Sliding friction across the scales: Thermomechanical interactions and dissipation partitioning

Abstract

A homogenization framework is developed for determining the complete macroscopic thermomechanical sliding contact response of soft interfaces with microscopic roughness. To this end, a micro–macro mechanical dissipation equality is first established which enables defining a macroscopic frictional traction. The derivation allows both contacting bodies to be deformable, thereby extending the commonly adopted setting where one of the bodies is rigid. Moreover, it forms a basis for the second step, where a novel micro–macro thermal dissipation equality is established which enables defining partitioning coefficients that are associated with the frictional dissipation as it is perceived on the macroscale. Finally, a comparison of the temperature fields from the original heterogeneous thermomechanical contact problem and an idealized homogeneous one reveals an identification of the macroscopic temperature jump. The computational implementation of the framework is carried out within an incrementally two-phase micromechanical test which delivers a well-defined macroscopic response that is not influenced by purely algorithmic choices such as the duration of sliding. Two-dimensional numerical investigations on periodic and random samples from thermo-viscoelastic boundary layers with unilateral and bilateral roughness demonstrate the temperature–velocity–pressure dependence of the macroscopic contact response.