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Title:Mind the gap: The shape of the free surface of a rubber-like material in proximity to a rigid contactor
Author(s):Fried, Eliot; Todres, Russell E.
Abstract:Extending Andreussi and Gurtin’s (1977) pioneering work on the wrinkling of a free surface, we investigate the wrinkling stability of an incompressible elastic-like half-space whose surface is proximate to a contactor. Assuming a plane-strain deformation and accounting for both surface prestress and curvature-dependence of the surface free-energy density, we impose balances of forces and torques both in the bulk and on the surface. From the resulting linearized bulk and superficial equations, we derive a quintic dimensionless dispersion relation and perform a parametric study to see when stable or unstable behavior of the free surface is manifested. In contrast to the quadratic dispersion relation of Andreussi and Gurtin (1977), we obtain a quintic dispersion relation. An anlysis of this dispersion relation shows that the combined effects associated with surface pre-stress, curvature-dependence of the surface free-energy density, and the interactions between the surface and the proximate contactor lead always to an increased number linearly stable wrinkled configurations.
Issue Date:2005-10
Publisher:Department of Theoretical and Applied Mechanics (UIUC)
Series/Report:TAM Reports 1077, (2005)
Genre:Technical Report
Publication Status:published or submitted for publication
Peer Reviewed:is peer reviewed
Date Available in IDEALS:2007-03-09
Is Version Of:Published as: Eliot Fried and Russell E. Todres. Mind the gap: The shape of the free surface of a rubber-like material in proximity to a rigid contactor. Journal of Elasticity, Vol. 80, No. 1-3, 2005, pp. 97- 151 (55). DOI: 10.1007/s10659-005-9019-z. Copyright 2005 Springer (Kluwer)

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  • Technical Reports - Theoretical and Applied Mechanics (TAM)
    TAM technical reports include manuscripts intended for publication, theses judged to have general interest, notes prepared for short courses, symposia compiled from outstanding undergraduate projects, and reports prepared for research-sponsoring agencies.

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