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Hyperelastic materials like gels and rubbers have numerous applications in daily life and industrial production. However, most traditional contact models for rough solids do not include the hyperelastic deformation mechanism. This paper extends the linear-elastic incremental equivalent contact model to study the contact processes of hyperelastic rough solids. For any specific surface separation, the contact stiffness is determined by the total area and number of the contact patches, as well as the instantaneous tangent modulus. Analogous to buckle theory, we introduce the hyperelasticity of materials through employing the tangent modulus. By integrating the stiffness of contact spots, the normal contact force is then obtained. The load-area relation predicted by the present model exhibits consistency with finite element results even up to a contact area fraction of 90%. For hyperelastic solids with self-affine fractal rough surfaces, we investigate the effect of surface morphologies on contact behaviors. This research will be helpful for further studies about the lubrication, leakage, and wear of contact interfaces.

In the contact of rough surfaces, most contact patches are at the scale of micrometers, and thus, their contact deformation can be dominated by the size-dependent plasticity. In this paper, we propose a new strategy to analyze the role of strain gradient plasticity in the contact response between a realistic rough surface and a rigid plane, which modifies the incremental contact model based on the mechanism-based gradient plasticity (MSGP) theory. For several different rough surfaces with their topography measured experimentally, the relations between applied load and real contact area are derived in a simple but effective way. It is found that strain gradient plasticity significantly increases the level of mean contact pressure. The hardening effect caused by strain gradient plasticity weakens somewhat as the contact area increases. Compared with previous methods, the present model might be more efficient and of wider application.