Combining X-ray tomography and digital volume correlation to measure 3D bulk mechanical fields in Hertzian contact mechanics

In this study, we revisit classical Hertzian contact theory through a novel experimental approach that enables in situ 3D imaging of contact mechanics using laboratory-based X-ray tomography. By employing a model contact system—a PDMS sphere indented into a PMMA plane—we measure the 3D displacement field within the deforming elastomeric PDMS sample during indentation using digital volume correlation (DVC).We introduce multiple methods to experimentally evaluate the stress field beneath the contact surface and directly compare it to the predicted Hertzian stress distribution. Our approach leverages DVC-based finite element simulations, where boundary conditions are fully derived from the experimentally measured displacement field. This eliminates reliance on contact assumptions or numerical contact algorithms, ensuring that the stress field is determined solely by experimental data.To our knowledge, this work presents the first experimentally driven characterization of a full-field stress distribution beneath the contact surface, demonstrating qualitative agreement with classical contact models. However, our findings also indicate that achieving quantitative agreement will require the development of more complex models, which do not currently exist, as well as advancements in DVC regularization schemes to account for surface-specific behaviors.While this paper focuses on normal loading conditions, the experimental setup and methodology are fully adaptable to any type of contact loading scenario.