Particle scale force sensor based on intensity gradient method in granular photoelastic experiments

Abstract

The intensity gradient method (G 2 method), namely computing the light intensity gradient-squared, is a widely used non-invasive experimental method to extract stress information from quasi-two-dimensional photoelastic granular materials. Previous works show that calibrated G 2 is an accurate measure of global stress. However, whether it can be used at the particle scale aside from the special case of diametric loading remains unclear. We test here the applicability and limitations of G 2 as particle scale stress indicator and specify its dependence on relevant experimental parameters of the particles, light conditions, and imaging system. We first propose an explicit formula to calculate the relationship between the G 2 value and stress based on the linear elasticity and photoelasticity theories, and then validate our formula by numerical and experimental tests. We find that G 2 is proportional to , the sum of magnitudes of the contact forces, for disc particles when forces are not large. We also observe that, for large enough resolution, G 2 does not change with the number of contacts as well as the direction of the contact forces under same value. However, we find that this relation between G 2 and is not universal for any particle shape. As an example, we show that a square particle can have dramatically different values of G 2 under the same contact forces with different contact types (point-edge contact and edge-edge contact).