Helical shear of an elastic, circular tube with a non-convex stored energy

DOI10.1007/BF00251548zbMath0529.73007OpenAlexW2077945297MaRDI QIDQ787705

G. P. MacSithigh, Roger L. Fosdick

Publication date: 1983

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00251548

zbMATH Keywords

existence theoremhelical shearproperties of solutionselastic, circular tubeexplicit formulae for minimizing statesfor well-determined set of boundary conditions solution exhibits discontinuous deformation gradient fieldinner surface fixedminimization problem of certain functionalnon-convex stored energyouter surface turned about its axis and displaced parallel to itstored energy density expressed as function of shear

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Uniqueness of solutions of dynamical problems in solid mechanics (74H25) Uniqueness of solutions of equilibrium problems in solid mechanics (74G30)

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Cites Work

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• Discontinuous deformation gradients in the finite twisting of an incompressible elastic tube
• Locally one-to-one mappings and a classical theorem on schlicht functions
• COMBINED AXIAL AND TORSIONAL SHEAR OF A TUBE OF INCOMPRESSIBLE ISOTROPIC ELASTIC MATERIAL
• Large elastic deformations of isotropic materials VI. Further results in the theory of torsion, shear and flexure