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Bifurcation and stability of homogeneous equilibrium configurations of an elastic body under dead-load tractions

Published online by Cambridge University Press:  24 October 2008

J. M. Ball  and
D. G. Schaeffer
J. M. Ball
Affiliation:
Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS
D. G. Schaeffer
Affiliation:
Department of Mathematics, Duke University, Durham, NC 27706
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Extract

In this paper we consider the equilibrium configurations of a homogeneous, incompressible, isotropic elastic body subjected to a uniform dead load surface traction of magnitude T whose direction is normal to the surface of the body in the reference configuration, and to no other forces. We concentrate on homogeneous equilibrium solutions, that is those for which the deformation gradient F is constant, and we study their bifurcations and stability (with respect to an appropriate static criterion) as T varies. Since it turns out that the equations for homogeneous equilibrium solutions, and the stability properties that we consider of these solutions, are independent of the shape of the body in the reference configuration, we can suppose if desired that this shape is a cube. (See Fig. 1.1.)

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 94 , Issue 2 , September 1983 , pp. 315 - 339
Copyright
Copyright © Cambridge Philosophical Society 1983

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