Modeling Hyperelastic Materials Nathan Hoffman

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Modeling Hyperelastic Materials Nathan Hoffman Review of Elastic Materials Strain Tensor Lamé Parameters Deformation Gradient Deformation Gradient Examples Greene Strain Tensor Saint Venant Kirchoff Model Figure from Fraldi et al. Volume

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Modeling Hyperelastic Materials Nathan Hoffman

Review of Elastic Materials

Strain Tensor

Lamé Parameters

Deformation Gradient

Deformation Gradient Examples

Greene Strain Tensor

Saint Venant – Kirchoff Model Figure from Fraldi et al.

Volume Change & Strain Energy Density Function

Neo-Hookean Model

Mooney-Rivlin Model

Polynomial or Generalized Rivlin Model

Ogden Model Ogden model fitted to data from pig skin, From Dwivedi et al.

Yeoh Model

Example of Using the energy density function in a model

What Model Should You Use? The Saint Venant – Kirchoff model is simple, computationally cheap, but not as accurate
Less work to fit
The Generalized Rivlin Model is generally more complex than necessary
Other models must be fitted to data. For modeling rubber different strain ranges are best fitted by different models:
Up to 100%: Neo-Hookean (simplest model)
150-200%: Mooney-Rivlin (not as simple)
0-Failure: Ogden (most complex)
specific range: Yeoh

Modeling Hyperelastic Materials Nathan Hoffman

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