Hybrid Deterministic–Microlevel Model of Normal Contact Stiffness for Textured Surfaces

Normal contact stiffness of textured interfaces is controlled by the load-bearing contribution of deterministic texture and by the nonlinear response of rough load-bearing regions. This study formulates a hybrid deterministic–microlevel model that couples regular relief patterns—including dimples, grooves, periodic ribs and scraped high points—with a micromechanical representation of plateau roughness. Depending on texture topology and scale hierarchy, the microlevel response is represented either by a Greenwood–Williamson (GW) statistical contact model with a smooth elastic–plastic (EP) transition or by a fractal contact model. The deterministic level accounts for open-area fraction, texture depth and load redistribution, and it includes a finite-gauge spectral correction for periodic ribs and grooves to account for the finite measurement window. In a metallic dimple benchmark, the hybrid deterministic-texture/GW–EP formulation yields a mean relative error of 16.3% across all data points in the two selected textured series. In a saturated square-wave benchmark, the finite-gauge spectral correction yields a mean relative error of 10.37% for the independent patterned points. A compliance-based topology criterion is then established to determine, from open-area fraction, element depth, applied load and the ratio between texture period and plateau-roughness spacing, whether stiffness is governed primarily by deterministic texture, by micro-roughness or by their coupled response. The resulting formulation supports early-stage design exploration without requiring a full three-dimensional contact calculation at every parameter point. Independent periodic three-dimensional checks for circular-dimple cells showed that the finest FE solution agreed with the spectral prediction of the deterministic normal approach within 1.2%; the correction estimated by direct unilateral BEM changed total stiffness by no more than approximately 5% in the tested texture-influenced case.