Abstract
In this study, contact problem for a homogeneous orthotropic layer loaded by a rigid cylindrical stamp is considered. The rigid cylindrical stamp slides over the contacting medium whose bottom surface is fixed to the ground in all directions. Using the integral transformation technique, the contact problem is formulated analytically into a singular integral equation. The resulting integral equation is converted to algebraic equations by using Gauss–Jacobi integration formulas and solved numerically. In addition to the analytical formulation, a finite element method (FEM) study is also conducted. The results that are obtained using FEM are compared with the results found using analytical formulation. It is found that the results obtained from analytical formulation and FEM study are in good agreement with each other. The primary intention of this paper is to demonstrate the effects of orthotropic material properties, geometrical properties and the coefficient of friction on the stresses generated due to the sliding motion of the rigid cylindrical stamp. The results of this study may provide benchmark results for engineers to be used in tribology applications involving friction and wear mechanisms.
Similar content being viewed by others
References
ANSYS: ANSYS Mechanical APDL Modeling and Meshing Guide, p. 15317. ANSYS Inc, Canonsburg, PA (2013)
ANSYS: ANSYS Mechanical APDL Contact Technology Guide, 17th edn, p. 15317. ANSYS Inc., Canonsburg, PA (2016)
ANSYS: ANSYS Mechanical APDL 18.1 Documentation, p. 15317. ANSYS Inc., Canonsburg, PA (2017)
Abhilash, M.N., Murthy, H.: Finite element analysis of 2-d elastic contacts involving fgms. Int. J. Comput. Methods Eng. Sci. Mech. 15(3), 253–257 (2014)
Alinia, Y., Beheshti, A., Guler, M.A., El-Borgi, S., Polycarpou, A .A.: Sliding contact analysis of functionally graded coating/substrate system. Mech. Mater. 94(Supplement C), 142–155 (2016)
Bagault, C., Nélias, D., Baietto, M.: Contact analyses for anisotropic half space: effect of the anisotropy on the pressure distribution and contact area. Int. J. Solids Struct. 134(3), 031401–031401–8 (2012)
Balci, M.N., Dag, S., Yildirim, B.: Subsurface stresses in graded coatings subjected to frictional contact with heat generation. J. Thermal Stresses 40(4), 517–534 (2017)
Barber, J., Ciavarella, M.: Contact mechanics. Int. J. Solids Struct. 37(1), 29–43 (2000)
Binienda, W., Pindera, M.: Frictionless contact of layered metal-matrix and polymer-matrix composite half planes. Compos. Sci. Technol. 50(1), 119–128 (1994)
Blazquez, A., Mantič, V., París, F.: Application of bem to generalized plane problems for anisotropic elastic materials in presence of contact. Eng. Anal. Bound. Elements 30(6), 489–502 (2006)
Chidlow, S., Teodorescu, M.: Two-dimensional contact mechanics problems involving inhomogeneously elastic solids split into three distinct layers. Int. J. Eng. Sci. 70(Supplement C), 102–123 (2013)
Chidlow, S., Teodorescu, M.: Sliding contact problems involving inhomogeneous materials comprising a coating-transition layer-substrate and a rigid punch. Int. J. Solids Struct. 51(10), 1931–1945 (2014)
Chidlow, S., Chong, W., Teodorescu, M.: On the two-dimensional solution of both adhesive and non-adhesive contact problems involving functionally graded materials. Eur. J. Mech. A/Solids 39(Supplement C), 86–103 (2013)
Choi, H.J.: On the plane contact problem of a functionally graded elastic layer loaded by a frictional sliding flat punch. J.Mech. Sci. Technol. 23(10), 2703–2713 (2009)
Choi, H.J., Paulino, G.H.: Thermoelastic contact mechanics for a flat punch sliding over a graded coating/substrate system with frictional heat generation. J. Mech. Phys. Solids 56(4), 1673–1692 (2008)
Choi, H.J., Thangjitham, S.: Stress analysis of multilayered anisotropic elastic media. J. Appl. Mech. 58, 382–387 (1991)
Chong, W., Chidlow, S.: Analysing the effects of sliding, adhesive contact on the deformation and stresses induced within a multi-layered elastic solid. Mech. Mater. 101(Supplement C), 1–13 (2016)
Dag, S., Guler, M.A., Yildirim, B., Ozatag, A.C.: Sliding frictional contact between a rigid punch and a laterally graded elastic medium. Int. J. Solids Struct. 46(22), 4038–4053 (2009)
Demirhan, N., Kanber, B.: Finite element analysis of frictional contacts of fgm coated elastic members#. Mech. Based Des. Struct. Mach. 41(4), 383–398 (2013)
England, A .H.: Complex and Variable Methods in Elasticity. Wiley, Hoboken (1971)
Erbas, B., Yusufoğlu, E., Kaplunov, J.: A plane contact problem for an elastic orthotropic strip. J. Eng. Math. 70(4), 399–409 (2011)
