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The estimation of bearing capacity for shallow foundations in swelling soil is an important and complex context. The complexity is due to the unsaturated swelling soil related to the drying and humidification environment. Hence, a serious study is needed to evaluate the effect of swelling potential soil on the foundation bearing capacity. The purpose of this paper is to analyze the bearing capacity of a rough square foundation founded on a homogeneous swelling soil mass, subjected to vertical loads.

A proposed numerical model based on the simulation of the swelling pressure in the initial state, followed by an elastoplastic behavior model may be used to calculate the foundation bearing capacity. The analyses were carried out using the finite-difference software (FLAC 3 D) with an elastic perfectly plastic Mohr–Coulomb constitutive model. Moreover, the numerical results obtained are compared with the analytical solutions proposed in the literature.

The numerical results were in good agreement with the analytical solutions proposed in the literature. Also, reasonable capacity and performance of the proposed numerical model.

The proposed numerical model is capable to predict the bearing capacity of the homogeneous swelling soil mass loaded by a shallow foundation. Also, it will be of great use for geotechnical engineers and researchers in the field.

The purpose of this paper is to investigate the influence of the resolution with which interfaces of fractal geometry are represented, on the contact area and consequently on the contact interfacial stresses. The study is based on a numerical approach. The paper focuses on the differences between the cases of elastic and inelastic materials having as primary parameter the resolution of the interface.

A multi‐resolution parametric analysis is performed for fractal interfaces dividing a plane structure into two parts. On these interfaces, unilateral contact conditions are assumed to hold. The computer‐generated surfaces adopted here are self‐affine curves, characterized by a precise value of the resolution δ of the fractal set. Different contact simulations are studied by applying a horizontal displacement s on the upper part of the structure. For every value of s, a solution is taken in terms of normal forces and displacements at the interface. The procedure is repeated for different values of the resolution δ. At each scale, a classical Euclidean problem is solved by using finite element models. In the limit of the finest resolution, fractal behaviour is achieved.

The paper leads to a number of interesting conclusions. In the case of linear elastic analysis, the contact area and, consequently, the contact interfacial stresses depend strongly on the resolution of the fractal interface. Contrary, in the case of inelastic analysis, this dependence is verified only for the lower resolution values. As the resolution becomes higher, the contact area tends to become independent from the resolution.

The originality of the paper lies on the results and the corresponding conclusions obtained for the case of inelastic material behaviour, while the results for the case of elastic analysis verify the findings of other researchers.

A new hybrid substrate technology for power electronic applications has been characterised by thermal resistance and mechanical stress measurements. The new substrate utilises thermal spray technology for deposition of dielectric layer and electrical conductors. The results are compared with the more established technology of alumina substrates with direct copper bonding (DCB) metallisation. Silicon test chips for thermal resistance and mechanical stress measurement were used for the characterisation. The experimental results were compared with finite element analysis and a reasonable agreement was found.

The purpose of this study is to propose a fractal model of thermal contact conductance (TCC) of rough surfaces considering substrate deformation. Three deformation modes of the asperity of the rough surface are considered, including elastic deformation, elastic–plastic deformation and full plastic deformation.

The influences of contact load, fractal dimension and fractal roughness on the TCC of the rough surface were studied.

The results show that the TCC of the rough surface increases with the increase of contact load. When D > 2.5, the larger the fractal dimension, the higher the increased rate of the TCC of the rough surface with the increase of contact load. The TCC of the rough surface increases with the increase of fractal dimension and decreases with the increase of fractal roughness. The TCC of the rough surface can be achieved by selecting a contact surface with roughness.

A fractal model of TCC of rough surfaces considering substrate deformation was established in this study. The achievements of this study provide some theoretical basis for the investigation of TCC of rough surfaces.

The purpose of this paper is to calculate the meshing stiffness of nutation face gear considering the roughness, establish the calculation method of time-varying meshing stiffness of rough tooth surface and analyze the influence of roughness, load and other factors on the meshing stiffness of tooth surface.

The Weierstrass–Mandelbrot (W-M) function in the Majumdar–Bhushan model is used to characterize the rough contact line of the tooth surface, the normal height and radius of the micro convex body are calculated and the contact flexibility of the contact point of the tooth surface is obtained. The contact flexibility and the bending shear deformation flexibility obtained previously are substituted into the improved deformation compatibility equation for iterative calculation, and the time-varying meshing stiffness of the nutation face gear considering the roughness is obtained.

Compared with ABAQUS finite element simulation results, it is found that the meshing stiffness curve of rough tooth surface is more gentle than that of smooth tooth surface, the meshing stiffness value is smaller and the meshing stiffness change is smaller at the position where the number of gear teeth coincide changes.

