Simulating the 3D photoelasticity forward problem in order to generate training images for deep learning

¹ Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt (DLR), 51170 Cologne, Germany
² Institut für Theoretische Physik, Universität zu Köln, 50937 Cologne, Germany
³ Max-Planck-Institut für Dynamik und Selbstorganisation, 37077, Göttingen, Germany
⁴ Hypatia Science-Consulting, 37081, Göttingen, Germany
⁵ Laboratoire Navier, École des Ponts ParisTech, Université Gustave Eiffel, CNRS, 77455 Marne-la-Vallée, France
⁶ Department of Physics, Faculty of Science, Kyoto Sangyo University, 603-8555 Kyoto, Japan

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Published online: 1 December 2025

Abstract

Images of two-dimensional granular packings obtained using photoelastic particles and a polariscope setup have successfully revealed inaccessible information such as inter-particle contacts, contact force distributions and force chain structures. Reproducing this success for a three-dimensional granular system requires a tomography setup and becomes therefore significantly more difficult. Most importantly, there is no analytical mathematical solution to the problem to reconstruct the three-dimensional stress field from the acquired images. Using a neural network to numerically predict the stress field could be a promising way forward. Training the network requires a dataset connecting photoelastic images with the knowledge of the internal stress state of the sample those images are taken from. Because the latter is not experimentally accessible, we describe here the framework of how to create the training data by simulating the forward problem of photoelasticity numerically with the following steps: simulation of stress tensor distribution within each particle given the contact forces, and simulation of photoelastic response (i.e., fringe patterns captured by a camera).