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Volumn 37, Issue 1-3, 2000, Pages 171-190

An extension of Key's principle to nonlinear elasticity

Author keywords

Finite deformations; Finite elements; Near incompressibility; Nonlinear elasticity; Variational formulation

Indexed keywords

ANISOTROPY; CONVERGENCE OF NUMERICAL METHODS; DEFORMATION; FINITE ELEMENT METHOD; FUNCTIONS; STRESSES;

EID: 0034144440     PISSN: 00220833     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1004734311626     Document Type: Article
Times cited : (16)

References (36)
  • 1
    • 0042021207 scopus 로고
    • Influence of Poisson's ratio on the condition of the finite elements stiffness matrix
    • I. Fried, Influence of Poisson's ratio on the condition of the finite elements stiffness matrix. Int. J. Sol. Struct. 9 (1973) 323-329.
    • (1973) Int. J. Sol. Struct. , vol.9 , pp. 323-329
    • Fried, I.1
  • 4
    • 0016105327 scopus 로고
    • Finite element analysis of incompressible material by residual energy balancing
    • I. Fried, Finite element analysis of incompressible material by residual energy balancing. Int. J. Sol. Struct. 10 (1974) 993-1002.
    • (1974) Int. J. Sol. Struct. , vol.10 , pp. 993-1002
    • Fried, I.1
  • 5
    • 0017921641 scopus 로고
    • Finite element analysis of rubber-like materials by a mixed model
    • T. Scharnorst and T. H. H. Pian, Finite element analysis of rubber-like materials by a mixed model. Int. J. Num. Meth. Engng. 12 (1978) 655-676.
    • (1978) Int. J. Num. Meth. Engng. , vol.12 , pp. 655-676
    • Scharnorst, T.1    Pian, T.H.H.2
  • 6
    • 0017984529 scopus 로고
    • Mixed finite element methods - Reduced and selective integration techniques: A unification of concepts
    • D. S. Malkus and T. J. R. Hughes, Mixed finite element methods - Reduced and selective integration techniques: A unification of concepts. Comp. Meth. Appl. Mech. Engng. 15 (1978) 63-81.
    • (1978) Comp. Meth. Appl. Mech. Engng. , vol.15 , pp. 63-81
    • Malkus, D.S.1    Hughes, T.J.R.2
  • 7
    • 0018296657 scopus 로고
    • A finite element approach for large strains of nearly incompressible rubber-like materials
    • S. Cescotto and G. Fonder, A finite element approach for large strains of nearly incompressible rubber-like materials. Int. J. Sol. Struct. 15 (1979) 589-605.
    • (1979) Int. J. Sol. Struct. , vol.15 , pp. 589-605
    • Cescotto, S.1    Fonder, G.2
  • 8
    • 0013318338 scopus 로고
    • A constrained element-by-element method for slightly compressible and incompressible materials and its parallel implementation on transputers
    • B. H. V. Topping and M. Papadrakakis (eds). Edinburgh: Civil-Comp. Press
    • M. H. B. M. Shariff, A constrained element-by-element method for slightly compressible and incompressible materials and its parallel implementation on transputers. In: B. H. V. Topping and M. Papadrakakis (eds), Advances in Parallel and Vector Processing for Structural Mechanics. Edinburgh: Civil-Comp. Press (1994) pp. 53-57.
    • (1994) Advances in Parallel and Vector Processing for Structural Mechanics , pp. 53-57
    • Shariff, M.H.B.M.1
  • 9
    • 0042522138 scopus 로고
    • On a finite element procedure for non-linear incompressible elasticity
    • S. N. Atluri, R. H. Gallagher and O. C. Zienkiewicz (eds). New York: Wiley-Interscience
    • M. Bercovier, Y. Hasbani, Y. Gilon and K. J. Bathe, On a finite element procedure for non-linear incompressible elasticity. In: S. N. Atluri, R. H. Gallagher and O. C. Zienkiewicz (eds), Hybrid and Mixed Element Methods. New York: Wiley-Interscience (1983) pp. 497-518.
    • (1983) Hybrid and Mixed Element Methods , pp. 497-518
    • Bercovier, M.1    Hasbani, Y.2    Gilon, Y.3    Bathe, K.J.4
  • 10
    • 0031072180 scopus 로고    scopus 로고
    • An extension of Herrmann's principle to nonlinear elasticity
    • M. H. B. M. Shariff, An extension of Herrmann's principle to nonlinear elasticity. Appl. Math. Mod. 21 (1997) 97-107.
    • (1997) Appl. Math. Mod. , vol.21 , pp. 97-107
    • Shariff, M.H.B.M.1
  • 11
    • 0028445932 scopus 로고
    • Aspects of the formulation and finite element implementation of large strain isotropic elasticity
