Caractérisation fractale de la rugosité tridimensionnelle d'une surface

López, Jesús María Rincón; Hansali, G.; Bosse, J.; Mathia, T.

doi:10.1051/jp3:1994294

Cited by 22 publications

(16 citation statements)

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“…It is now increasingly admitted that roughness must be considered in terms of amplitude and organization. 31 Previous works illustrated that the amplitude and organization of roughness concomitantly influence cell behavior. On smooth surfaces the bone cells were randomly oriented, although they were lined up parallel to the grooves in an end to end fashion in 5 m deep grooves.…”

Section: Introductionmentioning

confidence: 99%

Qualitative and quantitative study of human osteoblast adhesion on materials with various surface roughnesses

Anselme

Bigerelle

Noël

et al. 2000

J. Biomed. Mater. Res.

442

197

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We quantitatively evaluated the adhesion of human osteoblasts on orthopedic metallic substrates (Ti6Al4V alloy) with various surface roughnesses at several times after inoculation and studied its correlation with qualitative changes in the expression of adhesion proteins and with parameters extensively describing the surface topographies. Cells were orientated in a parallel order on polished surfaces. This orientation was not affected by residual grooves after polishing. On sandblasted surfaces the cells never attained confluence and had a stellate shape, and the cell layer had no particular organization. Extracellular matrix (fibronectin, type I collagen, osteopontin) and cytoskeletal protein (actin, vinculin) orientation reflected the cell layer organization. In our experiment human osteoblasts expressed alpha3beta1 integrin but not alpha2beta1 integrin. In addition to currently analyzed roughness magnitude parameters, we calculated roughness organization parameters (fractal dimension parameters) of the substrates. We observed lower adhesion and proliferation on less organized surfaces (i.e., sandblasted ones). The significant statistical correlation observed between fractal dimension parameters (describing surface roughness organization) and cell parameters adds a new concept to the studies of substratum roughness influence on cell behavior. An attempt at modelization of the cell-surface interaction was made that includes the influence of fractal dimensions parameters.

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Section: Introductionmentioning

confidence: 99%

Qualitative and quantitative study of human osteoblast adhesion on materials with various surface roughnesses

Anselme

Bigerelle

Noël

et al. 2000

J. Biomed. Mater. Res.

442

197

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“…Greenwood & Williamson's (1966) results focused attention on the importance of the asperity height distribution and many subsequent advances have been made in characterizing surfaces using random process theory (Nayak 1971;Whitehouse & Phillips 1978Greenwood 1984). At the same time, improvements in experimental methods have increased the bandwidth of surface pro le measurements and revealed the existence of a hierarchy of scales up to the limits of experimental discrimination (Mandelbrot 1982;Russ 1994;Lopez et al . 1994;Majumdar & Bhushan 1995).…”

Section: Introductionmentioning

confidence: 99%

Linear elastic contact of the Weierstrass profile

Ciavarella

Demelio

Barber

et al. 2000

Proc. R. Soc. Lond. A

207

171

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A contact problem is considered in which an elastic half-plane is pressed against a rigid fractally rough surface, whose pro le is de ned by a Weierstrass series. It is shown that no applied mean pressure is su¯ciently large to ensure full contact and indeed there are not even any contact areas of nite dimension|the contact area consists of a set of fractal character for all values of the geometric and loading parameters.A solution for the partial contact of a sinusoidal surface is used to develop a relation between the contact pressure distribution at scale n 1 and that at scale n. Recursive numerical integration of this relation yields the contact area as a function of scale. An analytical solution to the same problem appropriate at large n is constructed following a technique due to Archard. This is found to give a very good approximation to the numerical results even at small n, except for cases where the dimensionless applied load is large.The contact area is found to decrease continuously with n, tending to a power-law behaviour at large n which corresponds to a limiting fractal dimension of (2 D), where D is the fractal dimension of the surface pro le. However, it is not a`simple' fractal, in the sense that it deviates from the power-law form at low n, at which there is also a dependence on the applied load. Contact segment lengths become smaller at small scales, but an appropriately normalized size distribution tends to a limiting function at large n.

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“…We postulate that the transition stage II-stage III is linked to a change of the fractal properties of the profile. It is reported in the bibliography that fractal properties of profiles may be determined by autocorrelation functions [39,40]. For this reason the average autocorrelation function of all profiles is plotted in Fig.…”

Section: Stage Ii: the Fractal Stagementioning

confidence: 99%

Roughness characteristic length scales of micro-machined surfaces: A multi-scale modelling

Bigerelle

Gautier

Iost

2007

Sensors and Actuators B: Chemical

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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. AbstractThe MEMS structure integrity, their dynamic properties as well as their electrostatic characteristics, strongly depend on the achieved surfaces roughness produced by the micromachining process. It is therefore, not surprising that numerous works are devoted to propose relations between roughness and physical or mechanical properties in this field. Yet the issue is full of complexities since roughness parameters depend on the method used for their evaluation. This article introduces a new approach of the roughness characterization, based on the scaling analysis. Experimental results obtained on micro machined surfaces show that the range roughness amplitude depends on the scan length and that roughness amplitude follows three stages. The stage I is due to a smoothing effect of the surface induced by the tip radius of the profilometer, stage II presents a piecewise power-law roughness distribution until a critical length that characterises the fractal behaviour of the surface, and stage III is characterised by extreme values statistics. The fractal parameter, the extreme values estimators and the crossover between stages II and III are shown to be related to the micromachining process. As a result, an original probabilistic model based on the Generalized Lambda Distribution (GLD) is proposed to estimate the multi-scale roughness in the stage III. Finally, thanks to a Bootstrap protocol coupled with a Monte-Carlo simulation, the maximal roughness amplitude probability density function is estimated at a scale higher than the scanning length.

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Caractérisation fractale de la rugosité tridimensionnelle d'une surface

Cited by 22 publications

References 0 publications

Qualitative and quantitative study of human osteoblast adhesion on materials with various surface roughnesses

Qualitative and quantitative study of human osteoblast adhesion on materials with various surface roughnesses

Linear elastic contact of the Weierstrass profile

Roughness characteristic length scales of micro-machined surfaces: A multi-scale modelling

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