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The stress field in a pulled cork and some subtle points in the semi-inverse method of nonlinear elasticity. (English) Zbl 1130.74008
Summary: In an attempt to describe cork-pulling, we model a cork as an incompressible rubber-like material and consider that it is subject to a helical shear deformation superimposed onto a shrink fit and a simple torsion. It turns out that this deformation field provides an insight into the possible appearance of secondary deformation fields for special classes of materials. We also find that these latent deformation fields are woken up by normal stress differences. We present some explicit examples based on neo-Hookean, generalized neo-Hookean and Mooney-Rivlin forms of the strain-energy density. Using a simple exact solution found in the neo-Hookean case, we conjecture that it is advantageous to accompany the usual vertical axial force by a twisting moment, in order to extrude a cork from the neck of a bottle efficiently. Then we analyse departures from the neo-Hookean behaviour by exact and asymptotic analyses. In that process, we are able to give an analytic example of secondary (or latent) deformations in the framework of nonlinear elasticity.
MSC:
74B20 Nonlinear elasticity
74G75 Inverse problems in equilibrium solid mechanics
74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics
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