Recent advancements in fractal geometric-based nonlinear time series solutions to the micro-quasistatic thermoviscoelastic creep for rough surfaces in contact
type: Item
instance of: scholarly article
title: Recent advancements in fractal geometric-based nonlinear time series solutions to the micro-quasistatic thermoviscoelastic creep for rough surfaces in contact
zbMATH Open document ID: 1213.74307
DOI: 10.1155/2011/691270
author: Osama M. Abuzeid
author: Anas N. Al-Rabadi
author: Hashem S. Alkhaldi
published in: Mathematical Problems in Engineering
publication date: 2011-06-07T00:00:00Z
full work available at URL: https://eudml.org/doc/228006
review text: Summary: To understand the tripological contact phenomena, both mathematical and experimental models are needed. In this work, fractal mathematical models are used to model the experimental results obtained from literature. Fractal geometry, using a deterministic Cantor structure, is used to model the surface topography, where recent advancements in thermoviscoelastic creep contact of rough surfaces are introduced. Various viscoelastic idealizations are used to model the surface materials, for example, Maxwell, Kelvin-Voigt, Standard Linear Solid and Jeffrey media. Such media are modelled as arrangements of elastic springs and viscous dashpots in parallel and/or in series. Asymptotic power laws, through hypergeometric series, were used to express the surface creep as a function of remote forces, body temperatures and time. The introduced models are valid only when the creep approach of the contact surfaces is in the order of the size of the surface roughness. The obtained results using such models, which admit closed-form solutions, are displayed graphically for selected values of the systems' parameters; the fractal surface roughness and various material properties. Results obtained showed good agreement with published experimental results, where the utilized methodology can be further extended to the utilization for the contact of surfaces within micro- and nano-electronic devices, circuits and systems.
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 74M15
zbMATH DE Number: 5904910
Wikidata QID: Q56003604
MaRDI profile type: Publication
OpenAlex ID: W2087351321
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description: scientific article; zbMATH DE number 5904910