ENERGY ABSORPTION IN A LOAD–UNLOAD CYCLE OF KNEE IMPLANT USING FRACTAL MODEL OF ROUGH SURFACES

Fractals ◽  
2016 ◽  
Vol 24 (02) ◽  
pp. 1650020 ◽  
Author(s):  
MOHAMMAD HODAEI ◽  
KAMBIZ FARHANG
Keyword(s):  
Energy Absorption ◽  
Power Law ◽  
Rough Surfaces ◽  
Fractal Model ◽  
Roughness Measurement ◽  
Statistical Parameters ◽  
Implant Surface ◽  
Multi Scale ◽  
Surface Description ◽  
Relationship Of

Roughness measurement of knee implant surfaces is investigated. The study of roughness measurement show that the topography of knee implant surface is multi-scale and surface spectra follows a power law behavior. A magnification of rough surface topography implies that there is no difference between original and magnified profile of implant surface. For implant surface, statistical parameters such as variance of height, curvature, and slope are found to be scale-dependent. Fractal representation of implant surface shows that the size-distribution of the multi-scale contacts spots follows a power law and is characterized by the fractal dimension of implant surface. Fractal surface description of the rough surfaces of knee implant is used to obtain force–displacement relationship of the contact force. Using an approximate function through the fusion of two piecewise functions, energy absorption of a knee implant in a single cycle of load–unload is obtained.

Role of Fractal Geometry in Roughness Characterization and Contact Mechanics of Surfaces

1990 ◽  
Vol 112 (2) ◽  
pp. 205-216 ◽  
Author(s):  
A. Majumdar ◽  
B. Bhushan
Keyword(s):  
Fractal Dimension ◽  
Size Distribution ◽  
Power Law ◽  
Magnetic Tape ◽  
Fractal Geometry ◽  
Rough Surfaces ◽  
Statistical Parameters ◽  
Length Scales ◽  
Imperfect Contact ◽  
Contact Spots

A proper characterization of the multiscale topography of rough surfaces is very crucial for understanding several tribological phenomena. Although the multiscale nature of rough surfaces warrants a scale-independent characterization, conventional techniques use scale-dependent statistical parameters such as the variances of height, slope and curvature which are shown to be functions of the surface magnification. Roughness measurements on surfaces of magnetic tape, smooth and textured magnetic thin film rigid disks, and machined stainless steel surfaces show that their spectra follow a power law behavior. Profiles of such surfaces are, therefore, statistically self-affine which implies that when repeatedly magnified, increasing details of roughness emerge and appear similar to the original profile. This paper uses fractal geometry to characterize the multiscale self-affine topography by scale-independent parameters such as the fractal dimension. These parameters are obtained from the spectra of surface profiles. It was observed that surface processing techniques which produce deterministic texture on the surface result in non-fractal structure whereas those producing random texture yield fractal surfaces. For the magnetic tape surface, statistical parameters such as the r.m.s. peak height and curvature and the mean slope, which are needed in elastic contact models, are found to be scale-dependent. The imperfect contact between two rough surfaces is composed of a large number of contact spots of different sizes. The fractal representation of surfaces shows that the size-distribution of the multiscale contact spots follows a power law and is characterized by the fractal dimension of the surface. The surface spectra and the spot size-distribution follow power laws over several decades of length scales. Therefore, the fractal approach has the potential to predict the behavior of a surface phenomenon at a particular length scale from the observations at other length scales.

Fractal Model Developed for Elliptic Elastic-Plastic Asperity Microcontacts of Rough Surfaces

2004 ◽  
Vol 126 (4) ◽  
pp. 646-654 ◽  
Author(s):  
Jung Ching Chung ◽  
Jen Fin Lin
Keyword(s):  
Size Distribution ◽  
Power Law ◽  
Present Model ◽  
Rough Surfaces ◽  
Fractal Model ◽  
Distribution Functions ◽  
Real Contact Area ◽  
Elastic Plastic ◽  
Contact Surfaces ◽  
Contact Spots

An elastic-plastic asperity fractal model for analyzing the contact of rough surfaces is presented. Instead of using the power-law relation, which is widely used to predict the number, N, of contact spots with the area larger than the area of a′ in per unit apparent area, the size-distribution functions valid in the elastic, elastoplastic, and fully plastic deformations have been individually developed in the present model for contact surfaces with elliptic asperities. These three size-distribution functions can be used in the calculations of the N value. The error in the number N, which exists between the results predicted by the present model and those obtained from experiments, is greatly reduced as compared with the error arising between the experimental results and those predicted by the power-law model. If the topothesy, G, and the fractal dimension, D, of contact surfaces are properly chosen to conform to those given plasticity indices, the results predicted by the present model are considerably closer to that predicted by one published study. Changes in the ellipticity parameter of contact spots may introduce a substantial difference in the relationship established for the real contact area and the total load.