Erdogan, F., Delale, F.: The problem of internal and edge cracks in an orthotropic strip. J. Appl. Mech. 44(2), 237–242 (1978)
Guler, M.A.: Closed-form solution of the two-dimensional sliding frictional contact problem for an orthotropic medium. Int. J. Mech. Sci. 87(Supplement C), 72–88 (2014)
Guler, M.A., Gulver, Y.F., Nart, E.: Contact analysis of thin films bonded to graded coatings. Int. J. Mech. Sci. 55(1), 50–64 (2012)
Guler, M.A., Kucuksucu, A., Yilmaz, K., Yildirim, B.: On the analytical and finite element solution of plane contact problem of a rigid cylindrical punch sliding over a functionally graded orthotropic medium. Int. J. Mech. Sci. 120(Supplement C), 12–29 (2017)
He, L., Ovaert, T.C.: Three-dimensional rough surface contact model for anisotropic materials. J. Tribol. 130(2), 021402 (2008)
Hertz, H. R.: Über die berührung fester elastischer körper und über die härte. Verhandlungen des Vereins zur Beförderung des Gewerbfleis̈es, Berlin : Verein zur Beförderung des Gewerbefleisses 1882, 449–463 (1896)
Johnson, K.L.: Contact Mechanics. Cambridge University Press, Cambridge (2012)
Ke, L.-L., Wang, Y.-S.: Two-dimensional contact mechanics of functionally graded materials with arbitrary spatial variations of material properties. Int. J. Solids Struct. 43(18), 5779–5798 (2006)
Ke, L.-L., Wang, Y.-S.: Two-dimensional sliding frictional contact of functionally graded materials. Eur. J. Mech. A/Solids 26(1), 171–188 (2007)
Keer, L., Mowry, D.: The stress field created by a circular sliding contact on transversely isotropic spheres. Int. J. Solids Struct. 15(1), 33–39 (1979)
Krenk, S.: On the elastic constants of plane orthotropic elasticity. J. Compos. Mater. 13(2), 108–116 (1979)
Kucuksucu, A., Guler, M., Avci, A.: Closed-form solution of the frictional sliding contact problem for an orthotropic elastic half-plane indented by a wedge-shaped punch. Key Eng. Mater. 618, 203–225 (2014)
Lekhnitskii, S.G.: Theory of Elasticity of an Anisotropic Elastic Body (Holden-Day Series in Mathematical Physics). Tbh/Yes Dee, Chennai (1963). Please check and confirm the inserted publisher location is correct for the reference [34] and amend if necessary
Mindlin, R.: Compliance of elastic bodies in contact. J. Appl. Mech. 16, 259–268 (1949)
Muskhelishvili, N.I.: Singular Integral Equations: Boundary Problems of Function Theory and Their Application to Mathematical Physics (Dover Books on Mathematics). Dover Publications, Mineola (2011)
Muskhelishvili, N.I.: Some Basic Problems of the Mathematical Theory of Elasticity. Springer, Netherlands (2013)
Pagano, N.: Exact solutions for rectangular bidirectional composites and sandwich plates. J. Compos. Mater. 4(1), 20–34 (1970)
Popov, V.: Contact Mechanics and Friction: Physical Principles and Applications, 1st edn. Springer, Berlin (2010)
Rodriguez, N., Masen, M., Schipper, D.: A contact model for orthotropic-viscoelastic materials. Int. J. Mech. Sci. 74(Supplement C), 91–98 (2013)
Rodríguez-Tembleque, L., Buroni, F., Abascal, R., Sáez, A.: 3d frictional contact of anisotropic solids using bem. Eur. J. Mech. A/Solids 30(2), 95–104 (2011)
Shi, D., Lin, Y., Ovaert, T.C.: Indentation of an orthotropic half-space by a rigid ellipsoidal indenter. J. Tribol. 125(2), 223–231 (2003)
Sneddon, I .N.: Fourier Transforms. Dover Publications Inc, Mineola (1951)
Spence, D.A.: The hertz contact problem with finite friction. J. Elast. 5(3), 297–319 (1975)
Srinivas, S., Rao, A.: Bending, vibration and buckling of simply supported thick orthotropic rectangular plates and laminates. Int. J. Solids Struct. 6, 1463–1481 (1970)
Swanson, S.R.: Hertzian contact of orthotropic materials. Int. J. Solids Struct. 41, 1945–1959 (2004)
Turner, J.: Contact on a transversely isotropic half-space, or between two transversely isotropic bodies. Int. J. Solids Struct. 16, 409–419 (1966)
Willis, J.: Hertzian contact of anisotropic bodies. J. Mech. Phys. Solids 14(3), 163–176 (1966)
Yang, B., Pan, E.: Three-dimensional green’s functions in anisotropic trimaterials. Int. J. Solids Struct. 39(8), 2235–2255 (2002)
Zhou, Y.T., Lee, K.Y.: Exact solutions of a new, 2d frictionless contact model for orthotropic piezoelectric materials indented by a rigid sliding punch. Philos. Mag. 92(15), 1937–1965 (2012)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Comez, I., Yilmaz, K.B., Güler, M.A. et al. On the plane frictional contact problem of a homogeneous orthotropic layer loaded by a rigid cylindrical stamp. Arch Appl Mech 89, 1403–1419 (2019). https://doi.org/10.1007/s00419-019-01511-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00419-019-01511-6