In the process of calculating contact deformation, the fractal theory W-M function is used to characterize the contact line of the rough nutation face gear, and the deformation coordination condition considering roughness is improved. Therefore, the method of time-varying meshing stiffness considering roughness can obtain more accurate results, which provides theory and data for the subsequent dynamics analysis of the nutation face gear transmission.

This paper aims to investigate the effect of solder composition and roughness on early wetting behavior and interfacial reaction under atmospheric conditions.

High-speed photography is used to observe the early wetting and spreading process of the solder on the substrate in real time. The morphology of intermetallic compounds (IMCs) was observed by scanning electron microscopy, and the composition of IMCs micro bumps was determined by energy dispersive spectroscopy.

With a roughness range of 0.320–0.539 µm, the solder is distributed in an elliptical trilinear pattern along the grinding direction. With a roughness range of 0.029–0.031 µm, the solder spreads in the direction of grinding and perpendicular, forming a perfect circle (except in the case of Sn63Pb37 solder). The effect of three types of solder on early wettability is Sn63Pb37 > Sn96.5Ag3Cu0.5 > Sn. The wetting behavior is consistent with the Rn∼t model. The rapid spreading stage (Stage I) is controlled by the interfacial reaction with n1 values between 2.4 and 4. The slow spreading stage (stage II) is controlled by diffusion with n2 values between 4 and 6.7. The size of Cu6Sn5 formed on a rough substrate is greater than that produced on a smooth substrate.

Investigating the effect of solder composition and roughness on early wettability. This will provide a powerful guide in the field of soft brazing.

The purpose of this study is to establish a thermal contact conductance model of rough surfaces with inclination based on three-dimensional fractal theory.

The effects of contact load, inclination angle, fractal dimensional and fractal roughness on thermal contact conductance of rough surfaces were studied using numerical simulation.

The results show that the thermal contact conductance of the rough surface increases with the increase of contact load and fractal dimension and decreases with the increase of fractal roughness and inclination angle. The inclination angle of the rough surface has an important influence on the thermal contact conductance of the rough, and it is a factor that cannot be ignored in the study of the thermal contact conductance of rough surfaces.

A thermal contact conductance model of rough surfaces with inclination based on three-dimensional fractal theory was established in this study. The achievements of this study provide some theoretical basis for the investigation of the thermal contact conductance of rough surfaces.

The purpose of this study is to establish a fractal model of thermal contact conductance (TCC) of micro-segment gear considering friction coefficient.

The influences of friction coefficient, fractal dimension, fractal roughness and contact type on the TCC of the rough surface were studied by using numerical simulation.

The results show that with the increase of the friction coefficient, the TCC of the rough surface will decrease. As the fractal dimension increases or the fractal roughness decreases, the rough surface becomes smoother and the TCC becomes larger. Under the same load conditions, the TCC of the internal contact type is greater than that of the external contact type. In engineering practice, the desired TCC can be achieved by changing the contact type.

A fractal model of TCC of micro-segment gear considering friction coefficient was established in this study. The achievements of this study provide some theoretical basis for the investigation of the TCC of the gear.

The purpose of this study is to develop a normal contact stiffness (NCS) model among three disks of the assembled rotor system, which systematically considers the friction coefficient, the asperities interaction and the elastoplastic contact regime.

Based on the revised fractal theory, considering the friction effect, the elastoplastic contact regime and the asperities interaction in a simple way, the total NCS among three disks of the rod-fastening rotor bearing system is established. Effects of fractal dimension and roughness, friction coefficient, asperities interaction and material properties on the normal stiffness are investigated by simulations and the relevant comparisons are given for examining the reasonability of the proposed model.

NCS will decrease when asperities interaction and friction are included. As the load increases, the influences of asperities interaction and friction on stiffness become serious. NCS will be enhanced when the elastoplastic regime is considered.

A comprehensive NCS model is developed. It provides a theoretical basis for the modeling of the NCS for multi-interfaces.

The purpose of this paper is to propose a fractal model of thermal contact conductance (TCC) of rough surfaces based on cone asperity.

A detailed numerical study is conducted to examine the effects of contact load, fractal dimensional, fractal roughness and material properties on the TCC of rough surfaces.

The results indicate that when the fractal dimension D is less than 2.5, the TCC of rough surfaces increases nonlinearly with the increase of the contact load. However, when the fractal dimension D is greater than or equal to 2.5, the TCC of rough surfaces increases linearly with the increase of the contact load; the TCC of the rough surfaces increases with the increase of the fractal dimension D and the decrease of the fractal roughness G; the material parameters also have an influence on the TCC of the rough surfaces, and the extent of the effect on the TCC is related to the fractal dimension D.

A fractal model of TCC of rough surfaces based on cone asperity is established in this paper. Some new results and conclusions are obtained from this work, which provides important theoretical guidance for further study of TCC of rough surfaces.