    • C. Miehe, Aspects of the formulation and finite element implementation of large strain isotropic elasticity. Int. J. Numer. Methods Eng. 37 (1994) 1981-2004.
    • (1994) Int. J. Numer. Methods Eng. , vol.37 , pp. 1981-2004
    • Miehe, C.1
  • 12
    • 0028439271 scopus 로고
    • Incompressibility and axisymmetry: A modified mixed and penalty formulation
    • A. G. K. Jinka and R. L. Lewis, Incompressibility and axisymmetry: A modified mixed and penalty formulation. Int. J. Num. Meth. Engng. 37 (1994) 1623-1649.
    • (1994) Int. J. Num. Meth. Engng. , vol.37 , pp. 1623-1649
    • Jinka, A.G.K.1    Lewis, R.L.2
  • 13
    • 0026943103 scopus 로고
    • The use of orthogonal projections to handle constraints with applications to incompressible four-node quadrilateral elements
    • U. Hueck and H. L. Schreyer, The use of orthogonal projections to handle constraints with applications to incompressible four-node quadrilateral elements. Int. J. Num. Meth. Engng. 35 (1992) 1633-1661.
    • (1992) Int. J. Num. Meth. Engng. , vol.35 , pp. 1633-1661
    • Hueck, U.1    Schreyer, H.L.2
  • 14
    • 0026859383 scopus 로고
    • Linear finite-element equations for nonlinear deformation of slightly compressible elastic material
    • M. H. B. M. Shariff, Linear finite-element equations for nonlinear deformation of slightly compressible elastic material. Q. J. Mech. Appl. Math. 45 (1992) 169-181.
    • (1992) Q. J. Mech. Appl. Math. , vol.45 , pp. 169-181
    • Shariff, M.H.B.M.1
  • 15
    • 0010937792 scopus 로고
    • Finite deformation of an almost incompressible elastic solid
    • M. Reiner and D. Abir (eds). Oxford: Pergamon Press
    • A. J. M. Spencer, Finite deformation of an almost incompressible elastic solid. In: M. Reiner and D. Abir (eds), Second-order Effects in Elasticity, Plasticity and Fluid Dynamics. Oxford: Pergamon Press (1964) pp. 200-216.
    • (1964) Second-order Effects in Elasticity, Plasticity and Fluid Dynamics , pp. 200-216
    • Spencer, A.J.M.1
  • 16
    • 0041520301 scopus 로고    scopus 로고
    • BEM formulation for (3D) elastic incompressible solids
    • B. H. V. Topping (ed.). Edinburgh: Civil-Comp. Press
    • S. V. Tsinopoulos, D. Polyzos and D. E. Beskos, BEM formulation for (3D) elastic incompressible solids. In: B. H. V. Topping (ed.), Advances in Boundary Element Methods. Edinburgh: Civil-Comp. Press (1996) pp. 1-8.
    • (1996) Advances in Boundary Element Methods , pp. 1-8
    • Tsinopoulos, S.V.1    Polyzos, D.2    Beskos, D.E.3
  • 17
    • 0020831936 scopus 로고
    • A boundary integral equation of compression moduli of bonded rubber blocks
    • R. T. Fenner and R. M. Remzi, A boundary integral equation of compression moduli of bonded rubber blocks. J. Strain Anal. 18 (1983) 217-223.
    • (1983) J. Strain Anal. , vol.18 , pp. 217-223
    • Fenner, R.T.1    Remzi, R.M.2
  • 18
    • 0037677029 scopus 로고
    • BEM for finite-elasticity
    • N. Phan-Tien, BEM for finite-elasticity. Comp. Mech. 6 (1990) 205-219.
    • (1990) Comp. Mech. , vol.6 , pp. 205-219
    • Phan-Tien, N.1
  • 19
    • 0001619671 scopus 로고
    • Locking effects in the finite element approximation of elasticity problems
    • I. Babuska and M. Suri, Locking effects in the finite element approximation of elasticity problems. Num. Math. 62 (1992) 439-463.
    • (1992) Num. Math. , vol.62 , pp. 439-463
    • Babuska, I.1    Suri, M.2
  • 20
    • 0343892144 scopus 로고
    • University of Coventry, UK
    • PERFINE - The Manual, eds Barrett et al. University of Coventry, UK (1989).
    • (1989) ERFINE - the Manual
    • Barrett1
  • 21
    • 0013226853 scopus 로고    scopus 로고
    • A modified augmented Lagrangian method for nearly incompressible problems
    • B. H. V. Topping (ed.). Edinburgh: Civil-Comp. Press
    • M. H. B. M. Shariff, A modified augmented Lagrangian method for nearly incompressible problems, In: B. H. V. Topping (ed.), Developments in Computational Mechanics with High Performance Computing. Edinburgh: Civil-Comp. Press (1999) pp. 101-106.
    • (1999) Developments in Computational Mechanics with High Performance Computing , pp. 101-106
    • Shariff, M.H.B.M.1
  • 23
    • 0014570273 scopus 로고
    • A variational principle for incompressible and nearly incompressible anisotropic elasticity
