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Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 691270, 29 pages
Recent Advancements in Fractal Geometric-Based Nonlinear Time Series Solutions to the Micro-Quasistatic Thermoviscoelastic Creep for Rough Surfaces in Contact
1Mechanical Engineering Department, The University of Jordan, Amman 11942, Jordan
2Computer Engineering Department, The University of Jordan, Amman 11942, Jordan
Received 10 October 2010; Accepted 14 January 2011
Academic Editor: Ming Li
Copyright © 2011 Osama M. Abuzeid et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- T. A. Alabed, O. M. Abuzeid, and M. Barghash, “A linear viscoelastic relaxation-contact model of a flat fractal surface: a Maxwell-type medium,” International Journal of Advanced Manufacturing Technology, vol. 39, no. 5-6, pp. 423–430, 2008.
- F. M. Borodich and D. A. Onishchenko, “Similarity and fractality in the modelling of roughness by a multilevel profile with hierarchical structure,” International Journal of Solids and Structures, vol. 36, no. 17, pp. 2585–2612, 1999.
- J. A. Greenwood, “Problems with surface roughness,” in Fundamentals of Friction: Macroscopic and Microscopic Processes, I. L. Singer and H. M. Pollock, , Eds., pp. 57–76, Kluwer Academic Publishers, Boston, Mass, USA, 1992.
- A. Majumdar and B. Bhushan, “Role of fractal geometry in roughness characterization and contact mechanics of surfaces,” Journal of Tribology, vol. 112, no. 2, pp. 205–216, 1990.
- B. B. Mandelbrot, D. E. Passoja, and A. J. Paullay, “Fractal character of fracture surfaces of metals,” Nature, vol. 308, no. 5961, pp. 721–722, 1984.
- M. Li and W. Zhao, “Representation of a Stochastic Traffic Bound,” IEEE Transactions on Parallel and Distributed Systems, vol. 21, no. 9, pp. 1368–1372, 2010.
- M. Li and S. C. Lim, “Modeling network traffic using generalized Cauchy process,” Physica A, vol. 387, no. 11, pp. 2584–2594, 2008.
- M. Li, “Generation of teletraffic of generalized Cauchy type,” Physica Scripta, vol. 81, no. 2, Article ID 025007, 2010.
- B. B. Mandelbrot, The Fractal Geometry of Nature, W. H. Freeman, San Francisco, Calif, USA, 1982.
- J. Feder, Fractals, Physics of Solids and Liquids, Plenum Press, New York, NY, USA, 1988.
- K. L. Johnson, Contact Mechanics, Cambridge University Press, Cambridge, UK, 1985.
- J. A. Greenwood and J. B. P. Williamson, “Contact of nominally flat surfaces,” Proceedings of the Royal Society A, vol. 370, pp. 300–319, 1966.
- A. Majumdar and B. Bhushan, “Fractal model of elastic-plastic contact between rough surfaces,” Journal of Tribology, vol. 113, no. 1, pp. 1–11, 1991.
- F. M. Borodich and A. B. Mosolov, “Fractal roughness in the contact problems,” Journal of Applied Mathematics and Mechanics, vol. 56, no. 5, pp. 786–795, 1992.
- F. Borodich, “Fractals and surface roughness in EHL,” in Proceedings of the Iutam Symposium on Elastohydrodynamics and Micro-elastohydrodynamics, R. Snidle and H. Evans, Eds., pp. 397–408, 2006.
- T. L. Warren and D. Krajcinovic, “Fractal models of elastic-perfectly plastic contact of rough surfaces based on the Cantor set,” International Journal of Solids and Structures, vol. 32, no. 19, pp. 2907–2922, 1995.
- T. L. Warren, A. Majumdar, and D. Krajcinovic, “A fractal model for the rigid-perfectly plastic contact of rough surfaces,” ASME Journal of Applied Mechanics, Transactions, vol. 63, no. 1, pp. 47–54, 1996.
- O. Abuzeid, “Linear viscoelastic creep model for the contact of nominal flat surfaces based on fractal geometry: Maxwell type medium,” Dirasat, vol. 30, no. 1, pp. 22–36, 2003.
- O. M. Abuzeid, “A linear viscoelastic creep-contact model of a flat fractal surface: Kelvin-Voigt medium,” Industrial Lubrication and Tribology, vol. 56, no. 6, pp. 334–340, 2004.
