Ogden-type constitutive equations in finite elasticity of elastomers

A. D. Drozdov, M. Gottlieb

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


An explicit expression is derived for the strain energy of a chain under three-dimensional deformation with finite strains. For a Gaussian chain, this relation implies the Mooney-Rivlin constitutive law, while for non-Gaussian chains it results in novel constitutive equations. Based on a three-chain approximation, a formula is derived for the strain energy of a chain with excluded-volume interactions between segments. It is demonstrated that for self-avoiding chains with a stretched exponential distribution function of end-to-end vectors, the strain energy density of a network is described by the Ogden law with two material constants. For the des Cloizeaux distribution function, a constitutive equation is derived that involves three adjustable parameters. The governing equations are verified by fitting observations at uniaxial tension-compression and biaxial tension of elastomers. Good agreement is demonstrated between the experimental data and the results of numerical analysis.

Original languageEnglish
Pages (from-to)231-252
Number of pages22
JournalActa Mechanica
Issue number3-4
StatePublished - 1 Jun 2006

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanical Engineering


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