Week - 10 Hyperelastic Material Models
OBJECTIVE :
To compare the MAT 77 H- Hyperelastic material with the stress- strain data from a dog bone specimen with 100% strain.
HYPER ELASTIC MATERIAL :
A hyperelastic or green elastic material is a type of constitutive model for ideally elastic material for which the stress–strain relationship derives from a strain energy density function.
- They are used to represent large deformation, used to model unfilled or filled elastomers.
- They can be used to emulate Tissues, Foams, etc.
- Some of hyper elastic features are Ogden, Neo-Hookean, Mooney- Rivlin, Signorini, Yeoh and fleming, Arruda- Boyce.
PROCEDURE:
- Import the meshed model of Dog Bone Specimen.
- Keyword -> Part ->
- Create -> Section ->shell thickness is defined.
- Create -> Material ID -> Input density for the hyperelastic material and Poisson's ratio is defined for the hyperelastic material. Specific gauge length, Width, Thickness id defined.In which the stress strain data is to be defined on
- Define -> Curve -> Import the data from excel (.csv format) using Load XYData ->Accept -> Plot
- In material card, Input the Load Curve ID -> Accept -> Done.
- From the model, it should be simulated in manner of tensile experiment, in which the dog bone should be deformable along y direction, when it is pulled on x direction.
- SPC nodes are created to fix along all sides except Y in the specimen.
- On the opposite a node is created and constrained along Y.
To specify the motion for the specimen, create Prescribed_Motion_Set
- PSM is created using LCID. The strech ratio is about 100%
λ = 2,
ε = λ - 1
ε = 2 - 1=1
ε = ΔL/L=1
L = 145
CONTROL CARDS :
CONTROL_IMPLICIT_AUTO
- IAUTOset to 1 which automatically adjusts the timestep size.
CONTROL_IMPLICIT_GENERAL
IMFLAG activates implicit command
CONTROL_TERMINATION:
ASCII_Option Keyword Requests :
SECFORC - Cross Sectional Forces
GLSTAT - Global Data
Material Energy
ELOUT - Element Output Data
NODOUT - Nodal Displacemment, Velocity, Acceleration Data
SLEOUT - Sliding Interface Energies
DATABASE_BINARY_D3PLOT
DATABASE_EXTENT_BINARY
The material constats are extracted by running the model,
N:=Number of constants to solve for:
EQ.1: Solve for C10 and C01,
EQ.2: Solve for C10, C01, C11, C20, and C02,
EQ.3: Solve for C10, C01, C11, C20, C02, and C30
The Mooney-Rivlin constants for each case are stored in the d3hsp file
>> Case 1: N = 1 (First order polynomial)
| Mooney constant c1 = 0.1768E+00 |
| Mooney constant c2 = 0.1474E+00 |
Change the Number of constant value to 0. Input the constant values in C10 and C01.
We receive true stress & true strain from LS DYNA, in which it is converted into engineering stress and engineering strain.
| Strech Ratio | Stress (σₜ) | Strain (εₑ) = λ-1 | σₑ=(σₜ/(1+εₑ) | Eng.Strain | Eng.Stress | ||||
| 1.00E+00 | 0.00E+00 | 0 | 0 | 0 | 0 | ||||
| 1.03E+00 | 4.81E-02 | 0.025 | 0.046926829 | 2.50E-02 | 4.46E-02 | ||||
| 1.05E+00 | 9.52E-02 | 0.05 | 0.090695238 | 5.00E-02 | 8.67E-02 | ||||
| 1.08E+00 | 1.42E-01 | 0.075 | 0.131627907 | 7.50E-02 | 1.27E-01 | ||||
