ELECTRICAL CONTACT RESISTANCE, THERMAL CONTACT CONDUCTANCE AND ELASTIC INCREMENTAL STIFFNESS FOR A CLUSTER OF MICROCONTACTS: ASYMPTOTIC MODELLING by I. I. ARGATOV † (Department of Mechanical and Aerospace Engineering, New Mexico State University, Las Cruces, NM 88003, USA) [Received 10 August 2009. Revised 28 January 2010] Summary The paper concerns the problem of electrical conductance through a multiple discrete contact interface between two elastic bodies pressed against one another. Mathematically, similar problems arise in the theory of heat conduction between the contacting bodies in a vacuum as well as in the study of the incremental elastic contact problems with application to the elasticity–conductivity cross-property connections. The electrical contact resistance, thermal contact conductance and elastic incremental stiffness of a cluster of microcontacts have been expressed in terms of the harmonic capacity of the cluster. Several asymptotic models for approximate evaluating the contact resistance of a cluster of microcontacts have been constructed and their accuracy has been estimated. 1. Introduction The paper primarily deals with the problem of electrical conductance through a contact interface between two elastic bodies with rough surfaces pressed against one another. It is supposed that the actual contact areas are grouped into a cluster. A particular focus is placed on the resistance of the current between the bodies in contact (1). Mathematically, similar problems arise in the theory of heat conduction between the contacting bodies in a vacuum (2) as well as in the study of the incremental elastic contact problems (3) with application to the elasticity–conductivity cross- property connections (4). The theoretical study of electrical contact resistance of clusters was originated from the seminal work by Greenwood (5). The concept of Holm’s radius for a cluster of microcontacts was revisited in (6). Though, complete mathematical analysis of the current flow through multiple contact spots is very complex, the contact resistance being its integral characteristic can be analytically estimated in a number of situations that are of practical interest. In the present paper, we apply the asymptotic modelling approach (7, 8) for evaluating the contact resistance of a cluster of microcontacts distributed deterministically in a wide range of parameters of the cluster. Though we consider the case of microcontacts being distributed deterministically, it should be noted that the main results are directly generalized for clusters with randomly distributed microcontacts. Initially, we construct asymptotic models of multiple dilute contact with arbitrarily small contact spots. It is shown that the first-order asymptotic model coincides with the Greenwood model derived † 〈argatov@nmsu.edu〉 Q. Jl Mech. Appl. Math, Vol. 64. No. 1 c  The author 2010. Published by Oxford University Press; all rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org Advance Access publication 20 August 2010. doi:10.1093/qjmam/hbq018 Downloaded from https://academic.oup.com/qjmam/article/64/1/1/1899581 by guest on 02 August 2022