Force inference in granular materials: Uncertainty analysis and application to three-dimensional experiment design.

ABSTRACT

Interparticle forces are known to influence mechanical and physical properties of granular materials. A method for inferring forces in two-dimensional and three-dimensional experiments has recently been developed and applied to the problem of examining force statistics, energy dissipation, fracture mechanics, and force-property relations. However, a systematic analysis of uncertainties in the forces inferred through this method has not been undertaken. In this paper, our goal is therefore to perform such a systematic analysis. We first review and modify the force inference technique to eliminate its sensitivity to the choice of units and coordinate system origin. We then use discrete-element method simulations to perform a systematic study of how experimental uncertainties and data-processing errors lead to errors in inferred forces. For the considered experiments and simulations, we find that (1) errors in inferred force magnitudes and orientations increase as the ratio between particle stress uncertainties and a measure of stress imposed on the system increases, but remain small in the largest forces in a material; (2) the absence of a moderate number of particle stress tensors in the force inference procedure leads to negligible errors in inferred force magnitudes and orientations; and (3) particle stress tensors that cannot be directly measured during experiments can be "recovered" through the force inference procedure. Based on our results, we make recommendations for future experiment design to reduce uncertainties in inferred forces.