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Al–Mg–Si alloys are used in aircraft, train, and car manufacturing industries due to their advantages, which include non-corrosivity, low density, relatively low cost, high thermal and electrical conductivity, formability, and weldability. This study investigates the bulk mechanical properties of Al–Mg–Si alloys and the influence of the Si/Mg ratio on these properties. The Al cell was used as the starting structure, and then nine structures were modeled with varying percentages of aluminium, magnesium, and silicon. Elastic constant calculations were conducted using the stress–strain method as implemented in the quantum espresso code. This study found that the optimum properties obtained were a density of 2.762 g/cm3, a bulk modulus of 83.3 GPa, a shear modulus of 34.4 GPa, a Vickers hardness of 2.79 GPa, a Poisson’s ratio of 0.413, a Pugh’s ratio of 5.42, and a yield strength of 8.38 GPa. The optimum Si/Mg ratio was found to be 4.5 for most of the mechanical properties. The study successfully established that the Si/Mg ratio is a critical factor when dealing with the mechanical properties of the Al–Mg–Si alloys. The alloys with the optimum Si/Mg ratio can be used for industrial applications such as plane skins and mining equipment where these properties are required.

The search for biocompatible, non-toxic, and wear-resistant materials for orthopedic implant applications is on the rise. Different materials have been investigated for this purpose, some of which have proved successful. However, one challenge that has proven difficult to overcome is the balance between ductility and hardness of these materials. This study employed ab initio calculations to investigate the structural and mechanical properties of niobium nitride (NbN) alloyed with hafnium, indium, and zirconium, with the aim of improving its hardness. The calculations made use of density function theory within the quantum espresso package’s generalized gradient approximation, with Perdew–Burke–Ernzerhof ultrasoft pseudopotentials in all the calculations. It was found that addition of the three metals led to an improvement in both the shear and Young’s moduli of the alloys compared to those of the NbN. However, both the bulk moduli and the Poisson’s ratios reduced with the introduction of the metals. The Young’s moduli of all the samples were found to be higher than that of bone. The Vickers hardness of the alloys were found to be significantly higher than that of NbN, with that of indium being the highest. The alloys are therefore good for wear-resistant artificial bone implants in ceramic acetabulum, and also in prosthetic heads.

Mechanical compaction is often used to densify building earth blocks by reducing the void between the particles. Compacted stabilised earth involves a binder, which holds the particles of the materials together. The compaction and addition of binders to the earth can modify its transport, mechanical, and acoustical properties. In this study, the acoustic transmission coefficient, porosity, and airflow resistivity were investigated by varying the concentrations of water hyacinth ash (WHA) and sugarcane bagasse ash (SBA) binders. An acoustic test rig comprising an acoustic wave guide made from joined water pipes was employed to analyse the influence of the WHA and SBA binders on the acoustical performance of the earth blocks. It was found out that the measured acoustic wave transmission was sensitive to the variation in the composition of WHA and SBA in the earth blocks. Increasing the WHA concentration led to an increase in the acoustic transmission coefficient and porosity, but reduced the airflow resistivity of the compressed earth blocks; while increasing the SBA reduced the transmission coefficient and porosity, but increased the airflow resistivity. This shows that SBA has a stronger binding property than WHA, which is ideal for the manufacture of stronger earth blocks, while the higher porosity of the earth blocks obtained with WHA is good for the construction of porous walls, which is good for maintaining the airflow between the inside of buildings and the surrounding.

In this paper, a generalization of Poiseuille’s law for a self-similar fluid flow through a tube having a rough surface is proposed. The originality of this work is to consider, simultaneously, the self-similarity structure of the fluid and the roughness of the tube surface. This study can have a wide range of applications, for example, for fractal fluid dynamics in hydrology. The roughness of the tube surface presents a fractal structure that can be described by the surface fractal noninteger dimensions. Complex fluids that are invariant to changes in scale (self-similar) are modeled as a continuous medium in noninteger dimensional spaces. In this work, the analytical solution of the Navier–Stokes equations for the case of a self-similar fluid flow through a rough “fractal” tube is presented. New expressions of the velocity profiles, the fluid discharge, and the friction factor are determined analytically and plotted numerically. These expressions contain fractal dimensions describing the effects of the fractal aspect of the fluid and of that of the tube surface. This approach reveals some very important results. For the velocity profile to represent a physical solution, the fractal dimension of the fluid ranges between 0.5 and 1. This study also qualitatively demonstrates that self-similar fluids have shear thickening-like behavior. The fractal (self-similarity) nature of the fluid and the roughness of the surface both have a huge impact on the dynamics of the flow. The fractal dimension of the fluid affects the amplitude and the shape of the velocity profile, which loses its parabolic shape for some values of the fluid fractal dimension. By contrast, the roughness of the surface affects only the amplitude of the velocity profile. Nevertheless, both the fluid’s fractal dimension and the surface roughness have a major influence on the behavior of the fluid, and should not be neglected.