scholarly journals Non-Local and Multi-Scale Mechanisms for Image Inpainting

Sensors ◽  
2021 ◽  
Vol 21 (9) ◽  
pp. 3281
Author(s):  
Xu He ◽  
Yong Yin
Keyword(s):  
Markov Random Fields ◽  
Receptive Fields ◽  
Image Inpainting ◽  
Long Distance ◽  
Visual Appearance ◽  
Fine Grained ◽  
Multi Scale ◽  
Non Local ◽  
Relationship Of

Recently, deep learning-based techniques have shown great power in image inpainting especially dealing with squared holes. However, they fail to generate plausible results inside the missing regions for irregular and large holes as there is a lack of understanding between missing regions and existing counterparts. To overcome this limitation, we combine two non-local mechanisms including a contextual attention module (CAM) and an implicit diversified Markov random fields (ID-MRF) loss with a multi-scale architecture which uses several dense fusion blocks (DFB) based on the dense combination of dilated convolution to guide the generative network to restore discontinuous and continuous large masked areas. To prevent color discrepancies and grid-like artifacts, we apply the ID-MRF loss to improve the visual appearance by comparing similarities of long-distance feature patches. To further capture the long-term relationship of different regions in large missing regions, we introduce the CAM. Although CAM has the ability to create plausible results via reconstructing refined features, it depends on initial predicted results. Hence, we employ the DFB to obtain larger and more effective receptive fields, which benefits to predict more precise and fine-grained information for CAM. Extensive experiments on two widely-used datasets demonstrate that our proposed framework significantly outperforms the state-of-the-art approaches both in quantity and quality.

scholarly journals Extended power-law scaling of air permeabilities measured on a block of tuff

2012 ◽  
Vol 16 (1) ◽  
pp. 29-42 ◽  
Author(s):  
M. Siena ◽  
A. Guadagnini ◽  
M. Riva ◽  
S. P. Neuman
Keyword(s):  
Power Law ◽  
Structure Functions ◽  
Self Similarity ◽  
Scaling Exponents ◽  
Multi Scale ◽  
Sample Structure ◽  
Heavy Tailed ◽  
Non Gaussian ◽  
Nonlinear Fashion ◽  
Extended Power

Abstract. We use three methods to identify power-law scaling of multi-scale log air permeability data collected by Tidwell and Wilson on the faces of a laboratory-scale block of Topopah Spring tuff: method of moments (M), Extended Self-Similarity (ESS) and a generalized version thereof (G-ESS). All three methods focus on q-th-order sample structure functions of absolute increments. Most such functions exhibit power-law scaling at best over a limited midrange of experimental separation scales, or lags, which are sometimes difficult to identify unambiguously by means of M. ESS and G-ESS extend this range in a way that renders power-law scaling easier to characterize. Our analysis confirms the superiority of ESS and G-ESS over M in identifying the scaling exponents, ξ(q), of corresponding structure functions of orders q, suggesting further that ESS is more reliable than G-ESS. The exponents vary in a nonlinear fashion with q as is typical of real or apparent multifractals. Our estimates of the Hurst scaling coefficient increase with support scale, implying a reduction in roughness (anti-persistence) of the log permeability field with measurement volume. The finding by Tidwell and Wilson that log permeabilities associated with all tip sizes can be characterized by stationary variogram models, coupled with our findings that log permeability increments associated with the smallest tip size are approximately Gaussian and those associated with all tip sizes scale show nonlinear variations in ξ(q) with q, are consistent with a view of these data as a sample from a truncated version (tfBm) of self-affine fractional Brownian motion (fBm). Since in theory the scaling exponents, ξ(q), of tfBm vary linearly with q we conclude that nonlinear scaling in our case is not an indication of multifractality but an artifact of sampling from tfBm. This allows us to explain theoretically how power-law scaling of our data, as well as of non-Gaussian heavy-tailed signals subordinated to tfBm, are extended by ESS. It further allows us to identify the functional form and estimate all parameters of the corresponding tfBm based on sample structure functions of first and second orders.

scholarly journals Temperature Resistance of Mo3Si: Phase Stability, Microhardness, and Creep Properties

Metals ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 564 ◽  
Author(s):  
Olha Kauss ◽  
Susanne Obert ◽  
Iurii Bogomol ◽  
Thomas Wablat ◽  
Nils Siemensmeyer ◽  
...  
Keyword(s):  
Power Law ◽  
Phase Stability ◽  
Gas Turbines ◽  
Constitutive Models ◽  
Creep Properties ◽  
Multi Scale ◽  
Scale Modeling ◽  
Significant Difference ◽  
Before And After ◽  
Multi Phase

