The semi-circular bending method (SCB) is a useful test for evaluating the cracking resistance of asphalt mixtures with added reclaimed asphalt shingles. A mixture of the asphalt concrete AC 16 with 50/70 paving bitumen was used for the binder course test as a reference mix. The purpose of the paper is to evaluate two aging conditions (short-term and long-term) of the above-mentioned asphalt mixtures in relation to their fracture properties. Laboratory experiments are enhanced with the application of image processing techniques (digital image correlation and image segmentation) that account for the asphalt mixture heterogeneity. Consequently, they can provide a more detailed description of the specimen performance. Statistical analyses of the laboratory results indicate that the best sensitivity in terms of differentiating the tested mixtures, especially taking into account the aging conditions of the mixtures, was observed for the post-peak parameters such as the flexibility index (FI), toughness index (TI), and, above all, cracking resistance index (CRI), for which the average coefficient of the result variability is approximately 10%, while for the FI and TI parameters it is approximately 30%. Digital image correlation analyses provided a confirmative illustration of the aforementioned observation.

In this paper, we present an enhanced framework for the synthetic asphalt concrete (AC) microstructure generation for the numerical analysis purposes. It is based on the Voronoi tessellation concept with some necessary extensions that allow for the reliable generation of the aggregate particles of the given size distribution. The synthetic microstructure generation allows for faster numerical modeling of the novel materials. It can partially replace the X-ray computed tomography approach, which is frequently used in such analysis. Our framework is a kind of compilation of the known techniques with the enhancements applied to expedite the microstructure modeling process. Therefore, the generated microstructure is used in the numerical upscaling to model the macroscale asphalt concrete properties. We restrict ourselves (in this paper only) to the 2D elastic computations. We also assume the perfect bonding between these two materials and the static load for the sake of simplicity. The upscaling is performed by the multiscale finite element method (MsFEM). A short recapitulation of the MsFEM foundations as well as the numerical test comparing the overkill mesh solution with the upscaled one is provided in the paper. The test results confirm that the whole presented methodology can serve as a fast and reliable tool for the tests on novel asphalt mixtures and other heterogeneous materials. It can reduce the cost of the design process substituting some of the laboratory experiments, giving the opportunity to test the developed constitutive models and expedite the numerical analysis itself.

In this paper, we deal with the issue of asphalt concrete microstructure recognition for further numerical analysis. An efficient reconstruction of the underlying microstructure makes the composite analysis more reliable. We propose for this purpose a methodology based on the image processing and focus on a two-dimensional case (it can be easily used as a part of the 3D geometry reconstruction, however). Initially obtained geometry of the inclusions is further simplified to reduce the cost of the finite element mesh generation. Three straightforward geometry simplification algorithms are used to perform this process in a controlled way. Subsequently, we present the solutions of two problems, i.e., heat flow and elasticity (plane strain), in order to illustrate the effectiveness of the whole elaborated methodology. The numerical results were obtained using the finite element method. Consequently, an error analysis is demonstrated in order to refer the overkill mesh solutions to the ones presented in this study. The main finding of this paper is the efficient methodology dedicated to a digital reconstruction of the asphalt concrete microstructure by the image processing. It can be also extended to other materials exhibiting similar microstructure.

In this paper, we present a new approach to model the steady-state heat transfer in heterogeneous materials. The multiscale finite element method (MsFEM) is improved and used to solve this problem. MsFEM is a fast and flexible method for upscaling. Its numerical efficiency is based on the natural parallelization of the main computations and their further simplifications due to the numerical nature of the problem. The approach does not require the distinct separation of scales, which makes its applicability to the numerical modeling of the composites very broad. Our novelty relies on modifications to the standard higher-order shape functions, which are then applied to the steady-state heat transfer problem. To the best of our knowledge, MsFEM (based on the special shape function assessment) has not been previously used for an approximation order higher than p = 2, with the hierarchical shape functions applied and non-periodic domains, in this problem. Some numerical results are presented and compared with the standard direct finite-element solutions. The first test shows the performance of higher-order MsFEM for the asphalt concrete sample which is subject to heating. The second test is the challenging problem of metal foam analysis. The thermal conductivity of air and aluminum differ by several orders of magnitude, which is typically very difficult for the upscaling methods. A very good agreement between our upscaled and reference results was observed, together with a significant reduction in the number of degrees of freedom. The error analysis and the p-convergence of the method are also presented. The latter is studied in terms of both the number of degrees of freedom and the computational time.

Computing the pseudoinverse of a matrix is an essential component of many computational methods. It arises in statistics, graphics, robotics, numerical modeling, and many more areas. Therefore, it is desirable to select reliable algorithms that can perform this operation efficiently and robustly. A demanding benchmark test for the pseudoinverse computation was introduced. The stiffness matrices for higher order approximation turned out to be such tough problems and therefore can serve as good benchmarks for algorithms of the pseudoinverse computation. It was found out that only one algorithm, out of five known from literature, enabled us to obtain acceptable results for the pseudoinverse of the proposed benchmark test.