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**Fractal geometry-based hypergeometric time series solution to the hereditary thermal creep model for the contact of rough surfaces using the Kelvin-Voigt medium.**
*(English)*
Zbl 1425.74335

Summary: 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.

### MSC:

74M15 | Contact in solid mechanics |

74F05 | Thermal effects in solid mechanics |

74H10 | Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics |

62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |

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\textit{O. M. Abuzeid} et al., Math. Probl. Eng. 2010, Article ID 652306, 22 p. (2010; Zbl 1425.74335)

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