Osama M. Abuzeid

Linear viscoelastic creep model for the contact of nominal flat surfaces based on fractal geometry : Standard linear solid (SLS) material

The objective of this study is to construct a continuous mathematical model that describes the frictionless contact between a nominally flat (rough) viscoelastic punch and a perfectly rigid foundation. The materials behavior is modeled by assuming a complex viscoelastic constitutive law, the standard linear solid (SLS) law. The model aims at studying the normal compliance (approach) of the punch surface, which will be assumed to be quasistatic, as a function of the applied creep load. The roughness of the punch surface is assumed to be fractal in nature. The Cantor set theory is utilized to model the roughness of the punch surface. An asymptotic power law is obtained, which associates the creep force applied and the approach of the fractal punch surface. This law is only valid if the approach is of the size of the surface roughness. The proposed model admits an analytical solution for the case when the deformation is linear viscoelastic. The modified analytical model shows a good agreement with experimental results available in the literature.

A linear viscoelastic creep‐contact model of a flat fractal surface: Kelvin‐Voigt medium

The objective of this paper is to construct a continuous model for the viscoelastic contact of a nominal flat punch and a smooth surface of a rigid half‐space. The considered model aims at studying the normal approach as a function of the applied load. The proposed model assumes the punch surface material to behave according to Kelvin‐Voigt viscoelastic material. The punch surface, which is known to be fractal in nature, is modelled in this work using a deterministic Cantor structure. An asymptotic power law, deduced using iterative relations, is used to express the punch surface approach as a function of the remote force when the approach of the punch surface and the half space is in the order of the size of the surface roughness. The results obtained using this model, which admits closed form solution, are displayed graphically for selected values of the system parameters; the fractal surface roughness and various material properties. The obtained results showed good agreement with published experimental results.

A linear thermo‐visco‐elastic creep model for the contact of nominal flat surfaces based on fractal geometry

The objective of this paper is to construct a continuous model for the thermo‐visco‐elastic contact of a nominal flat, non‐smooth, punch and a smooth surface of a rigid half‐space. The considered model aims at studying the normal approach as a function of the applied loads and temperatures. The proposed model assumes the punch surface material to behave according to the linear Kelvin‐Voigt visco‐elastic material. The punch surface, which is known to be fractal in nature, is modeled in this work using a deterministic Cantor structure. An asymptotic power low, deduced using approximate iterative relations, is used to express the punch surface approach as a function of the remote forces and bulk temperatures when the approach of the punch surface and the half space is in the order of the size of the surface roughness. The results obtained using this model, which admits closed form solution, are displayed graphically for selected values of the system parameters; the fractal surface roughness and various material properties. The obtained results showed good agreement with published experimental results.

Fractal Geometry-Based Hypergeometric Time Series Solution to the Hereditary Thermal Creep Model for the Contact of Rough Surfaces Using the Kelvin-Voigt Medium

This paper aims at constructing a continuous hereditary creep model for the thermoviscoelastic contact of a rough punch and a smooth surface of a rigid half-space. The used model considers the rough surface as a function of the applied load and temperatures. The material of the rough punch surface is assumed to behave as Kelvin-Voigt viscoelastic material. Such a model uses elastic springs and viscous dashpots in parallel. The fractal-based punch surface is modelled using a deterministic Cantor structure. An asymptotic power law, deduced using approximate iterative relations, is used to express the punch surface creep which is a time-dependent inelastic deformation. The suggested law utilized the hypergeometric time series to relate the variables of creep as a function of remote forces, body temperatures, and time. The model is valid when the approach of punch surface and half space is in the order of the size of the surface roughness. The closed-form results are obtained for selected values of the system parameters; the fractal surface roughness and various material properties. The obtained results show good agreement with published experimental results, and the methodology can be further extended to other structures such as the Kelvin-Voigt medium within electronic circuits and systems.

Thermal creep model of rough fractal surfaces in contact: viscoelastic standard linear solid

Purpose – The purpose of this paper is to construct a continuous time series model to study the thermal creep of rough surfaces in contact.Design/methodology/approach – For normal loading, the contact between rough surfaces can often be modeled as the contact of an effective surface with a rigid fiat surface. A solution for the deformation of such equivalent surface, generated using fractal geometry, can be modified. However, in this study only the case of a single rough surface in contact with a rigid flat surface is considered. In the interface, the material is assumed to follow the idealized constitutive viscoelastic standard linear solid (SLS) model. Fractal geometry, through Cantor set theory, is utilized to model the roughness of the surface.Findings – An asymptotic time series power law is obtained, which associates the creep load, the buck temperature and the creep of the fractal surface.Originality/value – This law is only valid as long as the creep is of the size of the surface roughness. The mo...