I appreciate the comments made about the paper and the additional references. It is true that Eq. (4), taken from Johnson’s book, is Mindlin’s solution from his 1949 paper, and due credit should have been given. Moreover, as Johnson pointed out, a full stick solution for a Hertzian contact problem will have singularities. However, as stated in the paper: “This work is an attempt to obtain the representative qualitative features and scaling of the PSTD phenomenon without modeling the details of the single asperity solution, i.e., the traction fields on the asperity-asperity interface.” The assumption that, on average, the behavior follows the Mindlin-based solution is admittedly crude, but tractable analytically. This simple relationship minimized the complexity of the resulting expressions as compared to ones based on empirical relationships, e.g., Tabor’s work, and allowed for a clearer analysis of the basic mechanisms and population dynamics. More specifically, the need for substantial assumptions about the details of the asperity-asperity constitutive interaction are in counterpoint with the assumptions of smooth asperity surface geometry with well-defined radii of curvature. I assume that most researchers would agree that there are no precisely hemispherical asperities identifiable outside of the realm of theory and some artificial geometries created in the laboratory. So, given the lack of characterization of the details of asperity behavior, I think it is best to view asperities as merely actors in an ensemble, with the ensemble determining the observable behavior. Extension of the work to more detailed interactions, including those cited in the Discussion, is straightforward and is left for future work.
Skip Nav Destination
Article navigation
Discussions
Closure to “Discussion of ‘A Greenwood–Williamson Model of Small-Scale Friction’ ” (2008, ASME J. Appl. Mech., 75, p. 045501)
Reese Jones
Reese Jones
Sandia National Laboratories
, Livermore, CA 94551
Search for other works by this author on:
Reese Jones
Sandia National Laboratories
, Livermore, CA 94551J. Appl. Mech. Jul 2008, 75(4): 045502 (1 pages)
Published Online: May 15, 2008
Article history
Received:
September 6, 2007
Revised:
September 26, 2007
Published:
May 15, 2008
Article
Article discussed|
View article
Citation
Jones, R. (May 15, 2008). "Closure to “Discussion of ‘A Greenwood–Williamson Model of Small-Scale Friction’ ” (2008, ASME J. Appl. Mech., 75, p. 045501)." ASME. J. Appl. Mech. July 2008; 75(4): 045502. https://doi.org/10.1115/1.2870268
Download citation file:
754
Views
Get Email Alerts
Cited By
Mechanics of a Tunable Bistable Metamaterial With Shape Memory Polymer
J. Appl. Mech (January 2025)
Phase Diagrams for Anticlastic and Synclastic Bending Curvatures of Hexagonal and Reentrant Honeycombs
J. Appl. Mech (January 2025)
Nucleation of Fracture: The First-Octant Evidence Against Classical Variational Phase-Field Models
J. Appl. Mech (January 2025)
Related Articles
Interface Properties Due to Microslip From Vibration Measurement
J. Tribol (January,2001)
Study of Interfacial Phenomena Affecting Thermosonic Wire Bonding in Microelectronics
J. Tribol (July,2003)
Elastohydrodynamic Lubrication: A Gateway to Interfacial Mechanics—Review and Prospect
J. Tribol (October,2011)
Related Proceedings Papers
Related Chapters
Heat Generated in Pipe Flows Due to Friction
Everyday Heat Transfer Problems: Sensitivities to Governing Variables
Friction and Wear of Polymers and Composites
Tribology of Mechanical Systems: A Guide to Present and Future Technologies
Surface Analysis and Tools
Tribology of Mechanical Systems: A Guide to Present and Future Technologies