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Multiscale Fluid-Solid Interaction in Heterogeneous Materials and Interfaces

Final Report Summary - MULTISCALEFSI (Multiscale Fluid-Solid Interaction in Heterogeneous Materials and Interfaces)

Fluid-solid interaction (FSI) governs nature. From soft tissue modeling to lubrication technology, FSI problems in biomechanics and engineering are a major challenge in computational science. This challenge is further intensified by the multiscale structure of materials and interfaces as well as by the finite configurational change (FCC) that a microstructure experiences under large deformations.
The goal of this research was to investigate novel computational strategies for the modeling and analysis of multiscale FSI in heterogeneous materials and interfaces with FCC on all scales and homogenization as the core scale-transition technique. The examples that will motivate and guide this research were potential biological and industrial applications of the novel computational framework: (1) soft porous materials such as the articular cartilage that functions together with pore-level fluids in order to provide mechanical support, and (2) textured interfaces in bearings and polymeric seals that deliver improved tribological performance for rotating machinery. Overall, the investigations that were envisaged had the potential to contribute to an improved understanding of the microscopic FSI basis of classical porous media and lubrication theories, thereby enabling future research on scaffold and texture design optimization. After a relocation from Germany to Turkey, the fellowship was aimed to support the researcher in establishing an internationally recognized group as an assistant professor by strengthening and extending his expertise and European collaborations.

Research towards the stated goals was carried out along two major branches. On the one branch, robust homogenization theories allowed the identification of a strong similarity between porous media and hydrodynamic lubrication formulations on the macroscale as well as between their microscopic mathematical formulations. Although porous media poses a three-dimensional problem and lubrication is intrinsically two-dimensional, the latter is in some sense more general due to the fact that the surfaces interacting with the fluid are additionally in motion. In view of this similarity, attention was focused to lubrication interfaces with random and periodic micro-heterogenities, the former often referred to as roughness while the latter is often referred to as texture. Research carried out in this context displayed how the interface dynamics can be very accurately projected onto the macroscale problem solution, while avoiding significant costs that would be associated with a direct numerical resolution of the micro-heterogeneous problem. This was realized through robust homogenization theories which addressed spatial variations in the microscopic properties. Additional research also verified that temporal variations can also be efficiently reflected through proper averaging approaches. In all regimes, the significant influence of interface deformation, i.e. finite configurational change, was also demonstrated via deformation-induced anisotropic response of the interface. In view of a rapidly increasing focus on complex interface texture, supported by significant advances in micro-manufacturing techniques over the past 10 years, attention was then focused to the design of textures that would deliver desired microscopic and macroscopic performances. Hence, although originally aimed as a future topic of research, a high-impact contribution was made by addressing this increasingly important scientific issue in a timely manner. Moreover, in collaboration with researchers that joined the same institution over the duration of this project, efficient Boundary Element Method techniques were applied to the high-fidelity resolution of the microscopic response, resulting in a technique that can accurately predict the macroscopic response in all ranges of textures dimensions, i.e. an ability to address absolute length scale effects was assessed (relevant publication under review). In these investigations, the underlying microscopic equation is the classical Reynolds equation of hydrodynamic lubrication. Since a core idea of the project was to address finite configurational changes, an investigation was carried out on the limitations of this equation along the second branch of research. Interestingly, it was found that this classical equation is unable to address technologically relevant soft interfaces where deformation plays a prominent physical role. A suitable generalization of the equation to ensure a mathematically and physically sound interface response was then realized. Finally, in the context of computational tribology, an important complementary topic is contact. Here, research was carried out through a very recently proposed numerical technique, namely isogeometric analysis. Novel discretization and optimization techniques were applied to challenging contact problems and the significant advantages of the developed methods were extensively demonstrated, thereby paving the way for a future numerical technique where lubrication could be addressed together with contact.

Overall, the summarized research activities involved a national collaboration as well as international collaborations that were established during the course of this project (with Germany, Japan, Poland and the Netherlands). 1 graduate student was involved (Master's level) and 2 undergraduate students participated. All of these students contributed to the publications emanating from the research activities of the group. Over the course of four years, the researcher leading this research established a group which produced close to 20 publications in areas that were directly or closely related to the topic of the project, and presented the results in more than 20 presentations (invited talks, keynote lectures, conferences). The funding of the project allowed the researcher and the students to travel to summer schools and conferences, helped host short stays of researchers, and covered equipment expenses.

All activities of the research group that was responsible for this project may be reached through the website .