Novel interface discretisation methods for contact mechanics

This thesis’ main scope is the presentation of two different methodologies for the analysis of contact problems involving morphologically complex or rough surfaces. Both approaches rely on the Finite Element Method (FEM) as the chosen computational framework. They hinge on the definition of an interface finite element used to model the space encompassed by two solids incontact. This kind of interface element is shared with the field of non-linear fracture mechanics, employed for the simulation of non-linear crack growth according to Cohesive Zone Model (CZM). Here, for the first time, the formulation is extensively applied to contact mechanics. With no further modifications, the interface element is suited for the solution of contact problems involving smooth and conformal interfaces, exploiting a node-to node approach and a penalty formulation for the enforcement of the contact constraints. The element is enriched with specific characteristics that allow for the solution of rough contact problems yet maintaining a very simple mesh discretisation, both using a single-scale and a multiscale approach. In the single-scale approach, a novel methodology is exploited that considers an equivalent flat interface and accounts for the actual geometry by a suitable correction of the standard normal gap. In the multi-scale approach, the Boundary Element Method (BEM) is exploited for solving, at a micro-scale, the normal contact problem of a rough rigid indenter making contact with an elastic half-space, according to a far-field displacement determined by the deformation imposed at a macro-scale. The solution in terms of averaged pressure and mean separation is then passed back to the macro-scale