Monday, 11 October 2004 - 3:55 PM

This presentation is part of : Horgan Symposium

Puncturing a thin elastic sheet

David J. Steigmann, University of California, University of California, Department of Mechanical Engineering, 6133 Etcheverry Hall, Berkeley, CA 94720

We use membrane theory to analyze the puncturing of a thin solid circular isotropic elastic sheet by a rigid axisymmetric indenter. A solution is obtained in which a hole is formed at the center of the sheet with an interior annulus in frictionless contact with the cylindrical surface. The contacting part is in a state of pure hoop stress with the corresponding hoop stretch exhibiting a strong singularity at the origin. Conditions are given ensuring that the solution has finite total energy and it is shown to be energetically favored over unpunctured states for transverse indenter displacements exceeding a finite critical value.

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