Mode switching and recursive bifurcation in granular materials

The existence of the "mode switching" and "recursive bifurcation" behavior in granular materials (sand triaxial-compression-test specimens) under shearing is revealed. Group-theoretic bifurcation theory is employed to categorize bifurcation modes through the observation of deformation patterns of these materials, and hence to detect the occurrence of recursive bifurcation. A bifurcation point search technique is developed and applied to a strain versus stress curve of a specimen to identify the presence of a series of bifurcation points associated with the recursive bifurcation. In addition, an imperfection sensitivity law is employed to testify the occurrence of mode switching between two dominant bifurcation modes. Curves of strain versus stress undergoing mode switching and recursive bifurcation are simulated well by the bifurcation equation. The predominant role of mode switching and recursive bifurcation in shearing behavior of the granular materials is clearly demonstrated and fully described with the use of the bifurcation theory.