Three-invariant model and bifurcation analysis of deformation bands for a sandstone subjected to true triaxial loading paths.

This paper presents a general three-invariant model to evaluate the theoretical prediction of strain localization against laboratory measurements performed during mechanical loading experiments, for a high-porosity Vosges sandstone (North-Eastern France). The model is based on a mean stress and Lode angle-dependent yield surface, calibrated using extensive experimental data from mechanical tests in triaxial, biaxial and true triaxial loading conditions. The general expression of a three-invariant and non-associated constitutive relation is then developed for 10 true triaxial loading paths, performed at constant mean stresses and prescribed Lode angles. The Rice's criterion by bifurcation analysis enables the theoretical prediction of deformation bands (onset, orientation and volumetric strain). The qualitative evolution of predicted band kinematics, as well as quantitative values obtained for the 10 loading paths, proves to be in good agreement with experimental observations from full-field characterization of localized zones. The relevance and predictiveness of the presented three-invariant model are further evidence by comparisons with simplified, associated and two-invariant models using the same initial dataset. [ABSTRACT FROM AUTHOR]