Elliptic yield cap constitutive modeling for high porosity sandstone

Field and laboratory investigators have observed thin, tabular zones of localized compressional deformation without shear in high porosity sandstone. These compaction bands display greatly reduced porosity, and may affect the withdrawal of fluids from reservoirs. Studies addressing band formation as a type of strain localization predict the onset of the bands in a range of constitutive parameters roughly consistent with experiments, but are highly dependent on the constitutive relation used. In particular, the hardening modulus in shear and the slope of the yield surface in a plot of shear stress versus mean compressive stress are critical to localization predictions. Previous yield cap constitutive models employed a single deformation criterion, linking hydrostatic and shear response. In this work, we propose an elliptic yield cap model employing separate inelastic deformation parameters along each axis of the ellipse. The two deformation parameters allow the proposed surface to change in aspect ratio as it deforms, and allow a negative hardening modulus in shear without a negative hydrostatic modulus. Some cases with simplified modeling are shown for illustrative purposes, followed by a comparison with existing models. The proposed model displays similar strain behavior to the other models, but predicts localization under less restrictive conditions.