Mind the gap: The shape of the free surface of a rubber-like material in proximity to a rigid contactor

Fried, Eliot; Todres, Russell E.

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Description

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.

Issue Date

2005-10

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.

Publisher

Department of Theoretical and Applied Mechanics (UIUC)

Series/Report Name or Number

TAM Reports 1077, (2005)

ISSN

0073-5264

Type of Resource

text

Language

en

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http://hdl.handle.net/2142/335

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