The two-dimensional indentation problem of an elastic layer by either a wedge with a rounded tip or a flat punch with rounded corners in the presence of friction is investigated numerically. Contact stresses and deformations are presented when the layer is either bonded or resting without friction on a rigid foundation. Moreover, a set of asymptotic solutions for the contact pressure is obtained for an unbonded thin layer (the contact width is significantly larger than the layer thickness). The effects of several parameters on the results are examined.
HertzH.über die Berührung fester elasischer Körper (On the contact of elastic soilds)J. reine und angewandte Mathematik, 1896, 92, 156–171. For English translation see Miscellaneous Papers by H. Hertz (Eds Jones and Shott), 1896 (Macmillan, London).
2.
SchubertG.Zur fraga der druckverteilung unter elestisch gelagerten tragwerkenIng. Arch., 1942, 13, 132–161.
3.
CiavarellaM.HillsD. H.MonnoG.Contact problems for a wedge with rounded apexInt. J. Mech. Sci., 1998, 10, 977–988.
4.
CiavarellaM.HillsD. H.MonnoG.The influence of rounded edges on indentation by a flat punchProc. Instn Mech. Engrs, Part C: J. Mechanical Engineering Science, 1998, 12 (C4), 319–328.
5.
SteuermanI. Ya.Contact Problem of the Theory of Elasticity, 1949 (Gostekhteoretizdat, Moscow).
6.
JaffarM. J.The effect of sinusoidal roughness profile upon rolling plane layered contactTribology Int., 2001, 34, 171–180.
7.
BentallR. H.JohnsonK. L.An elastic strip in plane rolling contactInt. J. Mech. Sci., 1968, 10, 637–663.
8.
AleksandrovV. M.On plane contact problems of the theory of elasticity in the presence of adhesion or frictionJ. Appl. Mathematics and Mechanics, 1970, 34, 232–243.
9.
GladwellG. M. L.Contact Problems in Classical Elasticity, 1980 (Sijthoff and Noordhoff, Alphen aan den Rijn).
10.
JaffarM. J.Effect of friction on subsurface stresses in sliding line contact of multilayered elastic solidsInt. J. Solids Structs, 2000, 37, 6571–6575.
