Research Papers

Asymptotic Stress Fields for Complete Contact Between Dissimilar Materials

[+] Author and Article Information
Kisik Hong

Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109-2125
e-mail: kisik@umich.edu

M. D. Thouless

Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109-2125;
Department of Materials Science and
University of Michigan,
Ann Arbor, MI 48109-2125
e-mail: thouless@umich.edu

Wei Lu

Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109-2125
e-mail: weilu@umich.edu

J. R. Barber

Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109-2125
e-mail: jbarber@umich.edu

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received August 24, 2018; final manuscript received September 28, 2018; published online October 18, 2018. Assoc. Editor: Shengping Shen.

J. Appl. Mech 86(1), 011009 (Oct 18, 2018) (6 pages) Paper No: JAM-18-1488; doi: 10.1115/1.4041618 History: Received August 24, 2018; Revised September 28, 2018

We investigate the influence of material dissimilarity on the traction fields at the corners of a contact between an elastic right-angle wedge and an elastic half-plane. The local asymptotic fields are characterized in terms of the properties of the leading eigenvalue for cases of slip and stick as a function of the Dundurs bimaterial parameters α and β, and the coefficient of friction f. Permissible values of α and β are partitioned into two possible ranges, one where behavior is qualitatively similar to the case where the indenting wedge is rigid [α = 1] and the other where behavior is similar to the case where the materials are the same [α = β = 0]. The results give insight into the high local stresses at the edge of a contact between elastically dissimilar bodies and can also be used to evaluate the effectiveness of mesh refinement in corresponding finite element models.

Copyright © 2019 by ASME
Your Session has timed out. Please sign back in to continue.


Williams, M. L. , 1952, “ Stress Singularities Resulting From Various Boundary Conditions in Angular Corners of Plates in Extension,” ASME J. Appl. Mech., 19(4), pp. 526–528. http://resolver.caltech.edu/CaltechAUTHORS:20140730-111744170
Churchman, C. M. , and Hills, D. A. , 2006, “ General Results for Complete Contacts Subject to Oscillatory Shear,” J. Mech. Phys. Solids, 54(6), pp. 1186–1205. [CrossRef]
Karuppanan, S. , Churchman, C. M. , Hills, D. A. , and Giner, E. , 2008, “ Sliding Frictional Contact Between a Square Block and an Elastically Similar Half-Plane,” Eur. J. Mech., 27(3), pp. 443–459. [CrossRef]
Churchman, C. M. , and Hills, D. A. , 2006, “ Slip Zone Length at the Edge of a Complete Contact,” Int. J. Solids Struct., 43(7–8), pp. 2037–2049. [CrossRef]
Kim, H. K. , Hills, D. A. , and Paynter, R. J. , 2014, “ Asymptotic Analysis of an Adhered Complete Contact Between Elastically Dissimilar Materials,” J. Strain Anal., 49(8), pp. 607–617. [CrossRef]
Cox, B. , 1990, “ Pellet-Clad Interaction (PCI) Failures of Zirconium Alloy Fuel Claddinga Review,” J. Nucl. Mater., 172(3), pp. 249–292. [CrossRef]
Dundurs, J. , 1969, “ Discussion of Edge-Bonded Dissimilar Orthogonal Elastic Wedges Under Normal and Shear Loading,” ASME J. Appl. Mech., 36(3), pp. 650–652. [CrossRef]
Gdoutos, E. E. , and Theocaris, P. S. , 1975, “ Stress Concentrations at the Apex of a Plane Indenter Acting on an Elastic Half-Plane,” ASME J. Appl. Mech., 42(3), pp. 688–692. [CrossRef]
Comninou, M. , 1976, “ Stress Singularity at a Sharp Edge in Contact Problems With Friction,” Z. Für Angew. Math. und Phys. ZAMP, 27(4), pp. 493–499. [CrossRef]
Bogy, D. B. , 1971, “ Two Edge-Bonded Elastic Wedges of Different Materials and Wedge Angles Under Surface Tractions,” ASME J. Appl. Mech., 38(2), pp. 377–386. [CrossRef]
Flicek, R. C. , Ramesh, R. , and Hills, D. A. , 2015, “ A Complete Frictional Contact: The Transition From Normal Load to Sliding,” Int. J. Eng. Sci., 92, pp. 18–27. [CrossRef]
Spence, D. A. , 1973, “ An Eigenvalue Problem for Elastic Contact With Finite Friction,” Proc. Cambridge Philos. Soc., 73(1), pp. 249–268. [CrossRef]
Barber, J. R. , Davies, M. , and Hills, D. A. , 2011, “ Frictional Elastic Contact With Periodic Loading,” Int. J. Solids Struct., 48(13), pp. 2041–2047. [CrossRef]
Comninou, M. , and Dundurs, J. , 1982, “ An Educational Elasticity Problem With Friction—Part 2: Unloading for Strong Friction and Reloading,” ASME J. Appl. Mech., 49(1), pp. 47–51. [CrossRef]
Turner, J. R. , 1979, “ The Frictional Unloading Problem on a Linear Elastic Half-Space,” IMA J. Appl. Math., 24(4), pp. 439–469. [CrossRef]


Grahic Jump Location
Fig. 1

(a) A quarter-plane (right-angle wedge) indenting a half-plane and (b) Sign convention for normal traction p and shear traction q. At a trailing edge, q = fp, and at a leading edge, q = –fp.

Grahic Jump Location
Fig. 2

Characteristics of the first slip eigenvalue λ1(s) (trailing edge—leading edge) with different friction coefficients: (a) f = 0.2, (b) f = 0.4, (c) f = 0.6, and (d) f = 0.8

Grahic Jump Location
Fig. 3

Lowest eigenvalue versus friction coefficient for contact between elastically similar materials (α = β = 0)

Grahic Jump Location
Fig. 4

Partition of the Dundurs parallelogram

Grahic Jump Location
Fig. 5

Contour plots of the critical friction coefficients: (a) fc and (b) fa



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In