k(crit), which is zero if normality is satisfied and slightly positive if not, for either shear or compaction bands. For sigma(c) larger than the transition value, compaction bands are the only mode of localized deformation predicted, and kcrit becomes increasingly negative with increasing sigma(c). For sigma(c) smaller than the transition value, both shear bands and compaction bands are possible, but the value of kcrit is larger for shear bands. These results are consistent with experimental observations of compaction bands on relatively flat portions of the stress versus strain curve, corresponding to k(crit) approximate to 0, and with their occurrence in a limited range of sigma(c). As sigma(c) is decreased from the transition value, the predicted angle between the normal to the shear band and the maximum compression direction increases rapidly from 0degrees (for a compaction band) to 20degrees - 30degrees. This rapid increase provides a possible explanation for the infrequent observation of very low angle shear bands.