A general expression for linearized properties of swollen elastomers undergoing large deformations

Dai Okumura, Hironori Kawabata, Shawn A. Chester

Research output: Contribution to journalArticle

Abstract

In this study, we develop a general expression for the linearized properties of swollen elastomers undergoing large deformations. The free energy function of swollen elastomers is assumed to obey the Frenkel–Flory–Rehner hypothesis, i.e., the elastic and mixing contributions are additive. The elastic strain energy is not assumed to have a particular form but is assumed only to be a function of a set of strain-invariants. A linearization procedure is used to obtain the general expression for the Young's modulus and Poisson's ratio under an arbitrary base state. The derived expression includes a characteristic term, which has the ability to describe a transient state between the extreme states prescribed by two distinct conditions. The verification is performed by estimating the shear modulus and considering the original Flory–Rehner framework. In addition, to show the usefulness, an extended Gent model is examined to elucidate the interactions between limiting chain extensibility and the second strain-invariant.

Original languageEnglish (US)
Article number103805
JournalJournal of the Mechanics and Physics of Solids
Volume135
DOIs
StatePublished - Feb 2020

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elastomers
Elastomers
Elastic moduli
Poisson ratio
Strain energy
Linearization
Free energy
linearization
modulus of elasticity
estimating
free energy
shear
interactions
energy

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

Keywords

  • Constitutive behavior
  • Finite strain
  • Hyperelasticity
  • Solvent migration
  • Swelling

Cite this

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title = "A general expression for linearized properties of swollen elastomers undergoing large deformations",
abstract = "In this study, we develop a general expression for the linearized properties of swollen elastomers undergoing large deformations. The free energy function of swollen elastomers is assumed to obey the Frenkel–Flory–Rehner hypothesis, i.e., the elastic and mixing contributions are additive. The elastic strain energy is not assumed to have a particular form but is assumed only to be a function of a set of strain-invariants. A linearization procedure is used to obtain the general expression for the Young's modulus and Poisson's ratio under an arbitrary base state. The derived expression includes a characteristic term, which has the ability to describe a transient state between the extreme states prescribed by two distinct conditions. The verification is performed by estimating the shear modulus and considering the original Flory–Rehner framework. In addition, to show the usefulness, an extended Gent model is examined to elucidate the interactions between limiting chain extensibility and the second strain-invariant.",
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author = "Dai Okumura and Hironori Kawabata and Chester, {Shawn A.}",
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A general expression for linearized properties of swollen elastomers undergoing large deformations. / Okumura, Dai; Kawabata, Hironori; Chester, Shawn A.

In: Journal of the Mechanics and Physics of Solids, Vol. 135, 103805, 02.2020.

Research output: Contribution to journalArticle

TY - JOUR

T1 - A general expression for linearized properties of swollen elastomers undergoing large deformations

AU - Okumura, Dai

AU - Kawabata, Hironori

AU - Chester, Shawn A.

PY - 2020/2

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N2 - In this study, we develop a general expression for the linearized properties of swollen elastomers undergoing large deformations. The free energy function of swollen elastomers is assumed to obey the Frenkel–Flory–Rehner hypothesis, i.e., the elastic and mixing contributions are additive. The elastic strain energy is not assumed to have a particular form but is assumed only to be a function of a set of strain-invariants. A linearization procedure is used to obtain the general expression for the Young's modulus and Poisson's ratio under an arbitrary base state. The derived expression includes a characteristic term, which has the ability to describe a transient state between the extreme states prescribed by two distinct conditions. The verification is performed by estimating the shear modulus and considering the original Flory–Rehner framework. In addition, to show the usefulness, an extended Gent model is examined to elucidate the interactions between limiting chain extensibility and the second strain-invariant.

AB - In this study, we develop a general expression for the linearized properties of swollen elastomers undergoing large deformations. The free energy function of swollen elastomers is assumed to obey the Frenkel–Flory–Rehner hypothesis, i.e., the elastic and mixing contributions are additive. The elastic strain energy is not assumed to have a particular form but is assumed only to be a function of a set of strain-invariants. A linearization procedure is used to obtain the general expression for the Young's modulus and Poisson's ratio under an arbitrary base state. The derived expression includes a characteristic term, which has the ability to describe a transient state between the extreme states prescribed by two distinct conditions. The verification is performed by estimating the shear modulus and considering the original Flory–Rehner framework. In addition, to show the usefulness, an extended Gent model is examined to elucidate the interactions between limiting chain extensibility and the second strain-invariant.

KW - Constitutive behavior

KW - Finite strain

KW - Hyperelasticity

KW - Solvent migration

KW - Swelling

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