| 1.10E+00 | 1.87E-01 | 0.1 | 0.17 | 1.00E-01 | 1.64E-01 | ||||
| 1.13E+00 | 2.32E-01 | 0.125 | 0.206133333 | 1.25E-01 | 2.00E-01 | ||||
| 1.15E+00 | 2.76E-01 | 0.15 | 0.24026087 | 1.50E-01 | 2.34E-01 | ||||
| 1.18E+00 | 3.20E-01 | 0.175 | 0.272425532 | 1.75E-01 | 2.67E-01 | ||||
| 1.20E+00 | 3.64E-01 | 0.2 | 0.303 | 2.00E-01 | 2.98E-01 | ||||
| 1.23E+00 | 4.07E-01 | 0.225 | 0.331918367 | 2.25E-01 | 3.28E-01 | ||||
| 1.25E+00 | 4.49E-01 | 0.25 | 0.35952 | 2.50E-01 | 3.56E-01 | ||||
| 1.28E+00 | 4.92E-01 | 0.275 | 0.385882353 | 2.75E-01 | 3.83E-01 | ||||
| 1.30E+00 | 5.34E-01 | 0.3 | 0.411076923 | 3.00E-01 | 4.09E-01 | ||||
| 1.33E+00 | 5.77E-01 | 0.325 | 0.435169811 | 3.25E-01 | 4.34E-01 | ||||
| 1.35E+00 | 6.19E-01 | 0.35 | 0.458296296 | 3.50E-01 | 4.58E-01 | ||||
| 1.38E+00 | 6.61E-01 | 0.375 | 0.480581818 | 3.75E-01 | 4.81E-01 | ||||
| 1.40E+00 | 7.03E-01 | 0.4 | 0.502 | 4.00E-01 | 5.03E-01 | ||||
| 1.43E+00 | 7.45E-01 | 0.425 | 0.522666667 | 4.25E-01 | 5.24E-01 | ||||
| 1.45E+00 | 7.87E-01 | 0.45 | 0.54262069 | 4.50E-01 | 5.45E-01 | ||||
| 1.48E+00 | 8.29E-01 | 0.475 | 0.561966102 | 4.75E-01 | 5.65E-01 | ||||
| 1.50E+00 | 8.71E-01 | 0.5 | 0.580666667 | 5.00E-01 | 5.84E-01 | ||||
| 1.53E+00 | 9.13E-01 | 0.525 | 0.598885246 | 5.25E-01 | 6.03E-01 | ||||
| 1.55E+00 | 9.56E-01 | 0.55 | 0.616516129 | 5.50E-01 | 6.20E-01 | ||||
| 1.58E+00 | 9.98E-01 | 0.575 | 0.633714286 | 5.75E-01 | 6.38E-01 | ||||
| 1.60E+00 | 1.04E+00 | 0.6 | 0.650625 | 6.00E-01 | 6.55E-01 | ||||
| 1.63E+00 | 1.08E+00 | 0.625 | 0.667076923 | 6.25E-01 | 6.71E-01 | ||||
| 1.65E+00 | 1.13E+00 | 0.65 | 0.682424242 | 6.50E-01 | 6.87E-01 | ||||
| 1.68E+00 | 1.17E+00 | 0.675 | 0.698507463 | 6.75E-01 | 7.02E-01 | ||||
| 1.70E+00 | 1.21E+00 | 0.7 | 0.713529412 | 7.00E-01 | 7.17E-01 | ||||
| 1.73E+00 | 1.26E+00 | 0.725 | 0.728695652 | 7.25E-01 | 7.32E-01 | ||||
| 1.75E+00 | 1.30E+00 | 0.75 | 0.742857143 | 7.50E-01 | 7.46E-01 | ||||
| 1.78E+00 | 1.35E+00 | 0.775 | 0.757746479 | 7.75E-01 | 7.60E-01 | ||||
| 1.80E+00 | 1.39E+00 | 0.8 | 0.771666667 | 8.00E-01 | 7.73E-01 | ||||
| 1.83E+00 | 1.43E+00 | 0.825 | 0.785205479 | 8.25E-01 | 7.86E-01 | ||||
| 1.85E+00 | 1.48E+00 | 0.85 | 0.798918919 | 8.50E-01 | 7.99E-01 | ||||
| 1.88E+00 | 1.52E+00 | 0.875 | 0.812266667 | 8.75E-01 | 8.11E-01 | ||||
| 1.90E+00 | 1.57E+00 | 0.9 | 0.825789474 | 9.00E-01 | 8.23E-01 | ||||
| 1.93E+00 | 1.61E+00 | 0.925 | 0.838441558 | 9.25E-01 | 8.35E-01 | ||||
| 1.95E+00 | 1.66E+00 | 0.95 | 0.851282051 | 9.50E-01 | 8.47E-01 | ||||
| 1.98E+00 | 1.71E+00 | 0.975 | 0.864303797 | 9.75E-01 | 8.58E-01 | ||||
| 2.00E+00 | 1.75E+00 | 1 | 0.8765 | 1 | 8.69E-01 |
Engineering Strain = Stretch -1
Engineering Stress = True Stress/Stretch
>> Case II: N = 2 (Second order polynomial)
| Hyperelastic Constant C10= 0.2595E+00 |
| Hyperelastic Constant C01= 0.4594E-01 |
| Hyperelastic Constant C11= -0.2092E-01 |
| Hyperelastic Constant C20= 0.2914E-02 |
| Hyperelastic Constant C02= 0.1016E-02 |
| Hyperelastic Constant C30= 0.0000E+00 |
Change the Number of constant value to 0. Input the constant values in C10 and C01.
