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The introduced numerical model accounts for scenarios where the lubricant quantity is significant yet discontinuous, leading to the formation of trapped compressible lubricant pockets at the contact interface. Additionally, it incorporates the plastic behavior of solid surfaces through a simple plastic saturation method, enabling comprehensive analysis of contact area, pressure distribution, and variations in the friction coefficient for different lubricant types, densities, and surface roughness levels. Comparison with experiments demonstrates that the developed model can estimate the influence of partial lubrication on the friction coefficients during aluminum sheet deep-drawing. Notably, the study reveals that when the lubricant quantity is insufficient to fill the gap, even minor adjustments in its distribution can affect the friction behavior of aluminum during forming processes.