Computational homogenisation of soft porous materials and interfaces
Homogenisation is the process of characterising a system with a few parameters while retaining its basic characteristics. The computational counterpart of this process was at the centre of the EU-funded project MULTISCALEFSI (Multiscale fluid-solid interaction in heterogeneous materials and interfaces). The objective was to investigate whether homogenisation can be applied to estimate properties of fluid-solid interaction on the macroscale as well as the microscale. Researchers focused on lubrication interfaces with random and periodic micro-heterogeneities – referred to as roughness and texture, respectively. Inhomogeneous porous materials with fluid-filled pores are ubiquitous. Human bones fall under this category. Bone fluid serves as a carrier of nutrition elements to the porous bone scaffold. The fast growth of computing power and developments in microstructure reconstruction indicate that soon it will be possible to model details. Nevertheless, homogenisation offers a computationally inexpensive alternative. The MULTISCALEFSI team demonstrated that interface dynamics could be accurately projected onto the macroscale solution. Importantly, computational costs associated with a direct numerical solution of the micro-heterogeneous problem were avoided. Besides addressing spatial fluctuations in microscopic properties, researchers also succeeded in capturing temporal variations through appropriate averaging. In addition, interface deformations could be reproduced effectively through the anisotropic response of the interface. Over the past years, significant advances have been made in micromanufacturing. The MULTISCALEFSI approach to accommodate both fluid and solid phases under the same constitutive laws and accurately model their interaction will contribute to the design of surfaces with the desired microscopic and macroscopic performance. When combined with the boundary element method, the macroscopic response of the fluid-solid interface to a broad range of pore dimensions can be assessed. In these investigations, the classical Reynolds equation of hydrodynamic lubrication can be employed to describe finite configuration changes. A generalisation of the equation was proposed to ensure both a mathematically and physically sound response of soft interfaces. MULTISCALEFSI has resulted in a deeper understanding of the macroscopic response of textured surfaces, with important implications for ongoing efforts to reduce friction and wear.
