Homogenization of periodically structured contact interfaces

Abstract This contribution presents a homogenization approach for the computationally efficient modeling of two-dimensional solid bodies that interact through structured surfaces. Instead of resolving the detailed microscale geometry, the method introduces a finite-thickness surrogate layer that captures the essential mechanical response of the structured contact zone. The proposed formulation is based on the description of microscale quantities, such as (normal) gap and relative sliding velocity, which are transferred to the macroscale using internal volumetric variables. The elastic behavior of the surrogate layer is identified through a mean-field homogenization approach that accounts for the non-linear dependency of stress response on the relative slip. As a result, the anisotropic and history-dependent behavior of the interface can be captured within the model. The proposed method is validated using two benchmark problems: a vertical stack of two structured blocks and a knurled interference fit. In both cases, the finite-thickness layer accurately reproduces the mechanical response of the fully resolved model, i.e., stick–slip transitions, hysteresis, and partial interface separation. The good agreement with the reference solutions, combined with a significant reduction in computational cost, demonstrates the potential of the method for efficient multi-scale interface modeling.