Week - 10 Hyperelastic Material Models

COMPARISON AND CONCLUSION OF HYPER ELEASTIC MATERIALS MODELLING DATA

AIM :

• To use the given material engineering stress and engineering strain values to form a perfect curve fit of hyperelastic cards by using LS-dyna.

OBJECTIVE :

• To calculate the Mooney rivin and Ogden material constants and compare both using stress-strain data from a dogbone specimen is performed with uniaxail tensile test with 100 percent strain.

DATA BASE :

(i) Engineering strain (mm/mm) and  Engineering stress (Mpa) of hyperelastic models.

   

DELIVERALBLES:

• Compare the two material models with detailed report.
• The comparison should be shown from the d3hsp file and using simulation.

SOFTWARE USED :

• Solver tool - LS-Prepost 4.7.17 and LS-Run 1.0.100838.

PROCEDURAL STEPS :

STEP 1:  Import the K file of dogbone specimen.

1. Imported the K format type of file using LS-Prepost software.
2. File > Import > LS-Dyna keyword file > browsed to selected the K type of file > imported it.
3. In order to check the keywords contained in the file we have to follow the below steps.
4. Side bar > model and part > keyword manager > checked the model.

    

STEP 2: Define a curve.

1. Define a curve [for example, load (ordinate value) as a function of time (abscissa value)], often loosely referred to as a load curve. The ordinate may represent something other than a      load however, as in the case of curves for constitutive models.
2. Before define a curve , we have to copy the Engineering stress and engineering strain values in excel sheet and saved as CV(coma delimited) format.
3. In order to define a curve by the following steps.
4. Side bar > model and part > keyword manager >define > curve > LCID is 1 > import the CV format XY data > insert > accept and done.

    

    

CASE 1: HYPERELASTIC MATERIAL MODELLING N=1

STEP 3 : Creation of hyper elastic rubber material card for dogbone specimen.

1. To create the material card for dogbone specimen by the following steps.
2. I had prefereed to choose material type is MAT_077_HYPERELASTIC RUBBER.
3. This is Material Type 77. This material model provides a general hyperelastic rubber model combined optionally with linear viscoelasticity as outlined by Christensen [1980].
4. Side bar > model and part > keyword manager > MAT > all > MAT_077_HYPERELASTIC RUBBER.
5. Created new ID is 1 and give title is hyper_elastic_rubber_dogbone_specimen and specified the properties value as gm-mm-ms unit system.

     

    Where,

•      Ro-Density of hyperelastic rubber= 0.001049 gm /mm³.
•      PR- poissons ratio = 0.4997
•      N parameter in the *MAT77_H material card represents the order of polynomial for which the constants are required to solve. This involves N1, N2, and N3 cases                           where constants are solved along with stretch and true stress data.

The Mooney-Rivlin constants for each polynomial order cases are:-

N1 Solves for Two Polynomials C10, C01

N2 Solves for five  Polynomials C10, C01, C11, C20, C02

N3 Solves for Six  Polynomials C10, C01, C11, C20, C02, C30

The SW, SGL, and ST parameters are set to unity as we have a stress-strain load curve unlike in the case of force-displacement data that requires specimen dimensions.

SW-Specimen Width-1mm

SGL-Specimen Gauge Length-1mm

ST-Specimen Thickness-1mm

STEP 4: Creation of section card for dogbone specimen

1. In this section element formulation ,integration rule ,nodal thickness and cross sectional properties are defined.
2. Created the section shell for dogbone specimen.
3. Side bar > model and part > keyword manager >all > section >specified the thickness value is 1.5 mm > accept and done.

    

STEP 5: Assign the material card and section card to the dogbone specimen part.

1. Inorder to create the dogbone specimen part by the following steps.
2. Side bar > model and part > keyword manager >model > part > assigned the MID and SECID cards to dogbone specimen part >accept and done.

 

STEP 6: Define a boundary condition.

1. During the tensile test the nodes at the fixed end is constrained in the  X,y&Z direction is constrained because of expansion during the tensile test.
2. Inorder to create boundary condition by the following steps .
3. Sidebar> model > create entity > boundary > spc > create > selected the node by path > nodes at the fixed end is constrained in X,Y & Z direction > apply and done.

   

   

STEP 7   : Define a precribed motion boundary condition at free end nodes of the specimen.
STEP 7A : Define a curve for precribed motion.
1. Before creation of prescribed motion at free nodes of the specimen we need to define a load curve for that prescribed motion.
2. In order to create a curve by the following steps.
3. Side bar > model and part > keyword manager >define > curve > LCID is 1001 > specify XY data > insert > accept and done.

    

    

STEP 7B : Creation of node set for the displacement at free end of the specimen.
1. In order to create the node set by the following steps.
2. Sidebar > model > create entity > set data > set node > selected the nodes at free end of dogbone specimen > apply and done.

   

STEP 7C : Assign the Nodeset id and load curve to the boundary precribed motion set.
1. In order to create the prescribed motion set at free end by the following steps.
2. Side bar > model and part > keyword manager > BOUNDARY_PRESCRIBED_MOTION_SET > assigned nodeset id 2 , DOF is 1 , VAD is 2 and assigned load curve for displacement LCID is 1001 > accept and done.

IMPLICIT ANALYSIS
Now run this file using an implicit solver. Additional control implicit cards are used to run this simulation in an implicit solver.

STEP 8: Define a control cards
Simulation of implicit analysis and define related control parameters such as CONTROL_IMPLICIT_GENERAL , CONTROL_IMPLICIT_SOLUTION ,CONTROL_IMPLICIT_SOLVER & CONTROL_IMPLICIT_AUTO.

STEP 8A : Define a CONTROL_IMPLICIT_GENERAL card.
1. In order to create control implicit general card by the following methods.
2. Sidebar > model > keyword manager > all > CONTROL > IMPLICIT_GENERAL >IMFLAG is 1 (implicit analysis) and dt is 0.05 and other parameter remain same > accept and done.

    

STEP 8B : