Validation and correction of photoelastic techniques for frictional granular systems

Abstract Photoelasticity is a popular tool to measure the internal stresses of many transparent materials, with numerous industrial, medical and research applications. Importantly for this work, photoelastic techniques can be used to provide quantitative diagnostics for experimental studies of two-dimensional granular flows of circular discs. In this paper, we introduce a novel photoelastic testing apparatus and present the first experimental validation of photoelastic techniques being used to quantify frictional forces acting on cylindrical particles. In this case, the forces acting on the photoelastic particles have both normal and tangential components. Additionally, we perform a quantitative error analysis and obtain bounds on the spatial imaging resolution required to produce accurate photoelastic results from experimental data. Our results verify that photoelasticity can be used reliably to calculate and quantify normal and tangential forces in experimental granular systems, and also give insight into the range of forcing conditions that photoelastic techniques are most accurate. This information is of critical importance to researchers who are designing, running and analysing photoelastic experiments. During our own experiments, we discovered a mathematical error in the widely used open-source Photoelastic Grain Solver (PeGS) code. Much of the current photoelastic research depends on the effectiveness of PeGS, and we found that the error leads to incorrect output from experimental data whenever there are tangential components to any of the inter-particle forces. In this work, we outline the error, quantify its effect and provide a fix to ensure accurate output from the code. The photoelastic community has corroborated and validated our updated version of the software, and we have amended the open-source version of the code to include the modifications outlined in this article.