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Variations on Ogden's model: close and distant relatives.

A E Ehret1,2, A Stracuzzi1,2

  • 1Empa, Swiss Federal Laboratories for Materials Science and Technology, Überlandstrasse 129, 8600 Dübendorf, Switzerland.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|August 29, 2022
PubMed
Summary
This summary is machine-generated.

Ogden's strain-energy function in rubber mechanics, featuring power law and Valanis-Landel hypothesis, allows molecular interpretation. This framework enables variations, embedding Ogden's theory within a family of hyperelastic models.

Keywords:
Ogden’s modelhyperelastic materialsmolecular statistical theoryphenomenological modelsrubber elasticity

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Area of Science:

  • Nonlinear elasticity
  • Polymer mechanics
  • Materials science

Background:

  • Ogden's strain-energy density function is a cornerstone in rubber mechanics.
  • Key features include the power law, truncated series, and Valanis-Landel hypothesis.
  • These features have recently gained a molecular statistical interpretation.

Purpose of the Study:

  • To explore the molecular statistical interpretation of Ogden's model.
  • To demonstrate how individual components of Ogden's function can be modified.
  • To embed Ogden's theory within a broader family of isotropic hyperelastic materials.

Main Methods:

  • Analyzing the power law, truncated series representation, and Valanis-Landel hypothesis.
  • Associating each feature with steps in developing strain-energy density from polymer statistical mechanics.
  • Developing a schematic to individually vary these components.

Main Results:

  • A molecular statistical interpretation of Ogden's strain-energy function was established.
  • The framework allows for individual variation of model components.
  • Ogden's theory is shown to be a specific case within a larger family of hyperelastic models.

Conclusions:

  • Ogden's model can be generalized by modifying its core components.
  • This provides a pathway to explore a wider range of hyperelastic material behaviors.
  • The study deepens the understanding of Ogden's model and its relationship to polymer physics.