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.

**[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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Additional Information

DOI:
https://doi.org/10.1090/qam/1292197

Article copyright:
© Copyright 1994
American Mathematical Society