Dynamic response, viscoelastic relaxation and boundary deformation in granular photoelasticity

Photoelasticity has become a widely used tool for quantifying stresses in quasi-two-dimensional experimental granular flows, providing valuable insight into the behaviour of inter-particle forces, typically for quasi-static flow geometries. Here we analyse high-inertial photoelastic collisions, and investigate the particle-scale dynamic response, relaxation due to viscoelasticity, and boundary deformation. Through high-speed experiments using impulsive loading of particles, we find that standard photoelastic theory fails under high-inertial conditions. In this work, we extend the photoelastic methodology to accurately capture forces acting on polymeric particles experiencing rapid changes in momentum. Our experiments highlight the influence of viscoelastic properties of our polymer particles, and we identify two key timescales to describe the viscoelastic relaxation. Importantly, we report the existence of fossil photoelasticity , showing that the photoelastic signal at a given moment in time may not accurately depict the instantaneous forces acting on a particle. In this work, we introduce a modified theoretical framework that accounts for particle deformation and so allows greater insight into the inter-particle contact mechanics of experimental granular systems. Our distributed-force approach to deriving photoelastic fringe patterns enables stress distributions along deformed particle boundaries, rather than through infinitesimal areas, to be extracted from experimental images. In this work, we perform high-speed experiments to subject photoelastic particles to highly inertial forces. We find that current theory fails to capture the inertial photoelastic response, and we provide an updated mathematical formulation to account for these unbalanced forces. We also observe important viscoelastic properties of photoelastic particles and develop a model to describe their leading-order relaxation behaviour. Finally, we introduce a framework to utilise particle boundary deformation, providing unprecedented insight into the spatial distribution of stresses acting on photoelastic particles.