On the Development of Volumetric Strain Energy Functions

[+] Author and Article Information
S. Doll, K. Schweizerhof

Institute for Mechanics, University of Karlsruhe, 76128 Karlsruhe, Germanye-mail: mechanik@bau-verm.uni-karlsruhe.de

J. Appl. Mech 67(1), 17-21 (Oct 12, 1999) (5 pages) doi:10.1115/1.321146 History: Received July 27, 1997; Revised October 12, 1999
Copyright © 2000 by ASME
Topics: Functions , Stress
Your Session has timed out. Please sign back in to continue.


Ogden, R. W., 1984, Non-Linear Elastic Deformations, Ellis Horwood, Chichester, UK.
Flory,  P. J., 1961, “Thermodynamic Relations for High Elastic Materials,” Trans. Faraday Soc., 57, pp. 829–838.
Penn,  R. W., 1970, “Volume Changes Accompanying the Extension of Rubber,” Trans. Soc. Rheol., 14, No. 4, pp. 509–517.
van den Bogert,  P. A. J., de Borst,  R., Luiten,  G. T., and Zeilmaker,  J., 1991, “Robust Finite Elements for 3D—Analysis of Rubber-Like Materials,” Eng. Comput., 8, pp. 3–17.
Ogden, R. W., 1982, “Elastic Deformations of Rubberlike Solids,” Mechanics of Solids, The Rodney Hill 60th Anniversary Volume H. G. Hopkins and M. J. Sewell eds., Pergamon Press, Tarrytown, NY, pp. 499–537.
Ciarlet, P. G., 1988, Mathematical Elasticity. Volume 1: Three Dimensional Elasticity, Elsevier, Amsterdam.
Liu,  C. H., and Mang,  H. A., 1996, “A Critical Assessment of Volumetric Strain Energy Functions for Hyperelasticity at Large Strains,” Z. Angew. Math. Mech., 76, No. S5, pp. 305–306.
Sussman,  T., and Bathe,  K. J., 1987, “A Finite Element Formulation for Nonlinear Incompressible Elastic and Inelastic Analysis,” Comput. Struct., 26, No. 1–2, pp. 357–409.
Simo,  J. C., 1988, “A Framework for Finite Strain Elastoplasticity Based on Maximum Plastic Dissipation and the Multiplicative Decomposition: Part I. Continuum Formulation,” Comput. Methods Appl. Mech. Eng., 66, pp. 199–219.
van den Bogert, P. A. J., and de Borst, R., 1990, “Constitutive Aspects and Finite Element Analysis of 3D Rubber Specimens in Compression and Shear,” NUMETA 90: Numerical Methods in Engineering: Theory and Applications, G. N. Pande and J. Middleton, eds., Elsevier Applied Science, Swansea, pp. 870–877.
Chang,  T. Y., Saleeb,  A. F., and Li,  G., 1991, “Large Strain Analysis of Rubber-Like Materials Based on a Perturbed Lagrangian Variational Principle,” Comput. Mech., 8, pp. 221–233.
Hencky,  H., 1933, “The Elastic Behavior of Vulcanized Rubber,” ASME J. Appl. Mech., 1, pp. 45–53.
Valanis,  K. C., and Landel,  R. F., 1967, “The Strain-Energy Function of a Hyperplastic Material in Terms of the Extension Ratios,” J. Appl. Phys., 38, No. 7, pp. 2997–3002.
Simo,  J. C., Taylor,  R. L., and Pfister,  K. S., 1985, “Variational and Projection Methods for Volume Constraint in Finite Deformation Elasto-Plasticity,” Comput. Methods Appl. Mech. Eng., 51, pp. 177–208.
Simo,  J. C., 1992, “Algorithms for Static and Dynamic Multiplicative Plasticity That Preserve the Classical Return Mapping Schemes of the Infinitesimal Theory,” Comput. Methods Appl. Mech. Eng., 99, pp. 61–112.
Roehl,  D., and Ramm,  E., 1996, “Large Elasto-Plastic Finite Element Analysis of Solids and Shells With the Enhanced Assumed Strain Concept,” Int. J. Solids Struct., 33, No. 20–22, pp. 3215–3237.
Simo,  J. C., and Taylor,  R. L., 1982, “Penalty Function Formulations for Incompressible Nonlinear Elastostatics,” Comput. Methods Appl. Mech. Eng., 35, pp. 107–118.
Ogden,  R. W., 1972, “Large Deformation Isotropic Elasticity: on the Correlation of Theory and Experiment for Compressible Rubberlike Solids,” Proc. R. Soc. London, Ser. A, 328, pp. 567–583.
Simo,  J. C., and Taylor,  R. L., 1991, “Quasi-Incompressible Finite Elasticity in Principal Stretches. Continuum Basis and Numerical Algorithms,” Comput. Methods Appl. Mech. Eng., 85, pp. 273–310.
Miehe,  C., 1994, “Aspects of the Formulation and Finite Element Implementation of Large Strain Isotropic Elasticity,” Int. J. Numer. Methods Eng., 37, pp. 1981–2004.
Kaliske,  M., and Rothert,  H., 1997, “On the Finite Element Implementation of Rubber-Like Materials at Finite Strains,” Eng. Comput., 14, pp. 216–232.
Liu, C. H., Hofstetter, G., Mang, H. A., 1992, “Evaluation of 3D FE-Formulations for Incompressible Hyperplastic Materials at Finite Strains,” Proceedings of the First European Conference on Numerical Methods in Engineering C. Hirsch, O. C. Zienkiewicz, and E. Oñate, eds., Sept. 7–11, Brussels, Belgium, Elsevier Science, Ltd., pp. 757–764.
Liu,  C. H., Hofstetter,  G., and Mang,  H. A., 1994, “3D Finite Element Analysis of Rubber-Like Materials at Finite Strains,” Eng. Comput., 11, pp. 111–128.
Murnaghan, F. D., 1951, Finite Deformation of an Elastic Solid, John Wiley and Sons, New York.


Grahic Jump Location
Curves of the first derivative ∂JU(J)/K
Grahic Jump Location
Curves of the second derivative ∂JJ2U(J)/K
Grahic Jump Location
Fitted curves of the first derivative ∂JU(J)/K
Grahic Jump Location
Fitted curves of the first derivative ∂JU(J)/K



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In