We present a new formulation of the boundary element method for simulating the nonadhesive and adhesive contact between an indenter of arbitrary shape and an elastic half-space coated with an elastic layer of different material. We use the Fast Fourier Transform-based formulation of boundary element method, while the fundamental solution is determined directly in the Fourier space. Numerical tests are validated by comparison with available asymptotic analytical solutions for axisymmetric flat and spherical indenter shapes.
KhademMPenkovOVYangHK, et al.Tribology of multilayer coatings for wear reduction: a review. Friction2017; 5: 248–262.
2.
PogrebnjakADBratushkaSNBeresnevVM, et al.Shape memory effect and superelasticity of titanium nickelide alloys implanted with high ion doses. Russian Chem Rev2013; 82: 1135.
3.
BecSTonckALoubetJL. A simple guide to determine elastic properties of films on substrate from nanoindentation experiments. Philosophic Mag2006; 86: 33–35. Taylor & Francis: 5347–5358.
4.
MeijersP. The contact problem of a rigid cylinder on an elastic layer. Appl Scient Res1968; 18: 353–383.
5.
JaffarMJ. Asymptotic behaviour of thin elastic layers bonded and unbonded to a rigid foundation. Int J Mech Sci1989; 31: 229–235.
6.
ConstantinescuAKorsunskyAMPisonO, et al.Symbolic and numerical solution of the axisymmetric indentation problem for a multilayered elastic coating. Int J Solids Struct2013; 50: 2798–2807.
7.
GuptaPKWalowitJA. Contact stresses between an elastic cylinder and a layered elastic solid. J Lubricat Technol1974; 96: 250–257.
8.
FabrikantVI. Elementary solution of contact problems for a transversely isotropic elastic layer bonded to a rigid foundation. J Appl Math Phys2006; 57: 464–490.
9.
StanGAdamsGG. Adhesive contact between a rigid spherical indenter and an elastic multi-layer coated substrate. Int J Solids Struct2016; 87: 1–10.
10.
PapangeloA. Adhesion between a power-law indenter and a thin layer coated on a rigid substrate. Facta Universitatis Series Mech Eng2018; 16: 19–28.
11.
PerssonBNJ. Contact mechanics for layered materials with randomly rough surfaces. J Phys Condens Matter2012; 24: 095008.
12.
PohrtRLiQ. Complete boundary element formulation for normal and tangential contact problems. Phys Mesomech2014; 17: 334–340.
13.
PohrtRPopovVL. Adhesive contact simulation of elastic solids using local mesh-dependent detachment criterion in boundary elements method. Facta Universitatis Series Mech Eng2015; 13: 3–10.
14.
ArgatovILiQPohrtR, et al.Johnson-Kendall-Roberts adhesive contact for a toroidal indenter. Proc R Soc Lond A Math Phys Eng Sci2016; 472(2191): DOI: 10.1098/rspa.2016.0218.
15.
LiQArgatovI. Onset of detachment in adhesive contact of an elastic half-space and flat-ended punches with non-circular shape : analytic estimates and comparison with numeric analysis. J Phys D Appl Phys2018. 145601. DOI: 10.1088/1361-6463/aab28b.
16.
PopovVLPohrtRLiQ. Strength of adhesive contacts: influence of contact geometry and material gradients. Friction2017; 5: 308–325.
17.
LiQPopovVL. Boundary element method for normal non-adhesive and adhesive contacts of power-law graded elastic materials. Computat Mech2017; 61: 319–329.
18.
SneddonIN. Fourier-transform solution of a Boussinesq problem for a hexagonally aeolotropic elastic half-space. J Mech Appl Math1992; 45: 607–616.
19.
Landau LD and Lifshitz EM. Theory of elasticity. Course of theoretical physics. 2nd ed. New York: Pergamon Press, 1970.
20.
VollebregtEAH. A new solver for the elastic normal contact problem using conjugate gradients, deflation, and an FFT-based preconditioner. J Computat Phys2014; 257: 333–351.
21.
GriffithAA. VI. The phenomena of rupture and flow in solids. Philosophic Trans R Soc Lond A Math Phys Eng Sci1921; 221: 163–198.
22.
PopovVL. Solution of adhesive contact problem on the basis of the known solution for non-adhesive one. Facta Universitatis Series Mech Eng2018; 16: 93–98.
23.
CiavarellaM. An approximate JKR solution for a general contact, including rough contacts. J Mech Phys Solids2018; 114: 209–218.
24.
YangF. Asymptotic solution to axisymmetric indentation of a compressible elastic thin film. Thin Solid Films2006; 515: 2274–2283.
25.
LiQPopovVL. Adhesive contact between a rigid body of arbitrary shape and a thin elastic coating. Acta Mechanica2019. 2019; 1: 1–7.
26.
ArgatovIIBorodichFMPopovVL. JKR adhesive contact for a transversely isotropic layer of finite thickness. J Phys D Appl Phys2015; 49: 45307.
27.
ShieldTWBogyDB. Multiple region contact solutions for a flat indenter on a layered elastic half space: plane-strain case. J Appl Mech1989; 56: 251–262.
28.
UrquhartEEPinderaMJ. Incipient separation between a frictionless flat punch and an anisotropic multilayered half plane. Int J Solids Struct1994; 31: 2445–2461.
29.
ChenLFUrquhartEEPinderaMJ. Microstructural effects in multilayers with large moduli contrast loaded by flat punch. AIAA J2005; 43: 962–973.
30.
KendallK. The adhesion and surface energy of elastic solids. J Phys D Appl Phys1971; 4: 1186.
