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On a straightening of compressible, nonlinearly elastic, annular cylindrical sectors. (English) Zbl 1001.74531
Summary: We consider the plane-strain straightening of annular cylindrical sectors composed of isotropic, compressible, nonlinearly elastic solids. For zero-body forces and boundary conditions of place, the existence and uniqueness of solutions are established under the assumption that the material satisfies the tension-extension condition. The result is illustrated by considering a compressible neo-Hookean material and a generalized Blatz-Ko material for which closed-form solutions are displayed. Also discussed are certain cases of nonexistence and nonuniqueness of solutions.

MSC:
74B20 Nonlinear elasticity
74G30 Uniqueness of solutions of equilibrium problems in solid mechanics
74G35 Multiplicity of solutions of equilibrium problems in solid mechanics
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