Elastic–plastic contact between two hemispheres: a comparison study of deformable and rigid bases

Abstract This study examines the elastic–plastic contact behavior between two hemispheres under varying diameter ratios, with a focus on the influence of base flexibility. The finite element method is used to analyze both rigid and deformable base conditions. Brass, which possesses elastic-perfectly plastic properties, is the material used in this study. The upper hemisphere has a constant diameter, whereas the lower hemisphere has a variable diameter. The results show that deformable bases exhibit greater lateral displacement and can distribute stress uniformly, thereby reducing peak stress zones. The deviation in maximum contact pressure between the deformable and rigid bases remains below 1% at low loads (≤ 1 kN), when the load increases to approximately 19% (DR1, 30 kN), 48% (DR2, 30 kN), 12% (DR4, 10 kN), and 16% (DR7, 6 kN) at higher loads. The maximum von Mises stress for DR7 also increases by approximately 37%, confirming that the stress is sensitive to base compliance. In contrast, rigid bases focus stresses within a narrower region, which may increase the risk of local failure. A convergence study ensures mesh reliability, and the results are validated against established models. Based on the findings from this study, it can be concluded that base flexibility plays a crucial role in stress redistribution, particularly at high diameter ratios. This study provides practical insights into the structural and mechanical systems subjected to localized contact, including forming dies and medical implants. The outcomes of this study contribute to improving durability and reliability in contact-based devices. However, the present analysis is limited to static loading and elastic–perfectly plastic material behaviour, without considering time-dependent or thermal effects, which will be addressed in future studies.