Abstract
In an earlier paper, the broadest classes of compressible isotropic strain energies that support irrotational universal deformations were identified and the problems of cylindrical and spherical inflation or compaction were solved in closed form for all of these strain energies. Similar closed form solutions of the problem of azimuthal shear are presented here.
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Collected Papers of R.S. Rivlin: Barenblatt, G.I., Joseph, D.D. (eds.), vol. 2. Springer, New York (1997)
Truesdell, C.A., Noll, W.: The nonlinear field theories of mechanics. In: Flügge, S. (ed.) Handbuch der Physik III/3. Springer (1965)
Ogden, R.W.: Non-linear elastic deformations. Ellis Horwood, Chichester (1984)
Ericksen, J.L.: Deformations possible in every compressible, isotropic, perfectly elastic material. J. Math. Phys. 34, 126–128 (1955)
John, F.: Plain strain problems for a perfectly elastic material of harmonic type. Comm. Pure Appl. Math. 13, 239–296 (1960)
Jafari, A.H., Abeyaratne, R., Horgan, C.O.: The finite deformation of a pressurized circular tube for a class of compressible materials. Z. Angew. Math. Phys. 35, 227–246 (1984)
Abeyaratne, R., Horgan, C.O.: The pressurized hollow sphere problem in finite elastostatics for a class of compressible materials. Int. J. Solids Struct. 20, 715–723 (1984)
Ogden, R.W., Isherwood, D.A.: Solution of some finite plane strain problems for compressible elastic solids. Q. J. Mech. Appl. Math. 31, 219–249 (1978)
Carroll, M.M.: Finite strain solutions in compressible finite elasticity. J. Elasticity. 20, 65–92 (1988)
Carroll, M.M.: Controllable deformations in compressible finite elasticity. Stab. Appl. Anal. Contin. Media 1, 373–384 (1991)
Murphy, J.G.: A family of solutions describing plane strain cylindrical inflation in finite, compressible elasticity. J. Elasticity. 45, 1–11 (1996)
Murphy, J.G.: A family of solutions describing spherical inflation in finite, compressible elasticity. Q. J. Mech. Appl. Math. 50, 35–45 (1997)
Carroll, M.M., Rooney, F.J.: Implications of Shield’s inverse deformation theorem for compressible finite elasticity. Z. Angew. Math. Phys. 56, 1048–1060 (2005)
Carroll, M.M.: Compressible isotropic strain energies that support universal irrotational finite deformations. Q. J. Mech. Appl. Math. 58, 601–614 (2005)
Murphy, J.G., Carroll, M.M.: Azimuthal shearing of special compressible materials. Proc. Royal Irish Acad. 93A, 209–230 (1993)
Polignone, D.A., Horgan, C.O.: Pure azimuthal shear of compressible nonlinearly elastic materials. Quart. Appl. Math. 50, 323–341 (1992)
Haughton, D.M.: Circular shearing of compressible elastic cylinders. Q. J. Mech. Appl. Math. 46, 471–486 (1993)
Beatty, M.F., Jiang, Q.: On compressible materials capable of sustaining axi-symmetric shear deformations. Part 2: Rotational. Q. J. Mech. Appl. Math. 50, 211–237 (1997)
Jiang, X., Ogden, R.W.: On azimuthal shear of a circular cylindrical tube of compressible elastic material. Q. J. Mech. Appl. Math. 51, 143–158 (1998)
Paullet, J.E., Warne, D.P., Warne, P.G.: Existence and Uniqueness of azimuthal shear solutions in compressible isotropic nonlinear elasticity. Math. Mech. Solids 3, 53–69 (1998)
Carroll, M.M.: Irrotational finite elastic deformations. J. Appl. Mech. Trans. ASME, in press (2007)
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Carroll, M.M. Azimuthal Shear in Compressible Finite Elasticity. J Elasticity 88, 141–149 (2007). https://doi.org/10.1007/s10659-007-9123-3
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DOI: https://doi.org/10.1007/s10659-007-9123-3