Heriot-Watt Mathematics Report Series
HWM97-29, 1 September 1997
Plane deformation and stability of an elastic layer with intrinsic boundary elasticity
D.G. Roxburgh and P. Connor
Abstract
Recently, Steigmann and Ogden (1997) developed a
nonlinear theory of elastic boundary coatings for elastic bodies which
are subject to plane strain deformations. In this paper we seek to
study the behaviour of a suitably coated isotropic, hyperelastic layer
which has
been subjected to a homogeneous, biaxial, plane strain deformation.
The stability of the layer is investigated by studying incremental
deformations about this finitely deformed state. For the case of
symmetrically coated layers, explicit bifurcation conditions are
obtained and stability inequalities are derived.
Particular strain-energy functions are then chosen and the bifurcation
conditions are investigated numerically. A numerical study of
asymmetrically coated layers is also carried out.
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