Global continuation in second-gradient nonlinear elasticity

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.