A nonlinear dynamical systems modelling approach unveils chaotic dynamics in simulations of large strain behaviour of a granular material under biaxial compression

Abstract

We consider bulk measurements of shear stress in a discrete element simulation of biaxial compression of a densely packed granular assembly in the failure regime in the presence of a single persistent shear band. The strain evolution of the stress ratio is treated as a time series and data based methods from nonlinear dynamical systems theory are applied to characterise the underlying dynamics - assuming a low-dimensional deterministic description. Standard nonlinear time series methods are used to characterise the psuedo-time series as consistent with chaos. Nonlinear modelling combined with novel complex network based descriptors of model simulations (which allow for a precise characterisation of the underlying dynamics) indicate that the original system can be described as a bistable transient chaotic dynamical system. There exist two different chaotic basins of attraction - one corresponding to slow and large amplitude dynamics and one to fast and small amplitude. The as yet unknown high-dimensional dynamics of multiscale grain rearrangments modelled here as the presence of dynamical noise forces the system to switch between the two regimes. © 2013 AIP Publishing LLC.