Mooney-Rivlin Material Model

W = C₁₀(I₁ - 3) + C₀₁(I₂ - 3)
where: W - strain energy density function, C₁₀ and C₀₁ - Mooney-Rivlin constants, I₁ and I₂ - strain invariants

🔧 Units Settings

°
📊 Applicability Ranges:
• Method 1 (Altidis-Warner): 35-70 Shore A
• Method 2 (Gent): 30-95 Shore A
-
kg/m³

Method 1: Altidis-Warner (2005)

Young's Modulus, E (Shore)
- MPa
Shear Modulus, G (Shore)
- MPa
Mooney-Rivlin Constant, C₁₀
- MPa
Mooney-Rivlin Constant, C₀₁
- MPa
Bulk Modulus, K
- MPa
Incompressibility Parameter, d
- MPa⁻¹
Poisson's Ratio, ν
- -

Method 2: Gent Formula

Young's Modulus, E₀ (Gent)
- MPa
Shear Modulus, G (Gent)
- MPa
Mooney-Rivlin Constant, C₁₀
- MPa
Mooney-Rivlin Constant, C₀₁
- MPa
Bulk Modulus, K
- MPa
Incompressibility Parameter, d
- MPa⁻¹
Poisson's Ratio, ν
- -

Yeoh Material Model

W = C₁₀(I₁ - 3) + C₂₀(I₁ - 3)² + C₃₀(I₁ - 3)³
where: W - strain energy density function, C₁₀, C₂₀, C₃₀ - Yeoh constants, I₁ - first strain invariant
📚 Calculation Methods:
Method 1 (Marckmann & Verron, 2006)
Unfilled rubber (NR, EPDM, SBR without fillers)

Method 2 (Yeoh, 1993)
Filled rubber (30-50 phr carbon black)

Method 3 (Seibert & Schöche, 2000)
Conservative approach for unknown rubbers

Method 1: Marckmann & Verron (2006) - Unfilled Rubber

Shear Modulus, G₀
- MPa
Yeoh Constant, C₁₀
- MPa
Yeoh Constant, C₂₀
- MPa
Yeoh Constant, C₃₀
- MPa

Method 2: Yeoh (1993) - Filled Rubber

Shear Modulus, G₀
- MPa
Yeoh Constant, C₁₀
- MPa
Yeoh Constant, C₂₀
- MPa
Yeoh Constant, C₃₀
- MPa

Method 3: Seibert & Schöche (2000) - Conservative Approach

Shear Modulus, G₀
- MPa
Yeoh Constant, C₁₀
- MPa
Yeoh Constant, C₂₀
- MPa
Yeoh Constant, C₃₀
- MPa

🚧 LS-DYNA Material Cards (Under Construction)

References

Mooney-Rivlin Model

1. Altidis P.A., Warner B.V. Analyzing hyperelastic materials with some practical considerations. Midwest ANSYS Users Group Conference, 2005.

2. Gent A.N. On the Relation between Indentation Hardness and Young's Modulus. Rubber Chemistry and Technology. 1958;31(4):896-906.

https://doi.org/10.5254/1.3542351

Yeoh Model (Third-Order Reduced Polynomial)

3. Marckmann, G., & Verron, E. (2006). Comparison of hyperelastic models for rubber-like materials. Rubber Chemistry and Technology, 79(5), 835-858.

https://doi.org/10.5254/1.3547969

4. Yeoh, O. H. (1993). Some forms of the strain energy function for rubber. Rubber Chemistry and Technology, 66(5), 754-771.

https://doi.org/10.5254/1.3538343

5. Seibert, D. J., & Schöche, N. (2000). Direct comparison of some recent rubber elasticity models. Rubber Chemistry and Technology, 73(2), 366-384.

https://doi.org/10.5254/1.3547597

Implementation Notes: The calculator implements two empirical correlations between Shore A hardness and Mooney-Rivlin parameters for rubber-like materials. Method 1 uses the Altidis-Warner approach, while Method 2 applies the Gent formula for Young's modulus estimation. The Yeoh model (W = C₁₀(I₁-3) + C₂₀(I₁-3)² + C₃₀(I₁-3)³) provides three calculation methods optimized for different rubber types: unfilled rubbers (Marckmann & Verron), carbon black filled rubbers (Yeoh), and a conservative approach for unknown materials (Seibert & Schöche).