- O. Abuzeid, “A viscoelastic creep model for the contact of rough fractal surfaces: Jeffreys’ type material,” in Proceedings of the 7th International Conference Production Engineering and Design for Development, Cairo, Egypt, 2006.
- O. M. Abuzeid and P. Eberhard, “Linear viscoelastic creep model for the contact of nominal flat surfaces based on fractal geometry: standard linear solid (SLS) material,” Journal of Tribology, vol. 129, no. 3, pp. 461–466, 2007.
- O. M. Abuzeid and T. A. Alabed, “Mathematical modeling of the thermal relaxation of nominally flat surfaces in contact using fractal geometry: Maxwell type medium,” Tribology International, vol. 42, no. 2, pp. 206–212, 2009.
- O. M. Abuzeid, A. N. Al-Rabadi, and H. S. Alkhaldi, “Fractal geometry-based hypergeometric time series solution to the hereditary thermal creep model for the contact of rough surfaces using the Kelvin-Voigt medium,” Mathematical Problems in Engineering, vol. 2010, Article ID 652306, 22 pages, 2010.
- O. Abuzeid, “Thermal creep model of rough fractal surfaces in contact: viscoelastic standard linear solid,” Industrial Lubrication and Tribology. In press.
- R. D. Mauldin and S. C. Williams, “On the Hausdorff dimension of some graphs,” Transactions of the American Mathematical Society, vol. 298, no. 2, pp. 793–803, 1986.
- D. Wójcik, I. Białynicki-Birula, and K. Zyczkowski, “Time evolution of quantum fractals,” Physical Review Letters, vol. 85, no. 24, pp. 5022–5025, 2000.
- A. N. Al-Rabadi, Reversible Logic Synthesis, Springer, Berlin, Germany, 2004.
- C. Cattani and A. Kudreyko, “Application of periodized harmonic wavelets towards solution of eigenvalue problems for integral equations,” Mathematical Problems in Engineering, vol. 2010, Article ID 570136, 8 pages, 2010.
- E. G. Bakhoum and C. Toma, “Dynamical aspects of macroscopic and quantum transitions due to coherence function and time series events,” Mathematical Problems in Engineering, vol. 2010, Article ID 428903, 2010.
- G. Toma, “Specific differential equations for generating pulse sequences,” Mathematical Problems in Engineering, vol. 2010, Article ID 324818, 11 pages, 2010.
- G. Mattioli, M. Scalia, and C. Cattani, “Analysis of large-amplitude pulses in short time intervals: application to neuron interactions,” Mathematical Problems in Engineering, vol. 2010, Article ID 895785, 15 pages, 2010.
- S. Y. Chen and Y. F. Li, “Determination of stripe edge blurring for depth sensing,” IEEE Sensors Journal, vol. 11, no. 2, pp. 389–390, 2011.
- S. Y. Chen and Q. Guan, “Parametric shape representation by a deformable NURBS model for cardiac functional measurements,” IEEE Transactions on Biomedical Engineering. In press.
- K. Falconer, Fractal Geometry, John Wiley &; Sons, Chichester, UK, 1990.
- P. S. Modenov and A. S. Parkhomenko, Geometric Transformations, vol. 1 of Euclidean and Affine Transformations, Academic Press, New York, NY, USA, 1965.
- R. F. Voss, “Random fractal forgeries,” in Fundamental Algorithms in Computer Graphics, R. A. Earnshaw, Ed., pp. 805–835, Springer, Berlin, Germany, 1985.
- A. Majumdar and C. L. Tien, “Fractal characterization and simulation of rough surfaces,” Wear, vol. 136, no. 2, pp. 313–327, 1990.
- J. Lopez, G. Hansali, H. Zahouani, J. C. Le Bosse, and T. Mathia, “3D fractal-based characterisation for engineered surface topography,” International Journal of Machine Tools and Manufacture, vol. 35, no. 2, pp. 211–217, 1995.
- M. Li, “Fractal time series—a tutorial review,” Mathematical Problems in Engineering, vol. 2010, Article ID 157264, 26 pages, 2010.
- M. Li and J.-Y. Li, “On the predictability of long-range dependent series,” Mathematical Problems in Engineering, vol. 2010, Article ID 397454, 9 pages, 2010.
