Elastoplastic model of normal contact stiffness of dry friction fractal surfaces

Based on the three-dimensional fractal theory and the assumption of equivalent rough surfaces, this study comprehensively considers the continuous and monotonic characteristics of asperity deformation during the contact process and incorporates the influence of interface friction. By introducing a domain extension factor, a fractal model of normal contact stiffness for joint surfaces is established, which correlates with the scale level of asperities. Through simulations of the proposed model, the effects of friction coefficient, fractal dimension, fractal characteristic length scale parameter, and normal contact load on normal contact stiffness were systematically analyzed. The model was validated against experimental data and compared with existing models, demonstrating its accuracy in numerical calculations of normal contact stiffness for practical joint surfaces and confirming its feasibility. The developed model has a relative error of 1.5%–4.5% and provides a theoretical foundation for the improvement of related mechanical structures.