    • S. W. Key, A variational principle for incompressible and nearly incompressible anisotropic elasticity.Int. J. Sol. Struct. 5 (1969) 951-964.
    • (1969) Int. J. Sol. Struct. , vol.5 , pp. 951-964
    • Key, S.W.1
  • 24
    • 0342586513 scopus 로고
    • Finite-amplitude oscillations of a spherical cavity in a nearly-incompressible elastic material
    • D. F. Parker, Finite-amplitude oscillations of a spherical cavity in a nearly-incompressible elastic material. Arch. of Mech. 30 (1978) 777-790.
    • (1978) Arch. of Mech. , vol.30 , pp. 777-790
    • Parker, D.F.1
  • 25
    • 0022889471 scopus 로고
    • The slowness surfaces of incompressible and nearly incompressible elastic materials
    • N. H. Scott, The slowness surfaces of incompressible and nearly incompressible elastic materials. J. Elasticity 16 (1986) 239-250.
    • (1986) J. Elasticity , vol.16 , pp. 239-250
    • Scott, N.H.1
  • 26
    • 0028397394 scopus 로고
    • Superconvergent boundary stress extraction and some experiments with adaptive pointwise error control
    • Q. Niu and M. Shepard, Superconvergent boundary stress extraction and some experiments with adaptive pointwise error control. Int. J. Num. Meth. Engng. 37 (1994) 877-891.
    • (1994) Int. J. Num. Meth. Engng. , vol.37 , pp. 877-891
    • Niu, Q.1    Shepard, M.2
  • 27
    • 84986937902 scopus 로고
    • A reformulation of the elastic field equations, in terms of displacements, valid for all admissible values of Poisson's ratio
    • L. R. Herrmann and R. M. Toms, A reformulation of the elastic field equations, in terms of displacements, valid for all admissible values of Poisson's ratio. J. Appl. Mech. 31 (1964) 148-149.
    • (1964) J. Appl. Mech. , vol.31 , pp. 148-149
    • Herrmann, L.R.1    Toms, R.M.2
  • 28
    • 84991028773 scopus 로고
    • Elasticity equations for incompressible and nearly incompressible materials by a variational theorem
    • L. R. Herrmann, Elasticity equations for incompressible and nearly incompressible materials by a variational theorem, AIAA J. 3 (1965) 1896-1900.
    • (1965) AIAA J. , vol.3 , pp. 1896-1900
    • Herrmann, L.R.1
  • 29
    • 0342586512 scopus 로고
    • Finite elastic deformation of a plane strain wedge-shaped radial crack in a compressible cylinder
    • M. Reiner and D. Abir (eds). Oxford: Pergamon Press
    • P. J. Blatz, Finite elastic deformation of a plane strain wedge-shaped radial crack in a compressible cylinder. In: M. Reiner and D. Abir (eds), Second-order Effects in Elasticity, Plasticity and Fluid Dynamics. Oxford: Pergamon Press (1964) pp. 145-161.
    • (1964) Second-order Effects in Elasticity, Plasticity and Fluid Dynamics , pp. 145-161
    • Blatz, P.J.1
  • 32
    • 0040900896 scopus 로고
    • Parallel finite element software for nonlinear stress problems
    • M. Valero et al. (eds). Amsterdam: IOS Press
    • M. H. B. M. Shariff, Parallel finite element software for nonlinear stress problems. In: M. Valero et al. (eds), Parallel Computing and Transputer Applications. Amsterdam: IOS Press (1992) pp. 1261-1270.
    • (1992) Parallel Computing and Transputer Applications , pp. 1261-1270
    • Shariff, M.H.B.M.1
  • 33
    • 0027642114 scopus 로고
    • A general approach to axial deformation of bonded elastic mounts of various cross-sectional shapes
    • M. H. B. M. Shariff, A general approach to axial deformation of bonded elastic mounts of various cross-sectional shapes. Appl. Math. Mod. 17 (1993) 430-436.
    • (1993) Appl. Math. Mod. , vol.17 , pp. 430-436
    • Shariff, M.H.B.M.1
  • 34
  • 35
    • 0001567544 scopus 로고
    • Volume changes associated with the deformation of rubber-like solids
    • R. W. Ogden, Volume changes associated with the deformation of rubber-like solids. J. Mech. Phys. Solids 24 (1976) 323-338.
    • (1976) J. Mech. Phys. Solids , vol.24 , pp. 323-338
    • Ogden, R.W.1
  • 36
    • 0019262099 scopus 로고
    • A fast incremental/iteration solution procedure that handles 'snap-through'
    • M. A. Crisfield, A fast incremental/iteration solution procedure that handles 'snap-through'. Comp. and Struc. 13 (1981) 55-62.
    • (1981) Comp. and Struc. , vol.13 , pp. 55-62
    • Crisfield, M.A.1


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