Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Finite strain solutions for a compressible elastic solid

Authors: M. M. Carroll and C. O. Horgan
Journal: Quart. Appl. Math. 48 (1990), 767-780
MSC: Primary 73G05
DOI: https://doi.org/10.1090/qam/1079919
MathSciNet review: MR1079919
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Several closed form finite strain equilibrium solutions are presented for a special compressible isotropic elastic material which was proposed as a model for foam rubber by Blatz and Ko. These solutions include bending of a cylindrical sector into another sector or a rectangular block, bending of a block into a sector, expansion, compaction or eversion of cylinders or spheres, and torsion and extension of circular cylinders or tubes.

References [Enhancements On Off] (What's this?)

  • [1] J. L. Ericksen, Deformations possible in every isotropic, incompressible, perfectly elastic body, Z. Angew. Math. Phys. 5, 466-489 (1954) MR 0066873
  • [2] J. L. Ericksen, Deformations possible in every compressible, isotropic, perfectly elastic material, J. Math. and Phys. 34, 126-128 (1955) MR 0070397
  • [3] M. Singh and A. C. Pipkin, Note on Ericksen's problem, Z. Angew. Math. Phys. 16, 706-709 (1965)
  • [4] P. K. Currie and M. Hayes, On non-universal finite elastic deformations, Finite Elasticity, Proceedings of IUTAM Symposium (D. E. Carlson and R. T. Shield, eds.), Martinus Nijhoff, The Hague, 1982, pp. 143-150 MR 676658
  • [5] F. John, Plane strain problems for a perfectly elastic material of harmonic type, Comm. Pure Appl. Math. 13, 239-296 (1960) MR 0118022
  • [6] R. W. Ogden and D. A. Isherwood, Solution of some finite plane-strain problems for compressible elastic solids, Quart. J. Mech. Appl. Math. 31, 219-249 (1978) MR 0489206
  • [7] E. Varley and E. Cumberbatch, Finite deformations of elastic materials surrounding cylindrical holes, J. Elasticity 10, 341-405 (1980)
  • [8] C. H. Wu, Plane-strain buckling of a crack in a harmonic solid subjected to crack-parallel compression, J. Appl. Mech. 46, 597-604 (1979)
  • [9] A. H. Jafari, R. Abeyaratne, and C. O. Horgan, The finite deformation of a pressurized circular tube for a class of compressible materials, Z. Angew. Math. Phys. 35, 227-246 (1984) MR 756407
  • [10] R. W. Ogden, Non-linear Elastic Deformations, Ellis Horwood, Chichester, 1984
  • [11] R. Abeyaratne and C. O. Horgan, The pressurized hollow sphere problem in finite elastostatics for a class of compressible materials, Int. J. Solids Struct. 20, 715-723 (1984) MR 768646
  • [12] L. T. Wheeler, Finite deformation of a harmonic elastic medium containing an ellipsoidal cavity, Internat. J. Solids Struct. 21, 799-804 (1985)
  • [13] D. T. Chung, C. O. Horgan, and R. Abeyaratne, The finite deformation of internally pressurized hollow cylinders and spheres for a class of compressible elastic materials, Internat. J. Solids Struct. 22, 1557-1570 (1986)
  • [14] P. J. Blatz and W. L. Ko, Application of finite elasticity to the deformation of rubbery materials, Trans. Soc. Rheol. 6, 223-251 (1962)
  • [15] M. F. Beatty, Topics in finite elasticity: hyperelasticity of rubber, elastomers, and biological tissues-- with examples, Appl. Mech. Reviews 40, 1699-1734 (1987)
  • [16] M. M. Carroll, Finite strain solutions in compressible isotropic elasticity, J. Elasticity 20, 65-92 (1988) MR 962367
  • [17] D. M. Haughton, Inflation of thick-walled compressible elastic spherical shells, IMA J. Appl. Math. 39, 259-272 (1987) MR 983745
  • [18] C. O. Horgan, Some remarks on axisymmetric solutions in finite elastostatics for compressible materials, Proc. Roy. Irish Acad. Sect. A 89, 185-193 (1989) MR 1051392
  • [19] J. K. Knowles and E. Sternberg, On the ellipticity of the equations of nonlinear elastostatics for a special material, J. Elasticity 5, 341-361 (1975) MR 0475115

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 73G05

Retrieve articles in all journals with MSC: 73G05

Additional Information

DOI: https://doi.org/10.1090/qam/1079919
Article copyright: © Copyright 1990 American Mathematical Society

American Mathematical Society