Analytical Investigation of Tensile Stress and Displacement Behaviour in Elastic Ring Specimens Under Diametral Compression

This study presents a comprehensive analytical-numerical framework for characterizing the progressive contact phenomena in Brazilian ring discs. By solving a dual trigonometric series representation of the contact problem, the model enables precise determination of contact pressure distributions, angular extents, and the ensuing load–displacement relationships. The proposed analytical methodology is rigorously validated against finite element method (FEM) simulations. Under diametral compression conditions, the numerical approach yields a peak load (P) and displacement (δ) of 25.2 kN and 0.0362 mm, respectively, which exhibit minor deviations (approximately 7.93% under a 10% load variation) relative to FEM-predicted values (23.2 kN and 0.0340 mm).The analysis reveals a progressive expansion of the contact half-angle under diametral compression, initially involving a small stress-intensive segment and incrementally increasing to approximately 7° at 25% load, 13° at 50% load, and nearly 20° immediately before fracture initiation. Finite element simulations closely replicated this contact-angle evolution, achieving about 20° at peak load.