Abstract
We consider three-dimensional elastic bodies characterized by a general class of stored-energy functions dependent upon the first and second gradients of the deformation. We assume that the dependence on the higher-order term ensures strong ellipticity. With only modest assumptions on the lower-order term, we use the Leray--Schauder degree to prove the existence of global solution continua to the Dirichlet problem. With additional, physically reasonable restrictions on the stored-energy function, we then demonstrate that our global solution branch is unbounded.
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