Shakedown in elastic contact problems with Coulomb friction

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES

卷:44

Article

Klarbring, A.²  Ciavarella, M.³  Barber, J. R.¹ 

[1] Univ Michigan, Dept Mech Engn, Ann Arbor, MI 48109 USA

[2] Linkoping Univ, Inst Technol, Div Mech, S-58183 Linkoping, Sweden

[3] Polytecn Bari, CEMEC, Ctr Excellence Computat Mech, I-70125 Bari, Italy

关键词: contact problems;    fretting fatigue;    shakedown;    Melan's theorem;    Coulomb friction;   

DOI  :  10.1016/j.ijsolstr.2007.06.013

来源: Elsevier

【 摘 要 】

Elastic systems with frictional interfaces subjected to periodic loading are sometimes predicted to 'shake down' in the sense that frictional slip ceases after the first few loading cycles. The similarities in behaviour between such systems and monolithic bodies with elastic-plastic constitutive behaviour have prompted various authors to speculate that Melan's theorem might apply to them - i.e., that the existence of a state of residual stress sufficient to prevent further slip is a sufficient condition for the system to shake down. In this paper, we prove this result for 'complete' contact problems in the discrete formulation (i) for systems with no coupling between relative tangential displacements at the interface and the corresponding normal contact tractions and (ii) for certain two-dimensional problems in which the friction coefficient at each node is less than a certain critical value. We also present counter-examples for all systems that do not fall into these categories, thus giving a definitive statement of the conditions under which Melan's theorem can be used to predict whether such a system will shake down. (c) 2007 Elsevier Ltd. All rights reserved.

【 授权许可】

Free