Negative stiffness, incompressibility, and strain localisation in particulate materials

In this paper, we consider two mechanisms capable of inducing strain localisation in particulate geomaterials in compression: the apparent negative stiffness and the incremental in-compressibility caused by dilatancy. It is demonstrated that the apparent negative stiffness can be produced by the rotation of clusters of particles in the presence of compression. The clusters are formed by connecting the particles by the bonds that still remain intact in the process of bond break-age in compression. We developed a 2D isotropic model of incremental incompressibility showing that a single strain localisation zone is formed inclined at 45^◦ to the direction of axial compressive loading. This mechanism of localisation was analysed through Particle Flow Code (PFC) 2D and 3D simulations. It is shown that, in the simulations, the peak stress (the onset of localisation) does correspond to the incremental Poisson’s ratio, reaching the critical values of 1 (in 2D) and 0.5 (in 3D).