Permeability is a parameter that measures the resistance that fluid faces when flowing through a porous medium. Usually, this parameter is determined in routine laboratory tests by applying Darcy’s law. Those tests can be complex and time-demanding, and they do not offer a deep understanding of the material internal microstructure. Currently, with the development of new computational technologies, it is possible to simulate fluid flow experiments in computational labs. Determining permeability with this strategy implies solving a homogenization problem, where the determination of the macro parameter relies on the simulation of a fluid flowing through channels created by connected pores present in the material’s internal microstructure. This is a powerful example of the application of fluid mechanics to solve important industrial problems (e.g., material characterization), in which the students can learn basic concepts of fluid flow while practicing the implementation of computer simulations. In addition, it gives the students a concrete opportunity to work with a problem that associates two different scales. In this work, we present an educational code to compute absolute permeability of heterogeneous materials. The program simulates a Stokes flow in the porous media modeled with periodic boundary conditions using finite elements. Lastly, the permeability of a real sample of sandstone, modeled by microcomputed tomography (micro-CT), is obtained.

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The aim of this work is to determine effective elastic properties of pultruded Glass Fiber Reinforced Polymer using micro-CT in conjunction with a two-step numerical homogenization technique. The two-step homogenization involves the segmentation of the material's layers, which was made here by means of a machine learning approach. The segmentation was validated through the comparison between the phase's volume fractions of samples obtained from the segmented images and laboratory tests. Further, a standard accuracy analysis in a 10-fold cross validation was performed. The samples' effective axial Young's modulus obtained by our numerical homogenization were compared to results obtained from experimental tests. For both the experimental tests and the image-based numerical analysis we considered samples extracted from the same profile. The two-step methodology allowed the homogenization of large volumes of the composite corresponding to the whole thickness of the profile, imaged with a high resolution. In addition to the axial effective Young's modulus, our methodology was also able to successfully provide all the other elastic properties along the three orthogonal directions, even the ones that are arduous to be obtained in laboratory setups.

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