In this paper, the study of the fully developed flow of a self-similar (fractal) power-law fluid is presented. The rheological way of behaving of the fluid is modeled utilizing the Ostwald–de Waele relationship (covering shear-thinning, Newtonian and shear-thickening fluids). A self-similar (fractal) fluid is depicted as a continuum in a noninteger dimensional space. Involving vector calculus for the instance of a noninteger dimensional space, we determine an analytical solution of the Cauchy equation for the instance of a non-Newtonian self-similar fluid flow in a cylindrical pipe. The plot of the velocity profile obtained shows that the rheological behavior of a non-Newtonian power-law fluid is essentially impacted by its self-similar structure. A self-similar shear thinning fluid and a self-similar Newtonian fluid take on a shear-thickening way of behaving, and a self-similar shear-thickening fluid becomes more shear thickening. This approach has many useful applications in industry, for the investigation of blood flow and fractal fluid hydrology.

In this paper, the influence of the transverse wave on sound propagation in a porous medium with a flexible structure is considered. The study is carried out in the time domain using the modified Biot theory obtained by the symmetry of the Lagrangian (invariance by translation and rotation). The viscous exchanges between the fluid and the structure are described by fractional calculus. When a sound pulse arrives at normal incidence on a porous material with a flexible structure, the transverse waves interfere with the longitudinal waves during propagation because of the viscous interactions that appear between the fluid and the structure. By performing a calculation in the Laplace domain, the reflection and transmission operators are derived. Their time domain expressions depend on the Green functions of the longitudinal and transverse waves. In order to study the effects of the transverse wave on the transmitted longitudinal waves, numerical simulations of the transmitted waves in the time domain by varying the characteristic parameters of the medium are realized whether the transverse wave is considered or not.

Ultrasound propagation in porous materials involves some higher order physical parameters whose importance depends on the acoustic characteristics of the materials. This article concerns the study of the influence of two parameters recently introduced, namely, the viscous and thermal surfaces, on the acoustic wave reflected by the first interface of a porous material with a rigid structure. These two parameters describe the fluid/structure interactions in a porous medium during the propagation of the acoustic wave in the high-frequency regime. Both viscous and thermal surfaces are involved in Laurent expansion, which is limited to the dynamic tortuosity and compressibility to a higher order and corrects the visco-thermal losses. A sensitivity study is performed on the modulus of the reflection coefficient at the first interface as a function of frequency and on the waveforms reflected by the porous material in the time domain. The results of this study show that highly absorbent porous materials are the most sensitive to viscous and thermal surfaces, which makes the consideration of these two parameters paramount for the characterization of highly absorbent porous materials using the waves reflected from the first interface.

A fractional-order wave equation is established and solved for a space of three dimensions using spherical coordinates. An equivalent fluid model is used in which the acoustic wave propagates only in the fluid saturating the porous medium; this model is a special case of Biot’s theory obtained by the symmetry of the Lagrangian (invariance by translation and rotation). The basic solution of the wave equation is obtained in the time domain by analytically calculating Green’s function of the porous medium and using the properties of the Laplace transforms. Fractional derivatives are used to describe, in the time domain, the fluid–structure interactions, which are of the inertial, viscous, and thermal kind. The solution to the fractional-order wave equation represents the radiation field in the porous medium emitted by a point source. An important result obtained in this study is that the solution of the fractional equation is expressed by recurrence relations that are the consequence of the modified Bessel function of the third kind, which represents a physical solution of the wave equation. This theoretical work with analytical results opens up prospects for the resolution of forward and inverse problems allowing the characterization of a porous medium using spherical waves.

In this paper, we present a fractal (self-similar) model of acoustic propagation in a porous material with a rigid structure. The fractal medium is modeled as a continuous medium of non-integer spatial dimension. The basic equations of acoustics in a fractal porous material are written. In this model, the fluid space is considered as fractal while the solid matrix is non-fractal. The fluid–structure interactions are described by fractional operators in the time domain. The resulting propagation equation contains fractional derivative terms and space-dependent coefficients. The fractional wave equation is solved analytically in the time domain, and the reflection and transmission operators are calculated for a slab of fractal porous material. Expressions for the responses of the fractal porous medium (reflection and transmission) to an acoustic excitation show that it is possible to deduce these responses from those obtained for a non-fractal porous medium, only by replacing the thickness of the non-fractal material by an effective thickness depending on the fractal dimension of the material. This result shows us that, thanks to the fractal dimension, we can increase (sometimes by a ratio of 50) and decrease the equivalent thickness of the fractal material. The wavefront speed of the fractal porous material depends on the fractal dimension and admits several supersonic values. These results open a scientific challenge for the creation of new acoustic fractal materials, such as metamaterials with very specific acoustic properties.