Loading–unloading contact analysis of a fractal rough surface with functional gradation

The present paper deals with a finite-element-based static loading–unloading analysis of a functionally graded rough surface contact with fractal characteristics. Two different gradation models, namely elastic and plastic gradations, are adopted. In these models, one out of yield strength and Young's modulus is varied spatially according to exponential functions, while the other is kept constant. In both these material models, separate inhomogeneity parameters control the variation of material properties. The gradation is such that throughout the top of the rough surface properties remain constant with variations in the depth direction being controlled by the above-mentioned parameters. Different fractal surfaces with different levels of roughness (governed by the values of fractal dimension and fractal roughness) have been analysed. The influence of the gradation parameters on the contact properties, viz. contact force, contact area, contact stress, etc., are investigated for both loading and unloading phases. It was found that for most of the loading phase, higher elastic, as well as plastic gradation parameter, causes higher contact force and contact area. However, in the case of the unloading of elastically graded surfaces, this trend is not maintained throughout. For the cases, where a substantial amount of yielding takes place during loading near the contact surface, the resulting contact area is found to be higher for the unloading phase in comparison with the same during the loading phase. The trend of plastic yielding at the vicinity of the contact surface is studied for varying gradation parameters. It is observed that the higher volume of yielded material is obtained for the higher value of elastic gradation parameter. On the other hand, the higher value of plastic gradation parameter causes more yielding to take place at the vicinity of the contact surface. Additionally, the effect of gradation on the energy dissipation due to plasticity after complete unloading is explored in detail.

Static and Dynamic Analysis of Deformable Fractal Surface in Contact With Rigid Flat

The chapter consists of static and dynamic analyses of a fractal rough surface in contact with a rigid flat. The fractal surface is constructed using modified Weierstrass-Mandelbrot function. A rigid flat surface touches the topmost point of the rough surface, which moves towards the rough surface and deforms it. Different contact parameters (e.g., contact force, contact area, contact stress, etc. for varying fractal and material properties are obtained through finite element based static analysis. A parameter denoting the degree of nonlinearity of the contact system is extracted from the force-displacement plot of the surface. This parameter is utilized to explain the dynamic behaviour of the fractal surface which vibrates under the influence of the externally excited rigid flat surface. The dynamic analysis of the contact system is carried out by modelling the contact interface as a single degree of freedom (SDOF) spring-mass-damper system. The dynamic behavior of the system is investigated in terms of frequency response curves, time-displacement plots, and phase plots.

Thermal diffusion and flow property of CO2/CH4 in organic nanopores with fractal rough surface

The kerogen is rich in complex pore networks with a random rough surface, which is a factor controlling the thermal diffusion and flow property of gases. In this work, we construct organic-rich nanopore with fractal surfaces by inserting and deleting carbon atoms. The adsorption ability, thermal diffusion property, and flow velocity of CO2 /CH4 in the nanopore are analyzed using with molecular simulations. The results showed that the adsorption capacity of CO2 is nearly twice that of CH4, which is decided by adsorption enthalpy, whereas the maximum thermal diffusion ability of CO2 is only 23.7% that of CH4. With external pressure gradients imposed on the system, the flow speed of CO2 was lower than that of CH4 for nanopores with different roughness. These findings provide a theoretical basis for the feasibility of CO2 exploitation of shale gas.

Dynamics of Deformable Fractal Surface in Contact with Harmonically Excited Rigid Flat

Dynamics of contact between a deformable fractal rough surface and a rigid flat is studied under harmonic excitation to the flat surface. Fractal surface is generated from the modified Weierstrass-Mandelbrot function and is imported to ANSYS to construct the finite element model of the same. A parameter called ‘nonlinearity exponent', is obtained from the force-displacement relationship of the rough surface and is used to find out the dynamic properties of the contacting interface using single spring-mass-damper model. The effect of variation in surface roughness and material properties on the system response is analyzed. The system exhibits superharmonic responses for different values of the nonlinearity exponent. The phase plot and time-displacement plots for the system are also furnished.