Direct numerical simulation and analysis of saturated deformable porous media.
详细信息
文摘
Applications of fluid infiltrated deformable porous media range from soil consolidation, filtration and absorbancy products, fabric and textiles to human tissue and bone modeling. Understanding the behaviour of these media under externally applied load is critical to the design and development of products related to these media. In deformable porous media, the geometrical complexity of the solid structure coupled with the need for a unified treatment of all the interacting phases makes a micromechanical approach of the problem intractable. Thus, the existing techniques, such as "Biots theory" or the "Theory of Porous Media" are based on homogenization techniques, in the sense that they assume the solid and all the fluid phases as a smeared media. These kind of approaches, in spite of their mathematical rigour, are not suitable for micromechanical investigations such as the effect of microstructure on the deformational behaviour or the constitutive relations in the media during deformation. In order to perform such investigations an approach based on direct numerical simulations, capable of leveraging the ever increasing computational power would be ideally suited. In this research work, a numerical scheme based on the hybrid lattice-Boltzmann finite-element method is developed to carry out the direct numerical simulations of deformable porous media. The method has been parallelized to make use of distributed computing. The efficiency and inherent parallel nature of the lattice Boltzmann method coupled with the robustness of finite element method implemented in a parallel framework provided by the highly scalable toolkit of PETSc lend as a powerful tool to not only tackle the problem of deformable porous media but also to undertake any problem involving complex interaction of fluid and solid phases in the linear elastic limit within the small to medium time and spatial scales. The method has been used to understand the deformational characteristics of model porous media made up of spheres and cylinders. The deformational response of the model porous media constructed in this fashion is compared to existing analytical solution. For the comparison, the bulk properties of the macroscopic porous media are obtained through the single phase properties of the constituent phases. The deformational behaviour is seen to match with the analytical solution closely. Thus it is found that macroscopic behaviour of a generic porous media can be recovered with the use of model porous media constructed with simplified geometries. This finding motivated research in using model porous geometries to represent the more complex real porous geometries in order to perform investigations of deformation on the latter. An attempt has been made to apply this technique to the complex geometries of "felt", a fibrous mat used in paper industries) to recover its deformational behaviour. These investigations lead to new understanding on the effect of fiber diameter on the bulk properties of a fibrous media and subsequently on the deformational behaviour of the media. Additionally this approach offers tremendous decrease in the computational load and meshing time, while providing capturing the relevant behavioural characteristics of the media without any approximations. Further the method has been used to investigate the constitutive relationships in deformable porous media that are effected by the microstructure of the solid phase. Particularly the relationship between permeability and porosity during the deformation of the media is investigated. Results show the need of geometry specific investigations.