Week - 10 Hyperelastic Material Models

OBJECTIVE :

1. To calculate the Mooney Rivilin and Ogden material constants by fitting the curve using the given engineering stress and engineering strain data.

2.Using the constants calculated for the Mooney-Rivilin and the Ogden material, Create the Material model for the Hyperelastic material.

3. Using the Hyperelastic material model for the dogbone specimen, carry the tensile test with 100 percent strain.

4. Compare the FEA data from the tensile test with the given engineering Stress and engineering Strain data.

 CASE SET UP :

CASE 1 : CURVE FITTING FOR MOONEY RIVILIN 

SUB CASE 1 : For N=1

 1. Creating the Hyperelastic material card

      The given engineering stress strain data is converted into a CSV(Comma Seperated Value) for uploading in to the LS-DYNA Keyword for the Hyperelastic material.i.e, *MAT_HYPERELASTIC_RUBBER(077_H). The Hyperelastic card *MAT_HYPERELASTIC_RUBBER(077_H) is created in the keyword manager and the necessary values for the rubber are entered such as density, poisson's ratio and the Specimen gauge lengths are entered to be as unit since, the given data is in terms of the per unit area. The unit system here is Kg/mm/sec. 

       After entering all the neccesary values of the rubber in the hyperelastic card, the flag for the no of constants to solve for is entered as "1".

i.e, for determining the constants C10 and C01.

Fig 1 Curve fitting for Mooney Rivilin at N=1

2. Creating the section card 

       The section card for the shell elements is created in the keyword manager and the the thickness is imparted to the shell elements. 

Fig 2 Creating the Section card for the Shell elements

3.Assigning the Section ID and the Material ID to the Specimen PartID

       The Section ID and the Material ID are assigned to the Dogbone Specimen part ID in the keyword for the *PART.

Fig 3 Assigning the Section and the Material to the Dog bone Specimen

4. Running the model for the simulation

       The model is run for the simulation without any boundary condition as the aim of this set up is to determin only the constants for the curve fitting.

5. Getting the Constants from the d3hsp file generated

        The Constants for the curve fitting for the condition N=1 is extracted from the generated d3hsp file. The Constants calculated for N=1 condition are c1 = 0.1768E+00 and c2 = 0.1474E+00 .

Fig 4 Mooney rivilin constants generated for condition N=1

SUB CASE 2 : For N=2

    All the steps are similar to the sub case for N=1 except the flag for the no of constants to be solved are changed to "2".i.e, for determining the constants C10, C01, C11, C20, and C02. The constants determined for this condition from the d3hsp file are as follows :

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

SUB CASE 3 : For N=3

           All the steps are similar to the sub case for N=1 except the flag for the no of constants to be solved are changed to "3".i.e, for determining the constants C10, C01, C11, C20, C02, and C30. The constants determined for this condition from the d3hsp file are as follows :

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

CASE 2 : CURVE FITTING FOR OGDEN RUBBER

              All the steps involved are similar to that of the CASE 1 i.e, the curve fitting for the Mooney Rivilin model except the material card that is being used here is *MAT_OGDEN_RUBBER. 

SUB CASE 1 : For N=1

The constants determined for this condition from the d3hsp file are as follows:

mu(1)= 9.1076024661337E-01

alpha(1)= 1.3427238801352E+00

 

SUB CASE 2 : For N=2

The constants determined for this condition from the d3hsp file are as follows:

mu(1)= 9.1564732574771E-01 
mu(2)= 2.2259557307116E+00 

alpha(1)= 1.3399091914039E+00

alpha(2)=-1.8434702588025E-03

SUB CASE 3 : For N=3

The constants determined for this condition from the d3hsp file are as follows:

mu(1)=-3.1842578663497E-02 
mu(2)= 2.6137553188494E-01 
mu(3)= 6.8199192354798E-01 

alpha(1)= 1.9263321407459E+00

alpha(2)= 1.5503405391191E+00

alpha(3)= 1.2887820957813E+00

 

CASE 3 : Actual FEA with Mooney Rivilin Model

SUB CASE 1 : For N=1

 1.Setting up the Boundary conditions:

        i. Creating the Single point constraint 

             The nodeset at the on the edge of the Specimen in the left hand side (in the x- direction) are constrained in all the degrees of freedom except for the traslational degree of freedom in y-direction.

Fig 5 Constraining one end of the Specimen in the all degrees of freedom

         The Node set on the neutral axis have to be constrained for all the degrees of freedom except for the translational in x-direction.

Fig 6 Constraining the Nodeset on the neutral axis in all degrees of freedom except for translational in x- direction

   ii. Creating the prescribed motion set card for applying the displacement

          The Prescribed motion of displacement is applied to all the nodeset of the edge of the specimen in the right end( in the x-direction). The Prescribed motion of the displacement is applied in the x-direction.The displacement vs time curve is plotted and is assigned for the displacement in the prescribed motion set card.

Fig 7 Creating the displacment vs Time curve for the Prescribed motion set

 

Fig 8 Applying the Displacement motion to the other edge of the specimen

 2.Creating the Material Card

         The material card *MAT_HYPERELASTIC_RUBBER(077_H) is created from the keyword manager and all the constants that were determined while curve fitting the for the condition N=1 are entered into the material card i.e., 

c1 = 0.1768E+00 and c2 = 0.1474E+00. The flag for the constants in the material card is entered as "0".