Mo-Si-B alloys are one of the most promising candidates to substitute Ni based superalloys in gas turbines. The optimization of their composition can be achieved more effectively using multi-scale modeling of materials behavior and structural analysis of components for understanding, predicting, and screening properties of new alloys. Nevertheless, this approach is dependent on data on the properties of the single phases in these alloys. The focus of this investigation is Mo3Si, one of the phases in typical Mo-Si-B alloys. The effect of 100 h annealing at 1600 °C on phase stability and microhardness of its three near-stoichiometric compositions—Mo-23Si, Mo-24Si and Mo-25Si (at %)—is reported. While Mo-23Si specimen consist only of Mo3Si before and after annealing, Mo-24Si and Mo-25Si comprise Mo5Si3 and Mo3Si before annealing. The latter is then increased by the annealing. No significant difference in microhardness was detected between the different compositions as well as after annealing. The creep properties of Mo3Si are described at 1093 °C and 1300 °C at varying stress levels as well as at 300 MPa and temperatures between 1050 °C and 1350 °C. Three constitutive models were used for regression of experimental results—(i) power law with a constant creep exponent, (ii) stress range dependent law, and (iii) power law with a temperature-dependent creep exponent. It is confirmed that Mo3Si has a higher creep resistance than Moss and multi-phase Mo-Si-B alloys, but a lower creep strength as compared to Mo5SiB2.

A FRACTAL MODEL FOR PREDICTING OXYGEN EFFECTIVE DIFFUSIVITY OF POROUS MEDIA WITH ROUGH SURFACES UNDER DRY AND WET CONDITIONS

Fractals ◽  
2021 ◽  
pp. 2150076
Author(s):  
BOQI XIAO ◽  
QIWEN HUANG ◽  
BOMING YU ◽  
GONGBO LONG ◽  
HANXIN CHEN
Keyword(s):  
Porous Media ◽  
Fractal Dimension ◽  
Oxygen Diffusion ◽  
Water Saturation ◽  
Rough Surfaces ◽  
Effective Diffusivity ◽  
Fractal Model ◽  
Relative Roughness ◽  
Oxygen Diffusivity ◽  
Dry And Wet Conditions

Oxygen diffusion in porous media (ODPM) with rough surfaces (RS) under dry and wet conditions is of great interest. In this work, a novel fractal model for the oxygen effective diffusivity of porous media with RS under dry and wet conditions is proposed. The proposed fractal model is expressed in terms of relative roughness, the water saturation, fractal dimension for tortuosity of tortuous capillaries, fractal dimension for pores, and porosity. It is observed that the normalized oxygen diffusivity decreases with increasing relative roughness and fractal dimension for capillary tortuosity. It is found that the normalized oxygen diffusivity increases with porosity and fractal dimension for pore area. Besides, it is seen that that the normalized oxygen diffusivity under wet condition decreases with increasing water saturation. The determined normalized oxygen diffusivity is in good agreement with experimental data and existing models reported in the literature. With the proposed analytical fractal model, the physical mechanisms of oxygen diffusion through porous media with RS under dry and wet conditions are better elucidated. Every parameter in the proposed fractal model has clear physical meaning, with no empirical constant.

scholarly journals A multi-scale FEM-BEM formulation for contact mechanics between rough surfaces

2019 ◽  
Vol 65 (3) ◽  
pp. 731-749
Author(s):  
Jacopo Bonari ◽  
Maria R. Marulli ◽  
Nora Hagmeyer ◽  
Matthias Mayr ◽  
Alexander Popp ◽  
...  
Keyword(s):  
Contact Mechanics ◽  
Rough Surfaces ◽  
Multi Scale

scholarly journals Mechanical Properties of Dye 3 Greenland Deep Ice Cores

1984 ◽  
Vol 5 ◽  
pp. 1-8 ◽  
Author(s):  
Nobuhiko Azuma ◽  
Akira Higashi
Keyword(s):  
Mechanical Properties ◽  
Grain Size ◽  
Power Law ◽  
Ice Core ◽  
Ice Cores ◽  
Uniaxial Stress ◽  
Strain Rates ◽  
Compression Tests ◽  
Polycrystalline Ice ◽  
Relationship Of

Uniaxial compression tests were carried out with specimens cut from several deep ice cores obtained at Dye 3, Greenland, in 1980 and 1981. The power law relationship of = Αση was obtained between the uniaxial strain-rate and the uniaxial stress σ. In a range of strain-rates between 10−8 and 10−7 s−1, the value of the power n for samples with strong single maximum fabric was approximately 4, significantly larger than the value of 3 which has been generally accepted from experiments using artificial polycrystalline ice. A work-hardening effect was found in the ice-core samples taken from a depth of 1900 m, which had a smaller grain size than the others. Recrystallization occurred when the temperature of the specimen was raised during the test and this ultimately caused the formation of the so-called diamond pattern ice fabric.

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