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 characterisa..