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Mathematics and Mechanics of Solids
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What's this?

Analysis of Shaft-Loaded Membrane Delamination Using Stationary Principles

Carmel Majidi

Department of Electrical Engineering & Computer Science University of California Berkeley, CA 94720, USA

Richard E. Groff

Department of Electrical Engineering & Computer Science University of California Berkeley, CA 94720, USA

Ron S. Fearing

Department of Electrical Engineering & Computer Science University of California Berkeley, CA 94720, USA

The following analysis investigates the delamination of an elastic membrane which on one side adheres to a smooth substrate while the other side is attached to a rigid cylindrical shaft. When the shaft is pulled perpendicularly from the substrate, this system is equivalent to the blister test of Malyshev and Salganik (International Journal of Fracture Mechanics, 1, 114 (1965)) and a solution is derived using the principle of minimum potential energy. Delamination can also be caused by rotating the shaft, which may be induced by a shear load and/or moment applied to the free end. For this more complicated system, an approximate solution is obtained from upper and lower bounds on strain energy that are derived from stationary principles with restricted deformation and stress fields, respectively. Beyond their applicability to blister tests, these results are relevant to the emerging study of biologically-inspired adhesives, as membranes constitute a critical attachment structure for a variety of wall-clinging organisms.

Key Words: Non-linear membrane theory • stationary principles • complementary energy • Hencky strain measure

This version was published on February 1, 2008

Mathematics and Mechanics of Solids, Vol. 13, No. 1, 3-22 (2008)
DOI: 10.1177/1081286506068823
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