Size-Dependent Effects and Surface Roughness in Contact Mechanics

Abstract With the increasing miniaturization of mechanical systems and the prevalence of rough surfaces in engineering applications, understanding and accurately characterizing the contact response at small scales has become crucial. This review article provides a comprehensive analysis of two significant aspects in the field of contact mechanics: the size-dependent response of single asperity due to strain gradients and surface effects, and the contact behavior of rough surfaces. The former forms the foundation for the latter analysis, as real surfaces are inherently rough and contact occurs at discrete asperities. At the microscale, strain gradients play a dominant role, as classical continuum mechanics fails to account for the intrinsic material length. Further downscaling to the nanoscale highlights the importance of surface effects due to the large surface-to-bulk ratio. The first section examines these distinct size-dependent effects and their implications for contact mechanics across different scales. The second section further focuses on the contact of rough surfaces, highlighting incremental contact models, contact behavior at large contact fraction where asperity interactions are significant, adhesive rough contact in soft materials, and experimental advances that improve the understanding and validation of these models. Together, these two topics underscore the need for refined theoretical and experimental approaches to accurately model and predict the contact behavior at small scales and with realistic multi-scale roughness.