Two-Dimensional Effects in the Necking of Elastic Bars

[+] Author and Article Information
S. A. Silling

Brown University, Division of Engineering, Providence, RI 02912

J. Appl. Mech 55(3), 530-535 (Sep 01, 1988) (6 pages) doi:10.1115/1.3125825 History: Received April 15, 1987; Revised December 04, 1987; Online July 21, 2009


Numerical solutions for incompressible hyperelastic bars undergoing smooth necking in plane strain show complex phenomena in which two-dimensional effects are inherently important. In long bars, the two-dimensional effects are confined to a transition zone between the necked and non-necked phases. In spite of the two-dimensional effects, the nominal stress in necked long bars is close to the Maxwell stress under certain conditions. For very long bars there are necked equilibrium deformations in which the overall stretch is less than that of the maximum in the constitutive relation.

Copyright © 1988 by ASME
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