Novel interface discretisation methods for contact mechanics

This thesis’ main scope is the presentation of two differentmethodologies 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 fracturemechanics, employed for the simulation of non-linear crackgrowth according to Cohesive Zone Model (CZM). Here, forthe first time, the formulation is extensively applied to contact mechanics. With no further modifications, the interfaceelement 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. Inthe 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 standardnormal 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 amacro-scale. The solution in terms of averaged pressure and mean separation is then passed back to the macro-scale.