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
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
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.
J. M. Golden and G. A. C. Graham, The steady-state plane normal viscoelastic contact problem, Internat. J. Engrg. Sci. 25, 277–291 (1987)
G. A. C. Graham and J. M. Golden, The three-dimensional steady-state viscoelastic indentation problem, Internat. J. Engrg. Sci. 26, 121–126 (1988)
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
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
J. M. Golden and G. A. C. Graham, Boundary Value Problems in Linear Viscoelasticity, Springer-Verlag, Berlin, Heidelberg, 1988
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)
J. M. Golden and G. A. C. Graham, The steady-state plane normal viscoelastic contact problem, Internat. J. Engrg. Sci. 25, 277–291 (1987)
G. A. C. Graham and J. M. Golden, The three-dimensional steady-state viscoelastic indentation problem, Internat. J. Engrg. Sci. 26, 121–126 (1988)
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
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
J. M. Golden and G. A. C. Graham, Boundary Value Problems in Linear Viscoelasticity, Springer-Verlag, Berlin, Heidelberg, 1988
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)
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC:
73T05,
73F99
Retrieve articles in all journals
with MSC:
73T05,
73F99
Additional Information
Article copyright:
© Copyright 1994
American Mathematical Society