Prediction of plane strain undrained diffuse instability and strain localization with non-coaxial plasticity

In this paper, undrained diffuse instability and strain localization of frictional materials under plane strain conditions were studied. Based on a 3D non-associated Mohr–Coulomb hardening model, the theoretical criteria for diffuse instability and strain localization were proposed by the second-order work theorem and the vanishing of the determinant of the acoustic tensor. The criteria were used to predict the instability characteristics of soil specimen in isotropically and anisotropically consolidated plane strain tests. The studies showed that, when the soil specimen was loaded under strain-controlled loading mode, the soil becomes potentially unstable slightly before the shear stress reaches its peak value. The initiation of diffuse instability accompanies with the peak of shear stress, and strain softening occurs with further loading. Strain localization was predicted by the vanishing of the determinant of the acoustic tensor, and it is shown to occur after the diffuse instability. The non-coaxial plasticity flow rule was adopted to improve the prediction the onset of strain localization, while the inclusion of non-coaxial plasticity flow rule shows no influence on diffuse instability. Both diffuse instability and strain localization occur at the hardening stage of the soil and result in the reduction of the deviatoric shear stress.