Strain Localization Simulation in Plane-Strain Biaxial Tests on Dense Hostun RF Sand Using Mixed XFEM and Integral Type Nonlocal Model

Strain-softening causes localization of the strain which is accompanied by an instantaneous vanishing of the stress. If the modeling approach for strain localization with softening does not contain a material lengthscale parameter, the numerical simulation suffers from the excessive mesh dependence. The nonlocal continuum concept has emerged as an effective means for regularizing the boundary value problems with strain softening. In this paper, the calculations were carried out with integral type nonlocal constitutive law to model properly the shear zone formation. For nonlocal plasticity, element size had a critical effect on the solution. Sufficiently refined meshes were required for an accurate solution without mesh dependency. The XFEM method was employed for simulation of high strain gradient in the localization band. It was shown that an extended finite element method can be applied to the problem to decrease the required mesh density close to the localization band. A new method based on the local bifurcation theory was proposed for the initiation and growth criterion of the strain localization interface. In the case of non associated constitutive model, the criterion for bifurcation was reduced to the singularity of the symmetric part of the acoustic tensor. Finally, the ability of the presented model to describe the behavior of granular materials was demonstrated by comparisons of the results of numerical calculations and drained biaxial tests on dense Hostun sand. Attention was laid on the effect of the regularization technique on the load–displacement curve and shear zone orientation. The calculated load–displacement curves coincided very well with experiment. In addition, the influence of mean effective stress was investigated. It was shown that when increasing the confining stress, the onset of strain localization was delayed. Shear band orientation were obtained similarly to those observed experimentally. The contours of symmetric part of the acoustic tensor indicated that shear banding initiated at, or shortly before peak.