Ogden Hyperelastic Model
Ogden Hyperelastic: Theoretical Foundations
What is the Ogden Model?
Professor, what kind of hyperelastic model is the Ogden model?
The Ogden Model (1972) directly describes the strain energy using principal stretch ratios ($\lambda_1, \lambda_2, \lambda_3$):
$N = 1 \sim 3$ term sum. $\mu_i, \alpha_i$ are material constants.
More parameters than Mooney-Rivlin?
$N = 3$ gives 6 parameters. More accurate at large strains (200%+) than Mooney-Rivlin's 2 parameters. Especially capable of simultaneous fitting for both tension and compression.
Summary
The Birth of the Ogden Model
This model, published by Ray Ogden in 1972, expresses strain energy with a polynomial of arbitrary order. It was said to reproduce synthetic rubber within 5% error for 2nd order and natural rubber within 1% for 3rd order. After its publication in the Journal of Mechanics that same year, its adoption spread rapidly in the tire design field.
Computational Methods for Ogden Hyperelastic
FEM Settings for Ogden
```
*HYPERELASTIC, OGDEN, N=3
mu1, alpha1, D1
mu2, alpha2, D2
mu3, alpha3, D3
```
Or:
```
*HYPERELASTIC, OGDEN, TEST DATA INPUT
*UNIAXIAL TEST DATA
stress, strain
*BIAXIAL TEST DATA
stress, strain
```
Automatic fitting is recommended.
Summary
Parameter Identification Sequence
The standard procedure for Ogden model parameter identification is uniaxial → equibiaxial → pure shear in that order. Treloar's 1944 experimental data for natural rubber is still used as a benchmark today. The standard procedure is to simultaneously identify all 6 parameters (μ₁~μ₃ and α₁~α₃) using least squares for a 3rd-order Ogden model.
Ogden Hyperelastic in Practice
Ogden in Practice
Used for tires, O-rings, large-deformation rubber components. For large strain problems where Mooney-Rivlin is insufficient.
Practical Checklist
Input Order in Abaqus
When defining the Ogden model in Abaqus/CAE, declare the order N first, then input μᵢ, αᵢ, Dᵢ in sequence. For N=3, there will be 3 parameter lines. In practice, setting Dᵢ≈0 (incompressibility assumption) can reproduce behavior equivalent to Poisson's ratio 0.4995 while reducing computational cost by about 15%.
Ogden Hyperelastic: Software & Solver Comparison
Tools for Ogden
Selection Guide
Supported Order by Solver
The supported order of the Ogden model varies by solver. Abaqus·LS-DYNA support up to N=6, MSC Marc supports theoretically unlimited (practical N=9), Nastran supports up to N=3 in SOL 400. NX Nastran provides cards OGDEN1~OGDEN3, using separate cards for each order.
Advanced Technology
Advanced Ogden
Related Topics
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