Onset of structural evolution in granular materials as a redundancy problem

Abstract

The present paper is concerned with the redundancy of equations describing the static equilibrium of a granular assembly in relation to emergent behavioural features in granular materials such as critical state, jamming transition, instabilities and yielding. It is proposed to link the concept of jamming to critical state phenomena by introducing a limiting micromechanical state at which large plastic (dissipative) structural evolution can occur, while static equilibrium is still maintained. Such a state, herein coined as a Stable Evolution State (SES), can be numerically determined based on a number of 2D Discrete Element Method (DEM) simulations on loose granular assemblies for a given interparticle friction, but with varying contact stiffnesses, and subjected to various loading paths. By tracing the evolutions of essential micro-variables such as fabric (contact normal) anisotropy, coordination number and rigidity ratio (ratio of mean contact force to contact stiffness and diameter) as well as the onset of plastic dissipation, a well-defined limit surface emerges in the space spanning coordination number, fabric anisotropy and rigidity ratio. Interestingly, the same surface is reached when conducting other DEM simulations on dense granular assemblies with the same interparticle friction along a variety of loading paths and control conditions, thereby verifying the existence of such a characteristic SES surface. This suggests a new reference state in granular materials which facilitates the mathematical formulation of multiscale constitutive laws as it provides an essential link to plastic yielding and critical state in geomaterials.