Abstract
The linearized equations governing the deformations of incompressible elastic bodies are discussed. The Dirichlet problem is formulated for this system of equations using the theory of elliptic systems due to Douglis and Nirenberg. A uniqueness theorem is proved. Necessary and sufficient conditions for uniqueness of solution to the Dirichlet problem are obtained for small deformations of a Mooney-Rivlin material which has been subjected to a finite homogeneous biaxial deformation.
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