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.
Original language | English (US) |
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Pages (from-to) | 103-115 |
Number of pages | 13 |
Journal | SIAM Journal on Mathematical Analysis |
Volume | 38 |
Issue number | 1 |
DOIs | |
State | Published - Mar 2006 |
All Science Journal Classification (ASJC) codes
- Analysis
- Computational Mathematics
- Applied Mathematics