Week - 10 Hyperelastic Material Models

TITLE: HYPERELASTIC MATERIAL MODELLING.

OBJECTIVE: To model a hyper elastic material from Raw data of stress and strain and compare the results with final simulation results.

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.Hyperelasticity provides a means of modeling the stress–strain behavior of such materials.

• A dog bone specimen is used to test the material modelling.

• Material is assigned and curve is define using define curve option.

• The following values of stress and strain is inserted in the curve to define the curve.
• Then I use the control implicit cards to run the simulation as implicit analysis.
• Implicit analysis is used for more accuracy of the results as its is a quasi static process.
• Boundary conditions are setup such that one side pf the dog bone is fixed and put opposite end to some displacement.
• The tensile specimen is stretch upto 100% strain.
• Measure length of the specimen is 145mm.

Engg strain = EXP(true strain)-1

1= EXP(true strain) -1

True strain = ln2=0.69

True strain = Change in length/True length 

0.69= Change in length/145

Change in length = 0.69 X 145 = 100mm

There the displacement provided in the simulation is 100mm.

MOONEY RIVLIN MODEL:

In this material model MAT 77H card is used as material card.In this model three constant N1,N2,N3 are solved to get the constants and the get the proper fit for the curve.

The constants are solved in d3hsp file from where stretch and stress values are taken and compared with the orginal values for the fit.

• Now from the extension and stress values engineering strain and stress is obtained and plotted to confirm the constants are correct.

• N1,N2 and N3 are plotted along the Raw data and it was a perfect fit for the curves.

• Now the value os N1,N2 and N3 are changed in the material card and the values of constants are insterted amnually and then simulated.
• From simulation stress and strain is plotted and saved such that from the files data is extracted and converted from true to engineering values.

• After simulation strain and stress data is plotted and compared with orginal data.

• From the plot it can be seen that N1 plot is much closer to the actual that is the raw data.

OGDEN MATERIAL:

All the cards are same as above except the material card.Here MAT 77O is used and the curve is defined in defined curve.

The constants are solved in d3hsp file from where stretch and stress values are taken and compared with the orginal values for the fit.

N1,

mu1= 0.8829362867

alpha1= 1.372864722

N2,

mu1= 1.563714969

alpha1=1.07491574402

mu2 = 1.689764877

alpha2= -0.2875385502

N3,

mu1= -6.15592160779

alpha1= -1.03166711072

mu2 = 2.8847356358

alpha2= -2.533187719153

mu3= -4.37923269633621

alpha3=-4.91334544782

• Now the value os N1,N2 and N3 are changed in the material card and the values of constants are insterted amnually and then simulated.
• From simulation stress and strain is plotted and saved such that from the files data is extracted and converted from true to engineering values.

• From the obtained plot its is clear that N1 constant is near to the actual data.

CONCLUSION:

• From this project it can be concluded that in both the cases of material modelling N1 is perfect fit for the data that was provided.
• The accuracy of the model depends upon the type of testing done.
• Knowledge of hyperelastic material model is obtained by using tensile test.
• Mooney Rivlin and Ogden material constants are deterimed and used further.