Consistent finite element procedures for nonlinear rubber elasticity with a higher order strain energy function

J. S. Chen, Kailasam Satyamurthy, L. R. Hirschfelt

Research output: Contribution to journalArticle

27 Citations (Scopus)

Abstract

The use of higher order terms in the Rivlin's polynomial strain energy density function is necessary to describe the elastic behavior of rubber undergoing very large and complex deformation. In this paper, the material response tensor for general Rivlin's strain energy density function is derived in a consistent manner such that both major and minor symmetries are retained. Lack of minor symmetry in the material response tensor will lead to numerical convergence difficulties, especially in shear dominant problems. The projection method is used to avoid volumetric locking due to the nearly incompressible nature of rubber. The relation between the numerical penalty number and the material bulk modulus is characterized. The importance of this relation is demonstrated in the study of the apparent Young's modulus of bonded rubber units. The need to include higher order terms in the strain energy density function is presented in the numerical examples. Several classical elasticity problems are also analyzed.

Original languageEnglish (US)
Pages (from-to)715-727
Number of pages13
JournalComputers and Structures
Volume50
Issue number6
DOIs
StatePublished - Mar 17 1994

Fingerprint

Strain Energy Density
Rubber
Strain Energy
Strain energy
Energy Function
Density Function
Probability density function
Elasticity
Higher Order
Finite Element
Tensors
Minor
Tensor
Elastic moduli
Volumetric Locking
Symmetry
Bulk Modulus
Elasticity Problem
Young's Modulus
Term

All Science Journal Classification (ASJC) codes

  • Civil and Structural Engineering
  • Modeling and Simulation
  • Materials Science(all)
  • Mechanical Engineering
  • Computer Science Applications

Cite this

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Consistent finite element procedures for nonlinear rubber elasticity with a higher order strain energy function. / Chen, J. S.; Satyamurthy, Kailasam; Hirschfelt, L. R.

In: Computers and Structures, Vol. 50, No. 6, 17.03.1994, p. 715-727.

Research output: Contribution to journalArticle

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