Current density inhomogeneities on electrodes (of physical, chemical, or optical origin) induce long-range electrohydrodynamic fluid motion directed toward the regions of higher current density. Here, we analyze the flow and its implications for the orderly arrangement of colloidal particles as effected by this flow on patterned electrodes. A scaling analysis indicates that the flow velocity is proportional to the product of the applied voltage and the difference in current density between adjacent regions on the electrode. Exact analytical solutions for the streamlines are derived for the case of a spatially periodic perturbation in current density along the electrode. Particularly simple asymptotic expressions are obtained in the limits of thin double layers and either large or small perturbation wavelengths. Calculations of the streamlines are in good agreement with particle velocimetry experiments near a mechanically generated inhomogeneity (a "scratch") that generates a current density larger than that of the unmodified electrode. We demonstrate that proper placement of scratches on an electrode yields desired patterns of colloidal particles.

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In this paper the analysis of failure and crack development in beams made of concrete is presented. The analysis was carried out on the basis of the performed experimental investigation and numerical simulations. A fictitious crack model based on nonlinear fracture mechanics was applied to investigate the development of strain softening of tensile concrete in plain concrete and slightly reinforced concrete beams. The role of strain softening was also discussed according to the inclined crack propagation in highly reinforced concrete beams. The analysis has brought the evidence that the mode of failure in flexural beams varies according to a longitudinal reinforcement ratio. A brittle failure due to the formation of a flexural crack takes place in plain and slightly reinforced concrete beams, and strain softening of tensile concrete is of paramount importance at failure crack initiation and propagation. A stable growth of numerous flexural cracks is possible in moderately reinforced concrete beams, and then the load carrying capacity is connected with reaching the yield stress of reinforcing steel or concrete crushing in the compression zone. In higher reinforced concrete beams without transverse reinforcement, brittle failure can take place due to shear forces and the development of diagonal cracks. However, strain softening of tensile concrete is not the only mechanism influencing the propagation of an inclined crack. Such mechanisms as aggregate interlock and dowel action of steel bars contribute more importantly to the development of failure crack. Keywords Strain softening • Fictitious crack model • Failure process The paper entitled "The analysis of failure in concrete and reinforced concrete beams with different reinforcement ratio", presented at the ICSID 2017 Conference has been considered for publication in the Special Issue of the Archive of Applied Mechanics Journal (AAM SI ICSID 2017).

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In the paper, the method of a numerical simulation concerning diagonal crack propagation in concrete beams was presented. Two beams reinforced longitudinally but without shear reinforcement were considered during the Finite Element Method analysis. In particular, a nonlinear method was used to simulate the crack evaluation in the beams. The analysis was performed using the commercial program ANSYS. In the numerical simulation, the limit surface for concrete described by Willam and Warnke was applied to model the failure of concrete. To solve the FEM-system of equations, the Newton-Raphson method was used. As the results of FEM calculations, the trajectories of total stains and numerical images of smeared cracks were obtained for two analyzed beams: the slender beam S5 of l eff = 1.8 m and the short beam S3k of l eff = 1.1 m. The applied method allowed to generate both fl exural vertical cracks and diagonal cracks in the shear regions. Some differences in the evaluation of crack patterns in the beams were observed. The greater number of fl exural vertical cracks which penetrated deeper in the beam S5 caused the lower stiffness and the greater deformation in the beam S5 compared to the short beam S3k. Numerical results were compared with the experimental data from the early tests performed by Słowik [3]. The numerical simulation yielded very similar results as the experiments and it confi rmed that the character of failure process altered according to the effective length of the member. The proposed numerical procedure was successfully verifi ed and it can be suitable for numerical analyses of diagonal crack propagation in concrete beams.