We receive true stress & true strain from LS DYNA, in which it is converted into engineering stress and engineering strain.
| Strech Ratio | Stress (σₜ) | Strain (εₑ) = λ-1 | σₑ=(σₜ/(1+εₑ) | Eng.Strain | Eng.Stress | ||||
| 1.00E+00 | 0.00E+00 | 0 | 0 | 0 | 0 | ||||
| 1.03E+00 | 4.56E-02 | 0.025 | 0.044526829 | 2.50E-02 | 4.46E-02 | ||||
| 1.05E+00 | 9.10E-02 | 0.05 | 0.086638095 | 5.00E-02 | 8.67E-02 | ||||
| 1.08E+00 | 1.36E-01 | 0.075 | 0.126511628 | 7.50E-02 | 1.27E-01 | ||||
| 1.10E+00 | 1.81E-01 | 0.1 | 0.164363636 | 1.00E-01 | 1.64E-01 | ||||
| 1.13E+00 | 2.25E-01 | 0.125 | 0.200266667 | 1.25E-01 | 2.00E-01 | ||||
| 1.15E+00 | 2.70E-01 | 0.15 | 0.234434783 | 1.50E-01 | 2.34E-01 | ||||
| 1.18E+00 | 3.14E-01 | 0.175 | 0.266893617 | 1.75E-01 | 2.67E-01 | ||||
| 1.20E+00 | 3.58E-01 | 0.2 | 0.298 | 2.00E-01 | 2.98E-01 | ||||
| 1.23E+00 | 4.01E-01 | 0.225 | 0.327591837 | 2.25E-01 | 3.28E-01 | ||||
| 1.25E+00 | 4.45E-01 | 0.25 | 0.35592 | 2.50E-01 | 3.56E-01 | ||||
| 1.28E+00 | 4.88E-01 | 0.275 | 0.383058824 | 2.75E-01 | 3.83E-01 | ||||
| 1.30E+00 | 5.32E-01 | 0.3 | 0.409 | 3.00E-01 | 4.09E-01 | ||||
| 1.33E+00 | 5.75E-01 | 0.325 | 0.433962264 | 3.25E-01 | 4.34E-01 | ||||
| 1.35E+00 | 6.18E-01 | 0.35 | 0.457925926 | 3.50E-01 | 4.58E-01 | ||||
| 1.38E+00 | 6.61E-01 | 0.375 | 0.480945455 | 3.75E-01 | 4.81E-01 | ||||
| 1.40E+00 | 7.04E-01 | 0.4 | 0.503071429 | 4.00E-01 | 5.03E-01 | ||||
| 1.43E+00 | 7.47E-01 | 0.425 | 0.524421053 | 4.25E-01 | 5.24E-01 | ||||
| 1.45E+00 | 7.90E-01 | 0.45 | 0.545034483 | 4.50E-01 | 5.45E-01 | ||||
| 1.48E+00 | 8.33E-01 | 0.475 | 0.564881356 | 4.75E-01 | 5.65E-01 | ||||
| 1.50E+00 | 8.76E-01 | 0.5 | 0.584066667 | 5.00E-01 | 5.84E-01 | ||||
| 1.53E+00 | 9.19E-01 | 0.525 | 0.602622951 | 5.25E-01 | 6.03E-01 | ||||
| 1.55E+00 | 9.62E-01 | 0.55 | 0.620516129 | 5.50E-01 | 6.20E-01 | ||||
| 1.58E+00 | 1.01E+00 | 0.575 | 0.638095238 | 5.75E-01 | 6.38E-01 | ||||
| 1.60E+00 | 1.05E+00 | 0.6 | 0.655 | 6.00E-01 | 6.55E-01 | ||||
| 1.63E+00 | 1.09E+00 | 0.625 | 0.670769231 | 6.25E-01 | 6.71E-01 | ||||
| 1.65E+00 | 1.13E+00 | 0.65 | 0.686666667 | 6.50E-01 | 6.87E-01 | ||||
| 1.68E+00 | 1.18E+00 | 0.675 | 0.702089552 | 6.75E-01 | 7.02E-01 | ||||
| 1.70E+00 | 1.22E+00 | 0.7 | 0.717058824 | 7.00E-01 | 7.17E-01 | ||||
