When two objects slide against each other, wear and friction occur at their interface. The accumulation of wear forms what is commonly referred to as a third-body''. Understanding third-body evolution has significant applications in industry, where controlling and measuring friction and wear is essential, notably to minimize energy losses. In the geomechanics community, the granular material localized in a fault, is known as gouge'' and understanding its frictional properties is crucial in the study of earthquake nucleation. The goal of this thesis is to develop a numerical tool that models the third-body and its surrounding regions to improve our understanding of its evolution.

The third-body is a localized amorphous region subject to severe deformation, while the regions surrounding the third-body, experience moderate strain and damage. We showed that the loading conditions applied on the surrounding regions and their distance from the contact interface have an impact on the third-body thickness evolution and frictional properties. Thus, to accurately capture the third-body behavior the surrounding regions should be represented which requires modeling large domains. To do so, a multiscale approach is developed in this thesis. The Discrete Element Method (DEM) is used to model the third-body where discretization is required, while the Finite Element Method (FEM) is utilized to model the surrounding regions, as continuum domains. In our model, both the FEM and DEM represent the same material.


To couple FEM and DEM, we generalized the bridging method originally used for regular lattices, to amorphous materials. This approach considers an overlapping region, where both continuum and discrete domain are linked by means of Lagrange multipliers. Two different types of formulations are considered: strong and weak. To test this approach, we considered a granular system without any cohesion, subject to confinement pressure. Several DEM sample sizes are tested to establish the minimum sample size at which constant elastic properties are obtained. This determines the material properties to use in the FEM and the minimum mesh size needed at the FEM/DEM interface to match material properties across both domains. The imposed pre-stress of the FE elements results in spurious forces, that we corrected. Then, this coupling method is used to model crack propagation and wear formation using an adhesive contact law.

To facilitate the growth of the third-body without being restricted by the finite size of the discrete domain, we implemented an adaptive coupling strategy. This strategy enables regions modeled with FEM to transition to discrete regions, thereby increasing the size of the discrete domain. The discrete expansion occurs if a criterion based on the average change of neighbors for each particle is satisfied. Implementing this approach requires several steps: first, adjusting coupling geometries, then, inserting a new particle layer, and finally, deactivating a FE element layer. The efficacy of this approach is demonstrated for both amorphous system, and a crystalline one. Lastly, we used this method to model the evolution of a third-body involving the insertion of elliptical rigid bodies at the contact interface.