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Foam fluid has found wide applications in oilfield development, such as profile control, water plugging, gas channeling control, fracturing, and so on. As a non-Newtonian fluid, the successful application of foam is significantly influenced by its structure. The foam texture, however, is complex and irregular, and becomes even more complicated in porous media by the boundary effects. Therefore, the description of dynamic foam structure is crucial and a quantitative description method for foam fluid is worth exploring. In this paper, the fractal characteristics of foam in porous media are verified and combined with foam microdisplacement experiment, and the fractal rule of foam is found. The relationship between fractal dimension and pressure is also discussed. The results show that foam has dynamic fractal characteristics during transport in porous media and the box-counting fractal dimension ranges from 1 to 2. Furthermore, the dynamic change of foam fractal dimension during transport in porous media could be divided into three stages. In the first stage when no foam forms, the fractal dimension is about 2; in the second unsteady foam stage, the fractal dimension is reduced from 1.9 to 1.6; the last one is the steady stage and the fractal dimension is almost constant (about 1.6). Besides, the fractal dimension of foam fluid is closely related to displacement pressure. Low pressure corresponds to higher fractal dimension, and high pressure corresponds to lower fractal dimension. Pressure is negatively linearly correlated with fractal dimension. These results are expected to enrich the understanding of the foam dynamic characteristics in their advanced applications.

In this study, the dynamic responses of a cracked beam layed on a visco-elastic foundation subjected to moving loads are calculated. An Euler–Bernoulli beam model is used to describe the beam behaviors. In addition, the beam has several open cracks one-sided with different depths. By using the Fourier transform, the dynamic responses of the beam are determined analytically in the frequency domain with the help of Green’s function. By coupling with the periodic supported beam model, an analytical model of the railway sleeper is developed. This model allows the fast calculation of the dynamic responses of a damaged sleeper. A dynamic computational model using the FEM method was also developed and compared to the analytical model. The results from the two methods are relatively comparable for three cases of beams without cracks, beams with one crack, and beams with two cracks.

Recently, vitrimers with a reversible N$\to$B coordination dynamic structure have garnered interest not only for their self-healing and reprocessable properties but also for their hydrolytic stability. Reported vitrimers with N$\to$B internal coordination dynamic structure were excessively rigid, limiting their stretchability and toughness. This study synthesized a cross-linking agent (DNCB) with a cyclic nitrogen-boron coordination structure. This agent was then used in copolymerization with n-butyl acrylate (BA) and 4-vinylphenylboronic acid (BOH) to create soft vitrimers. By systematically tuning the composition, soft vitrimers exhibit water resistance along with high viscoelasticity, stretchability, toughness, and adhesive properties against various substrates. The observed mechanical behavior is attributed to the rapid relaxation of N$\to$B coordination bonds and slow relaxation of B-O bonds in boroxine within the polymer network. It is anticipated that these soft vitrimers will be applied in adhesives, flexible electronics, and soft robotics due to their favorable properties.