| 1.73E+00 | 1.26E+00 | 0.725 | 0.731594203 | 7.25E-01 | 7.32E-01 | ||||
| 1.75E+00 | 1.31E+00 | 0.75 | 0.745714286 | 7.50E-01 | 7.46E-01 | ||||
| 1.78E+00 | 1.35E+00 | 0.775 | 0.75943662 | 7.75E-01 | 7.60E-01 | ||||
| 1.80E+00 | 1.39E+00 | 0.8 | 0.772777778 | 8.00E-01 | 7.73E-01 | ||||
| 1.83E+00 | 1.44E+00 | 0.825 | 0.78630137 | 8.25E-01 | 7.86E-01 | ||||
| 1.85E+00 | 1.48E+00 | 0.85 | 0.798918919 | 8.50E-01 | 7.99E-01 | ||||
| 1.88E+00 | 1.52E+00 | 0.875 | 0.8112 | 8.75E-01 | 8.11E-01 | ||||
| 1.90E+00 | 1.56E+00 | 0.9 | 0.823157895 | 9.00E-01 | 8.23E-01 | ||||
| 1.93E+00 | 1.61E+00 | 0.925 | 0.835324675 | 9.25E-01 | 8.35E-01 | ||||
| 1.95E+00 | 1.65E+00 | 0.95 | 0.846666667 | 9.50E-01 | 8.47E-01 | ||||
| 1.98E+00 | 1.70E+00 | 0.975 | 0.858227848 | 9.75E-01 | 8.58E-01 | ||||
| 2.00E+00 | 1.74E+00 | 1 | 0.869 | 1 | 8.69E-01 |
>> Case III: N = 3 (Third order polynomial)
| Hyperelastic Constant C10= 0.2611E+00 |
| Hyperelastic Constant C01= 0.4420E-01 |
| Hyperelastic Constant C11= -0.6074E-02 |
| Hyperelastic Constant C20= -0.2667E-02 |
| Hyperelastic Constant C02= -0.9968E-02 |
| Hyperelastic Constant C30= 0.1565E-03 |
Change the Number of constant value to 0. Input the constant values in C10, C01, C11, C20, C02, and C30
We receive true stress & true strain from LS DYNA, in which it is converted into engineering stress and engineering strain.
| Strech Ratio | Stress (σₜ) | Strain (εₑ) = λ-1 | σₑ=(σₜ/(1+εₑ) | Eng.Strain | Eng.Stress | ||||
| 1.00E+00 | 0.00E+00 | 0 | 0 | 0 | 0 | ||||
| 1.03E+00 | 4.56E-02 | 0.025 | 0.044517073 | 2.50E-02 | 4.46E-02 | ||||
| 1.05E+00 | 9.10E-02 | 0.05 | 0.086628571 | 5.00E-02 | 8.67E-02 | ||||
| 1.08E+00 | 1.36E-01 | 0.075 | 0.126511628 | 7.50E-02 | 1.27E-01 | ||||
| 1.10E+00 | 1.81E-01 | 0.1 | 0.164363636 | 1.00E-01 | 1.64E-01 | ||||
| 1.13E+00 | 2.25E-01 | 0.125 | 0.200266667 | 1.25E-01 | 2.00E-01 | ||||
| 1.15E+00 | 2.70E-01 | 0.15 | 0.234434783 | 1.50E-01 | 2.34E-01 | ||||
| 1.18E+00 | 3.14E-01 | 0.175 | 0.266978723 | 1.75E-01 | 2.67E-01 | ||||
| 1.20E+00 | 3.58E-01 | 0.2 | 0.298 | 2.00E-01 | 2.98E-01 | ||||
| 1.23E+00 | 4.01E-01 | 0.225 | 0.327591837 | 2.25E-01 | 3.28E-01 | ||||
| 1.25E+00 | 4.45E-01 | 0.25 | 0.35592 | 2.50E-01 | 3.56E-01 | ||||
| 1.28E+00 | 4.88E-01 | 0.275 | 0.383058824 | 2.75E-01 | 3.83E-01 | ||||
