Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Three-dimensional steady-state indentation problem for a general viscoelastic material

Authors: J. M. Golden, G. A. C. Graham and Q. Lan
Journal: Quart. Appl. Math. 52 (1994), 449-468
MSC: Primary 73T05; Secondary 73F99
DOI: https://doi.org/10.1090/qam/1292197
MathSciNet review: MR1292197
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Abstract: The steady-state problem is considered for periodic normal loading by a smooth, rigid indentor on a half-space exhibiting general viscoelastic behaviour. A technique is developed for summing the infinite series that arise. The method is applicable to the case in which the viscoelastic behaviour is described by a discrete spectrum model, in other words, by a finite sum of decaying exponentials. Numerical results are presented for two decay times. The extension to any number of decay times is straightforward.

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  • [1] J. M. Golden and G. A. C. Graham, The steady-state plane normal viscoelastic contact problem, Internat. J. Engrg. Sci. 25, 277-291 (1987)
  • [2] G. A. C. Graham and J. M. Golden, The three-dimensional steady-state viscoelastic indentation problem, Internat. J. Engrg. Sci. 26, 121-126 (1988)
  • [3] J. M. Golden and G. A. C. Graham, Stress, strain and area-controlled modes for the steady-state normal viscoelastic contact problem, Ocean waves mechanics, in Computational fluid dynamics and mathematical modelling (M. Rahman, ed.), Computational Mechanics Publ., Southampton, 1990, pp. 739-753
  • [4] J. M. Golden and G. A. C. Graham, A fixed length crack in a sinusoidally loaded general viscoelastic medium, in Continuum Mechanics and its Applications (G. A. C. Graham and S. K. Malik, eds.), Hemisphere, Washington, DC, 1989, pp. 171-188
  • [5] J. M. Golden and G. A. C. Graham, Boundary Value Problems in Linear Viscoelasticity, Springer-Verlag, Berlin, Heidelberg, 1988
  • [6] G. A. C. Graham and J. M. Golden, The generalized partial correspondence principle in linear viscoelasticity, Quart. Appl. Math. 46, 527-538; 49, 397 (1991) (1988)

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DOI: https://doi.org/10.1090/qam/1292197
Article copyright: © Copyright 1994 American Mathematical Society

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