Mechanics of isotropic points under frictional contacts: experimental and theoretical studies

Abstract

Understanding the mechanical behaviour of isotropic points (IPs)-regions of hydrostatic stress with zero shear-is essential for interpreting photoelastic fringe patterns and analysing load transfer in solid bodies. This study investigates IP formation and evolution in circular disks subjected to four-point loading using a combination of photoelastic experiments, digital image processing, and analytical modelling. A generalised stress framework based on superposition is developed to predict isochromatic fringe fields and IP locations for arbitrary combinations of normal and tangential contact forces. Beyond case-specific solutions, the study establishes a unified physical interpretation of fringe patterns based on the concepts of zero-shear loci, symmetry constraints, and stress-topology transitions. It is shown that symmetry governs the localisation of IPs along principal axes, while symmetry breaking leads to their migration into the disk interior. Under normal loading, IPs form along boundary-induced zero-shear regions and undergo coalescence and splitting, indicating transitions in stress topology. In contrast, tangential loading produces a persistent central isotropic point corresponding to a null stress state, resulting in qualitatively different fringe evolution. A novel inverse methodology is proposed to determine contact force components from experimentally measured IP coordinates. The results demonstrate that IP locations are invariant to the load magnitude but highly sensitive to the load direction, making them reliable indicators of the load geometry. The findings highlight isotropic points as fundamental descriptors of stress redistribution and fringe topology. While the present study focuses on a circular disk under four-point loading, the framework may be extended to more complex systems such as granular assemblies and contact-driven structures, subject to further investigation.