Fig 9 Creating the Material card for the Mooney rivilin model_N=1

 

3. Creating the Control cards for the Implicit analysis

        i. Adding the Implicit_Genral card

             In addition to the already existing cards, the Implicit_general control card is added in order to carry out the Implicit analysis. The IMFLAG value is kept at "1" in order for turning ON the flag for the Implcit analysis.

Fig 10 Creating the Implcit general card for turning the implicit flag ON

  

  ii.Creating the IMLICIT_AUTO card for automatic adjustment of timestep

                     The flag for the automatic adjustment of the timestep is turned ON by entering the value for AUTO in the IMPLICIT_AUTO card.

Fig 11 Creating the card Implicit_auto for automatic adjustment of the timestep

 iii. Creating the IMPLICIT_SOLUTION card for setting the limit for the no of iterations and the tolerance limit for the displacement relative convergence .

                                 The IMPLICIT_SOLUTION card is created for setting the limit for the no iterations at each timestep for convergance. In this card, the displacement realative convergance tolerance limit can also be set.

Fig 12 Creating the IMPLICIT_AUTO card for limiting the no of Iterations for each timestep and setting the tolerance limit for the displacement convergance

iv. Creating the IMPLICIT_SOLVER card 

                 This an optional card which  applies to implicit calculations. The linear equation solver performs the CPU-intensive stiffness matrix inversion.

Fig 13 Creating the IMPLICIT_SOLVER card

4.Creating the Control termination Card for the runtime

       The Simulation runtime is assigned by entering the ENDTIME in the Control Termination card that is created from the keyword manager.

Fig 14 Creating the control termination card for the Simulation runtime

5.Creating the Time History card for the Element Output

    The Keyword *DATABASE_HISTORY is created for the element whose stress and strain outputs are to be extracted with respect to time.

Fig 15 Creating the keyword DATABASE_HISTORY for the element whose stress and strain values are to be extracted

6.Creating the Keyword Dartabase for the Output

      i. Creating the ASCII card 

           The ASCII card is created in the keyword manager with the options for the GLSTAT, MATSUM & ELEOUT being checked on. The timesteps at which these results must be plotted are also entered in the box for the DT.

Fig 16 Creating the ASCII card for the DATABASE_OUTPUT

       ii. Creating the binary D3Plot card for the animation output

              The binary D3plot card with the timestep at which these outputs must be given out is mentioned in DT value.

Fig 17 Creating the D3plot card for the animation output

       iii. Creating the Binary_Extent card for the Strain output

                    The Extent_Binary card is created under the keyword *database in the keyword manager & the strainflag is made equal to one so that strain tensor data is written on the d3plot and the eleout.

Fig 18 Creating the extent_binary card for strain tensor data

SUBCASE 2 :For N=2

   All the steps involved are similar to the SUB CASE 1 except that in the material card the constants that were got at the time of curve fitting for the condition N=2 were got i.e. C10= 0.2595E+00, C01= 0.4594E-01, C11= -0.2092E-01, C20= 0.2914E-02 & C02= 0.1016E-02 are entered.

Fig 19 Creating the Mooney Rivilin material model for the condition N=2

SUBCASE 3 :For N=3

    All the steps involved are similar to the SUB CASE 1 except that in the material card the constants that were got at the time of curve fitting for the condition N=3 were got i.e.C10= 0.2611E+00, C01= 0.4420E-01, C11= -0.6074E-02, C20= -0.2667E-02, C02= -0.9968E-02, C30= 0.1565E-03.

Fig 20 Creating the Mooney Rivilin Material model for N=3

 

CASE 4: Actual FEA with Ogden Rubber Model

   All the Steps involved are similar to the CASE 3 except the material card.The Material card here used is the MAT_OGDEN_RUBBER. 

SUBCASE 1 : For N=1

                         In the material card the constants that were got at the time of curve fitting for the condition N=1 i.e, mu(1)= 9.1076024661337E-01, alpha(1)= 1.3427238801352E+00.

Fig 21 Creating the Material card Ogden Rubber for the condition N=1

SUBCASE 2 : For N=2

               In the material card the constants that were got at the time of curve fitting for the condition N=2 i.e, mu(1)= 9.1564732574771E-01, alpha(1)= 1.3399091914039E+00, mu(2)= 2.2259557307116E+00 & alpha(2)=-1.8434702588025E-03.

Fig 22 Creating the Material card Ogden Rubber for the condition N=2

SUBCASE 3 : For N=3

                   In the material card the constants that were got at the time of curve fitting for the condition N=3 i.e,  mu(1)=-3.1842578663497E-02 ,alpha(1)= 1.9263321407459E+00, mu(2)= 2.6137553188494E-01,alpha(2)= 1.5503405391191E+00, mu(3)= 6.8199192354798E-01  & alpha(3)= 1.2887820957813E+00.

Fig 23 Creating the Material card Ogden Rubber for the condition N=3

RESULTS :

Comparison of the Stress vs Strain Graph

INFERENCE : 

1. The non- convergence of the stress - strain curve for all the material models with the experimental data could be due to the coarser Mesh size and the difference in the loading condition .

2.The Mooney Rivilin Model with the condition N=3 converges the most with the experimental data due to the presence of more no of constants in the material model.

CONCLUSION :

1.The Curve fitting for Mooney Rivilin Hyperelastic material model and the Ogden_rubber was carried out successfully for different conditions

2. Using the Mooney Rivilin Hyperelastic material and the Ogden Rubber material model for the dogbone specimen ,the FEA simulation was carried out successfully.

3 The Comparison of the Engineering Stress vs Engineering Strain plot of the experimental and FEA data was carried out successfully.