Abstract
In this paper, we prove the uniqueness of the solution to certain simple displacement boundary value problems in the nonlinear theory of homogeneous hyperelasticity for a body occupying a star-shaped reference configuration Ω ⊂ Rn whose boundary ∂ Ω is subjected to an affine deformation i.e., there exists a constant n×n matrix F and a constant n vector b such that x ↦ Fx + b for all x∈ ∂ Ω. We consider all smooth equilibrium configurations satisfying this boundary condition. Clearly, the homogeneous deformation x ↦ Fx + b, for all \( x \in \bar{\Omega } \), is one such solution. Our aim is to prove under suitable hypotheses that it is the only such solution.
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Dedicated to J. L. Ericksen on his sixtieth birthday
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© 1986 Springer-Verlag Berlin Heidelberg
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Knops, R.J., Stuart, C.A. (1986). Quasiconvexity and Uniqueness of Equilibrium Solutions in Nonlinear Elasticity. In: The Breadth and Depth of Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61634-1_21
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DOI: https://doi.org/10.1007/978-3-642-61634-1_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-16219-3
Online ISBN: 978-3-642-61634-1
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