Abstract
Resisted by Coulomb friction, a rigid indentor slides at a constant arbitrary speed on a generalized neo-Hookean half-space under pre-stress. A dynamic steady-state situation in plane strain is assumed, and is treated as the superposition of contact-triggered infinitesimal deformations upon finite deformations due to pre-stress.
Exact solutions are presented for both deformations, and the infinitesimal component exhibits the anisotropy typically induced by pre-stress, and wave speeds that are sensitive to pre-stress. In view of the unilateral constraints of contact, these and other critical speeds define the sliding speed ranges for physically-acceptable solutions. In particular, a Rayleigh speed is the upper bound for subsonic sliding. Solutions are further constrained by the unilateral requirement that contact zone shear must oppose indentor/half-space slip.
The generic parabolic indentor is used for illustration, and it is found that traction continuity at the contact zone leading edge is lost for supersonic sliding and at the single sliding speed allowed in the frictionless limit in the trans-sonic range.
A range of acceptable pre-stresses is also identified; for pre-stresses that lie out of range, either a negative Poisson effect occurs, or the Rayleigh wave disappears, thereby precluding sliding in the subsonic range.
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References
J.W. Craggs and A.M. Roberts, On the motion of a heavy cylinder over the surface of an elastic half-space. ASME J. Appl. Mech. 24 (1967) 207-209.
F.P. Gerstle and G.W. Pearsall, The stress response of an elastic surface to a high-velocity, unlubricated punch. ASME J. Appl. Mech. 41 (1974) 1036-1040.
L.M. Brock, Sliding and indentation by a rigid half-wedge with friction and displacement coupling effects. Internat. J. Engrg. Sci. 19 (1981) 33-40.
L.M. Brock, Some analytical results for heating due to irregular sliding contact. Indian J. Pure Appl. Math. 27 (1996) 1257-1278.
H.G. Georgiadis and J.R. Barber, On the super-Rayleigh/subseismic elastodynamic indentation problem. J. Elasticity 31 (1993) 141-161.
L.M. Brock and H.G. Georgiadis, Sliding contact with friction on a thermoelastic solid at subsonic and supersonic speeds. J. Thermal Stresses (to appear).
M.F. Beatty and S.A. Usmani, On the indentation of a highly elastic half-space. Quart. J. Mech. Appl. Math. 28 (1975) 47-62.
L.M. Brock, Rapid sliding indentation with friction of a pre-stressed thermoelastic material. J. Elasticity 53 (1999) 161-188.
L.M. Brock, Rapid sliding contact on a highly elastic pre-stressed material. Internat. J. Non-Linear Mech. (to appear).
L.M. Brock and H.G. Georgiadis, Rapid sliding contact at arbitrary constant speeds on a highly elastic half-space (submitted for publication).
A.E. Green and W. Zerna, Theoretical Elasticity, 2nd edn. Oxford Univ. Press, London (1968).
C. Truesdell and W. Noll, The non-linear field theories of mechanics. In: W. Flugge (ed.), Handbuch der Physik, Vol. III/3. Springer, Berlin (1965).
R.C. Hibbeler, Mechanics of Materials, 3rd edn. Prentice-Hall, Saddle River, NJ (1997).
J.D. Achenbach, Wave Propagation in Elastic Solids. North-Holland, Amsterdam (1973).
N.I. Muskhelisvili, Some Basic Problems of the Mathematical Theory of Elasticity. Noordhoff International, Leyden (1975).
F. Erdogan, Mixed boundary value problems in mechanics. In: S. Nemat-Nasser (ed.), Mechanics Today, Vol. 4. Pergamon, New York (1976).
B. van der Pol and H. Bremmer, Operations Based on the Two-Sided Laplace Integral. Cambridge Univ. Press, Cambridge (1950).
G.F. Carrier and C.E. Pearson, Partial Differential Equations. Academic Press, New York (1988).
L.M. Brock, Analytical results for roots of two irrational functions in elastic wave propagation. J. Austral. Math. Soc., Ser. B 40 (1998) 72-79.
P.C. Chadwick, Thermoelasticity: the dynamical theory. In: I.N. Sneddon and R. Hill (eds), Mechanics Today, Vol. 1. North-Holland, Amsterdam (1960).
I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series and Products. Academic Press, New York (1980).
E. Hille, Analytic Function Theory, Vol. I. Blaisdell Publishing, Waltham, MA (1959).
B. Noble, Methods Based on the Wiener-Hopf Technique. Pergamon, New York (1958).
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Brock, L. Sliding Contact with Friction at Arbitrary Constant Speeds on a Pre-Stressed Highly Elastic Half-Space. Journal of Elasticity 57, 105–132 (1999). https://doi.org/10.1023/A:1007616120386
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DOI: https://doi.org/10.1023/A:1007616120386