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
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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.
- Jerald Laverne Ericksen, Deformations possible in every isotropic, incompressible, perfectly elastic body, Z. Angew. Math. Phys. 5 (1954), 466–489. MR 66873, DOI https://doi.org/10.1007/BF01601214
- J. L. Ericksen, Deformations possible in every compressible, isotropic, perfectly elastic material, J. Math. and Phys. 34 (1955), 126–128. MR 70397, DOI https://doi.org/10.1002/sapm1955341126
M. Singh and A. C. Pipkin, Note on Ericksen’s problem, Z. Angew. Math. Phys. 16, 706–709 (1965)
- David Emil Carlson and R. T. Shield (eds.), Proceedings of the IUTAM Symposium on Finite Elasticity, Martinus Nijhoff Publishers, The Hague, 1982. Held at Lehigh University, Bethlehem, Pa., August 10–15, 1980. MR 676658
- Fritz John, Plane strain problems for a perfectly elastic material of harmonic type, Comm. Pure Appl. Math. 13 (1960), 239–296. MR 118022, DOI https://doi.org/10.1002/cpa.3160130206
- R. W. Ogden and D. A. Isherwood, Solution of some finite plane-strain problems for compressible elastic solids, Quart. J. Mech. Appl. Math. 31 (1978), no. 2, 219–249. MR 489206, DOI https://doi.org/10.1093/qjmam/31.2.219
E. Varley and E. Cumberbatch, Finite deformations of elastic materials surrounding cylindrical holes, J. Elasticity 10, 341–405 (1980)
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)
- 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 (1984), no. 2, 227–246 (English, with German summary). MR 756407, DOI https://doi.org/10.1007/BF00947935
R. W. Ogden, Non-linear Elastic Deformations, Ellis Horwood, Chichester, 1984
- R. Abeyaratne and C. O. Horgan, The pressurized hollow sphere problem in finite elastostatics for a class of compressible materials, Internat. J. Solids Structures 20 (1984), no. 8, 715–723. MR 768646, DOI https://doi.org/10.1016/0020-7683%2884%2990060-X
L. T. Wheeler, Finite deformation of a harmonic elastic medium containing an ellipsoidal cavity, Internat. J. Solids Struct. 21, 799–804 (1985)
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)
P. J. Blatz and W. L. Ko, Application of finite elasticity to the deformation of rubbery materials, Trans. Soc. Rheol. 6, 223–251 (1962)
M. F. Beatty, Topics in finite elasticity: hyperelasticity of rubber, elastomers, and biological tissues— with examples, Appl. Mech. Reviews 40, 1699–1734 (1987)
- M. M. Carroll, Finite strain solutions in compressible isotropic elasticity, J. Elasticity 20 (1988), no. 1, 65–92. MR 962367, DOI https://doi.org/10.1007/BF00042141
- D. M. Haughton, Inflation and bifurcation of thick-walled compressible elastic spherical shells, IMA J. Appl. Math. 39 (1987), no. 3, 259–272. MR 983745, DOI https://doi.org/10.1093/imamat/39.3.259
- Cornelius O. Horgan, Some remarks on axisymmetric solutions in finite elastostatics for compressible materials, Proc. Roy. Irish Acad. Sect. A 89 (1989), no. 2, 185–193. MR 1051392
- J. K. Knowles and Eli Sternberg, On the ellipticity of the equations of nonlinear elastostatics for a special material, J. Elasticity 5 (1975), no. 3-4, 341–361. Special issue dedicated to A. E. Green. MR 475115, DOI https://doi.org/10.1007/BF00126996
J. L. Ericksen, Deformations possible in every isotropic, incompressible, perfectly elastic body, Z. Angew. Math. Phys. 5, 466–489 (1954)
J. L. Ericksen, Deformations possible in every compressible, isotropic, perfectly elastic material, J. Math. and Phys. 34, 126–128 (1955)
M. Singh and A. C. Pipkin, Note on Ericksen’s problem, Z. Angew. Math. Phys. 16, 706–709 (1965)
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
F. John, Plane strain problems for a perfectly elastic material of harmonic type, Comm. Pure Appl. Math. 13, 239–296 (1960)
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)
E. Varley and E. Cumberbatch, Finite deformations of elastic materials surrounding cylindrical holes, J. Elasticity 10, 341–405 (1980)
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)
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)
R. W. Ogden, Non-linear Elastic Deformations, Ellis Horwood, Chichester, 1984
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)
L. T. Wheeler, Finite deformation of a harmonic elastic medium containing an ellipsoidal cavity, Internat. J. Solids Struct. 21, 799–804 (1985)
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)
P. J. Blatz and W. L. Ko, Application of finite elasticity to the deformation of rubbery materials, Trans. Soc. Rheol. 6, 223–251 (1962)
M. F. Beatty, Topics in finite elasticity: hyperelasticity of rubber, elastomers, and biological tissues— with examples, Appl. Mech. Reviews 40, 1699–1734 (1987)
M. M. Carroll, Finite strain solutions in compressible isotropic elasticity, J. Elasticity 20, 65–92 (1988)
D. M. Haughton, Inflation of thick-walled compressible elastic spherical shells, IMA J. Appl. Math. 39, 259–272 (1987)
C. O. Horgan, Some remarks on axisymmetric solutions in finite elastostatics for compressible materials, Proc. Roy. Irish Acad. Sect. A 89, 185–193 (1989)
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)
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© Copyright 1990
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