- R. S. Sayles and T. R. Thomas, “Surface topography as a nonstationary random process,” Nature, vol. 271, no. 5644, pp. 431–434, 1978.
- S. R. Brown, “Simple mathematical model of a rough fracture,” Journal of Geophysical Research, vol. 100, no. 4, pp. 5941–5952, 1995.
- M. V. Berry and Z. V. Lewis, “On the Weierstrass-Mandelbrot fractal function,” Proceedings of the Royal Society London Series A, vol. 370, no. 1743, pp. 459–484, 1980.
- E. H. Lee and J. R. M. Radok, “The contact problems for viscoelastic bodies,” Journal of Applied Mechanics, vol. 27, pp. 438–444, 1960.
- T. C. T. Ting, “The contact stress between a rigid indenter and a viscoelastic half-space,” Journal of Applied Mechanics, vol. 33, pp. 845–854, 1966.
- T. C. T. Ting, “Contact problems in the linear theory of viscoelasticity,” Journal of Applied Mechanics, vol. 35, pp. 248–254, 1968.
- G. R. Nghieh, H. Rahnejat, and Z. M. Jin, “Contact mechanics of viscoelastic layered surface,” in Contact Mechanics. III, M. H. Aliabadi and A. Samarti, Eds., pp. 59–68, Computational Mechanics Publications, Boston, Mass, USA, 1997.
- K. J. Wahl, S. V. Stepnowski, and W. N. Unertl, “Viscoelastic effects in nanometer-scale contacts under shear,” Tribology Letters, vol. 5, no. 1, pp. 103–107, 1998.
- D. J. Whitehouse and J. F. Archard, “The properties of random surfaces of significance in their contact,” Proceedings of the Royal Society A, vol. 316, pp. 97–121, 1970.
- A. Lumbantobing, L. Kogut, and K. Komvopoulos, “Electrical contact resistance as a diagnostic tool for MEMS contact interfaces,” Journal of Microelectromechanical Systems, vol. 13, no. 6, pp. 977–987, 2004.
- V. S. Radchik, B. Ben-Nissan, and W. H. Müller, “Theoretical modeling of surface asperity depression into an elastic foundation under static loading,” Journal of Tribology, vol. 124, no. 4, pp. 852–856, 2002.
- Y. Zhao and L. Chang, “A model of asperity interactions in elastic-plastic contact of rough surfaces,” Journal of Tribology, vol. 123, no. 4, pp. 857–864, 2001.
- A. Signorini, “Sopra alcune questioni di elastostatica,” Atti della Societa Italiana per il Progresso delle Sceienze, 1933.
- P. E. D’yachenko, N. N. Tolkacheva, G. A. Andreev, and T. M. Karpova, The Actual Contact Area between Touching Surfaces, Consultant Bureau, New York, NY, USA, 1964.
- J. R. M. Radok, “Visco-elastic stress analysis,” Quarterly of Applied Mathematics, vol. 15, pp. 198–202, 1957.
- N. J. Distefano and K. S. Pister, “On the identification problem for thermorheologically simple materials,” Acta Mechanica, vol. 13, no. 3-4, pp. 179–190, 1972.
- T. Junisbekov, V. Kestelman, and N. Malinin, Stress Relaxation in Viscoelastic Materials, Science Publishers, Enfield, UK, 2nd edition, 2003.
- J. Boyle and J. Spencer, Stress Analysis for Creep, Butterworths-Heinemann, London, UK, 1st edition, 1983.
- W. S. Lee and C. Y. Liu, “The effects of temperature and strain rate on the dynamic flow behaviour of different steels,” Materials Science and Engineering A, vol. 426, no. 1-2, pp. 101–113, 2006.
- Z. Handzel-Powierza, T. Klimczak, and A. Polijaniuk, “On the experimental verification of the Greenwood-Williamson model for the contact of rough surfaces,” Wear, vol. 154, no. 1, pp. 115–124, 1992.
- W. Nowacki, Thermoelasticity, Pergamon Press, Oxford, UK, 2nd edition, 1986.
- A. Hashem, “Study on reloading stress relaxation behavior for high temperature bolted steel,” Journal of Advanced Performance Materials, vol. 6, no. 2, pp. 129–140, 1999.