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On extension and torsion of a compressible elastic circular cylinder. (English) Zbl 1045.74013
Summary: We examine the combined extension and torsion of a compressible isotropic elastic cylinder of finite extent. The equilibrium equations are formulated in terms of the principal stretches, and then are applied to the special case of pure torsion superimposed on a uniform extension (an isochoric deformation). Explicit necessary and sufficient conditions on the strain-energy function for the material to support this deformation with vanishing traction on the lateral surfaces of the cylinder are obtained. Some strain-energy functions satisfying these conditions are considered, existing results are recovered as special cases, and new results are obtained. We also point out how the strain-energy functions generated from the considered isochoric deformation (of a compressible material) can be used to generate energy functions and corresponding solutions for the incompressible theory.

MSC:
74B20 Nonlinear elasticity
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