| 1.30E+00 | 5.32E-01 | 0.3 | 0.409 | 3.00E-01 | 4.09E-01 | ||||
| 1.33E+00 | 5.75E-01 | 0.325 | 0.433962264 | 3.25E-01 | 4.34E-01 | ||||
| 1.35E+00 | 6.18E-01 | 0.35 | 0.457925926 | 3.50E-01 | 4.58E-01 | ||||
| 1.38E+00 | 6.61E-01 | 0.375 | 0.480945455 | 3.75E-01 | 4.81E-01 | ||||
| 1.40E+00 | 7.04E-01 | 0.4 | 0.503071429 | 4.00E-01 | 5.03E-01 | ||||
| 1.43E+00 | 7.47E-01 | 0.425 | 0.524421053 | 4.25E-01 | 5.24E-01 | ||||
| 1.45E+00 | 7.90E-01 | 0.45 | 0.544965517 | 4.50E-01 | 5.45E-01 | ||||
| 1.48E+00 | 8.33E-01 | 0.475 | 0.564881356 | 4.75E-01 | 5.65E-01 | ||||
| 1.50E+00 | 8.76E-01 | 0.5 | 0.584066667 | 5.00E-01 | 5.84E-01 | ||||
| 1.53E+00 | 9.19E-01 | 0.525 | 0.602622951 | 5.25E-01 | 6.03E-01 | ||||
| 1.55E+00 | 9.62E-01 | 0.55 | 0.620516129 | 5.50E-01 | 6.20E-01 | ||||
| 1.58E+00 | 1.01E+00 | 0.575 | 0.638095238 | 5.75E-01 | 6.38E-01 | ||||
| 1.60E+00 | 1.05E+00 | 0.6 | 0.655 | 6.00E-01 | 6.55E-01 | ||||
| 1.63E+00 | 1.09E+00 | 0.625 | 0.671384615 | 6.25E-01 | 6.71E-01 | ||||
| 1.65E+00 | 1.13E+00 | 0.65 | 0.686666667 | 6.50E-01 | 6.87E-01 | ||||
| 1.68E+00 | 1.18E+00 | 0.675 | 0.702089552 | 6.75E-01 | 7.02E-01 | ||||
| 1.70E+00 | 1.22E+00 | 0.7 | 0.717058824 | 7.00E-01 | 7.17E-01 | ||||
| 1.73E+00 | 1.26E+00 | 0.725 | 0.731594203 | 7.25E-01 | 7.32E-01 | ||||
| 1.75E+00 | 1.31E+00 | 0.75 | 0.745714286 | 7.50E-01 | 7.46E-01 | ||||
| 1.78E+00 | 1.35E+00 | 0.775 | 0.75943662 | 7.75E-01 | 7.60E-01 | ||||
| 1.80E+00 | 1.39E+00 | 0.8 | 0.772777778 | 8.00E-01 | 7.73E-01 | ||||
| 1.83E+00 | 1.44E+00 | 0.825 | 0.78630137 | 8.25E-01 | 7.86E-01 | ||||
| 1.85E+00 | 1.48E+00 | 0.85 | 0.798918919 | 8.50E-01 | 7.99E-01 | ||||
| 1.88E+00 | 1.52E+00 | 0.875 | 0.8112 | 8.75E-01 | 8.11E-01 | ||||
| 1.90E+00 | 1.56E+00 | 0.9 | 0.823157895 | 9.00E-01 | 8.23E-01 | ||||
| 1.93E+00 | 1.61E+00 | 0.925 | 0.835324675 | 9.25E-01 | 8.35E-01 | ||||
| 1.95E+00 | 1.65E+00 | 0.95 | 0.846666667 | 9.50E-01 | 8.47E-01 | ||||
| 1.98E+00 | 1.70E+00 | 0.975 | 0.858227848 | 9.75E-01 | 8.58E-01 | ||||
| 2.00E+00 | 1.74E+00 | 1 | 0.869 | 1 | 8.69E-01 |
Conclusion :
- By Comparing1st, 2nd & 3rd Order of polynomial. The best fit is of 1st degree of polynomial.
- The Mooney Rivlin is compared using stress-strain data from a Dogbone specimen tensile test with 100 percent strain rate and the results are verified.