Analysis of solid lubricating materials microstructures properties in the frame of cylindrical coordinates system and reduced micromorphic model

In this paper, we provide detailed variational formulations for the reduced micromorphic model in rectangular and cylindrical coordinates. In these formulations, the material is modeled as consisting of deformable particles that exhibit microstrain and macroscopic strain fields. This microstrain field is independent of the macroscopic strain field of the entire material. In addition, all the kinematical and kinetical variables, equations of motion, and boundary conditions are formulated depending on the displacement and microstrain fields. Here we define the conditions that give the reduced micromorphic model with decoupled equations of motion such that the displacement field is described as independent of the microstrain field. In addition, we show the applicability of the developed formulation to investigate the simple shear behavior of solid-lubricant cylindrical films. An analytical solution for this model is developed, and numerical results are represented to demonstrate the microstructural topology effects on the mechanics of the lubricant film. The formulations and revealed findings of the present study are important for the design of novel coating architectures materials.