Neo-Hookean Hyperelastic Model
Neo-Hookean Hyperelastic: Theoretical Foundations
Neo-Hookean Hyperelasticity
Professor, what kind of model is Neo-Hookean?
The simplest hyperelastic model. Strain energy:
Defined by a single parameter $C_{10}$ ($= G/2$, where $G$ is the shear modulus). A special case of Mooney-Rivlin with $C_{01} = 0$.
Just one parameter! It can be used when there's limited test data.
Neo-Hookean is reasonable up to moderate strains (around 50%). For large strains (over 100%), Mooney-Rivlin or Ogden models are needed.
Summary
The Naming of Neo-Hookean
The name Neo-Hookean (New Hookean) was given with the meaning of "modernizing (neo)" Hookean, i.e., Hooke's linear elastic law, for the nonlinear finite deformation regime. Ronald Rivlin established this term in his 1948 paper. The strain energy function W = C₁(I₁−3) is the simplest hyperelastic model with only one parameter, and because the stress-strain relationship can be solved analytically, it is still frequently used as a benchmark for verifying numerical algorithms.
Computational Methods for Neo-Hookean Hyperelastic
FEM Settings for Neo-Hookean
```
*HYPERELASTIC, NEO HOOKE
C10, D1
```
Nastran: MATHE, 1, MOONEY + $C_{01}=0$.
Summary
Small Strain Limit and Shear Modulus Relationship
The parameter C₁ of the Neo-Hookean model matches C₁ = μ/2 (μ: shear stiffness) in the small strain limit. That is, C₁ can be calculated from the elastic modulus E and Poisson's ratio ν without experiments (μ = E/2(1+ν)). This property justifies the practical approximation of directly using linear elastic material data to run Neo-Hookean analysis in the preliminary design stage of rubber components where detailed large deformation test data is unavailable.
Neo-Hookean Hyperelastic in Practice
Neo-Hookean in Practice
Used for conceptual design of rubber components, modeling of biological tissues (brain, muscle). First choice when test data is limited.
Practical Checklist
Medical Implants and Neo-Hookean
FEM analysis of silicone rubber breast implants and heart valve prostheses most frequently uses Neo-Hookean and Mooney-Rivlin models. The US FDA, in its guidance on structural analysis of medical devices (2019), recommends using hyperelastic models with confirmed Drucker stability for soft tissue/rubber-like material computational models. Neo-Hookean is designated as a First-choice model due to its proven property of always being stable if C₁>0.
Neo-Hookean Hyperelastic: Software & Solver Comparison
Tools
Supported by all solvers. The simplest hyperelastic model.
Comparison of Hyperelastic Model Implementations Across Vendors
ABAQUS, ANSYS, and Nastran all support Neo-Hooke, Mooney-Rivlin, and Ogden models, but their material constant fitting UIs differ. ABAQUS can simultaneously fit Mooney-Rivlin C10/C01 to tensile, compressive, and shear test data, while ANSYS uses uniaxial fitting as standard. A case study published in the Journal of Constitutive Models of Rubber reported that differences in fitting methods led to up to a 2x variation in predicted durability life for tire sidewall analysis.
Advanced Technology
Advanced
Origin of the Neo-Hooke Model: Statistical Mechanics of Rubber Elasticity
The Neo-Hookean hyperelastic model was derived in 1943 by Flory and Rehn from the molecular chain network theory of vulcanized natural rubber. It is a practical model with errors within 10% even at an elongation ratio of λ=3 for natural rubber with shear modulus G≈0.4 MPa. Today, it is widely used in ABAQUS and ANSYS for applications ranging from medical silicone catheters (G≈0.1 MPa) to tire compounds (G≈1.2 MPa).
Neo-Hookean Hyperelastic: Common Issues & Debugging
Troubles
Accuracy Degradation at Excessive Strains
It is well known from many experiments that Neo-Hookean underestimates stress when the stretch ratio λ≧2.5. For uniaxial tension of natural rubber, the stress difference between Mooney-Rivlin and Neo-Hookean at λ=3 can reach 20-40%. This discrepancy is due to the absence of the C₂ term (I₂ dependence). For parts where large deformation is expected (tire bead, O-ring compression), switching to a multi-parameter model like Mooney-Rivlin or higher should always be considered.
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