Elastic Stability of an Internally Constrained Hyperelastic Material

Feixia Pan
Department of Engineering Mechanics
University of Nebraska
Lincoln, NE
Ph.D. Advisor:  Dr. Millard F. Beatty

Date:  Friday, December 6, 1996
Time:  3:00 p.m.
Place:  306 Bancroft Hall


The development of the theory of finite elastic deformations in the first half of this century has opened the door for research on the elastic instability of massive bodies. It has been demonstrated that the loss of elastic stability is not restricted to thin bodies, but may occur in thick bodies or even in unbounded media.

In the present study, we use Euler's stability criterion to derive stability equations for a thick slab, a half-space, and a thick-walled cylindrical tube made of a Bell constrained material under static loading. For the slab problem, general stability equations for symmetric and asymmetric stability modes are presented and applied to five specific cases. Some interesting numerical results, verified theoretically, are presented. For the cylindrical tube problem, we recast our mathematical model in a form similar to that developed by Wilkes for the incompressible tube problem, and thus derive the stability equations. Three possible cases are examined for which the roots of the characteristic equation are real-valued, pure imaginary, or complex conjugate. Results for axisymmetric and bending type deflections are presented. The material stability problem is investigated by application of the wave speed criterion. Based on the wave speed criterion, it is shown that certain cases discussed in the slab problem are materially unstable and thus can be omitted.