Modelling and simulation in tribology of complex interfaces

Tribology is known as the science of surfaces in relative motion and involves complex interactions over multiple length and time scales. Therefore, friction, lubrication and wear of materials are intrinsically highly multiphysics and multiscale phenomena. Several modelling and simulation tools have been developed in the last decades, always requiring a trade-off between the available computational power and the accurate replication of the experimental results. Despite nowadays it is possible to model with extreme precision elastic problems at various scales, further eorts are needed for taking into account phenomena like plasticity, adhesion, wear, third-body friction and boundary and solid lubrication. The situation becomes even more challenging if considering non-conventional nano-, as in the case of polymer surfaces and interfaces, or microstructures, as for the hierarchical organisations observed in biological systems. Specically, biological surface structures have been demonstrated to present exceptional tribological properties, for instance in terms of adhesion (e.g., the gecko pad), superhydrophobicity (e.g., the lotus leaf) or fluid-dynamic drag reduction (e.g., the shark skin). This has suggested the study and development of hierarchical and/or bio-inspired structures for applications in tribology. Therefore, by taking inspiration from Nature, we investigate the effect of property gradients on the frictional behaviour of sliding interfaces, considering lateral variations in surface and bulk properties. 3D finite-element simulations are compared with a 2D spring-block model to show how lateral gradients can be used to tune the macroscopic coefficients of friction and control the propagation of detachment fronts. Complex microscale phenomena govern the macroscopic behaviour also of lubricated contacts. An example is represented by solid lubrication or third-body friction, which we study with 3D discreteelement simulations. We show the effects of surface waviness and of the modelling parameters on the macroscopic coefficient of friction. Many other natural systems present complex interfacial interactions and tribological behaviour. Plant roots, for instance, display optimised performance during the frictional penetration of soil, especially thanks to a particular apex morphology. Starting from experimental investigations of different probe geometries, we employ the discrete-element method to compute the expended work during the penetration of a granular packing, conrming the optimal bio-inspired shape. This has allowed to follow also an integrated approach including image acquisition and processing of the actual geometries, 3D printing, experiments and numerical simulations. Finally, another interesting example of advanced biological interface with optimised behaviour is represented by biosensing strucviii tures. We employ fluid-structure interaction numerical simulations for studying the response of spiders' trichobothria, which are among the most sensitive biosensors in Nature. Our results highlight the role of the fluid-dynamic drag on the system performance and allow to determine the optimal hair density observed experimentally. Both the third-body problem and the possibility to tune the frictional properties can be considered as the next grand challenges in tribology, which is going to live a "golden age" in the coming years. We believe the results discussed in this Doctoral Thesis could pave the way towards the design of novel bio-inspired structures with optimal tribological properties, for the future development of smart materials and innovative solutions for sliding interfaces.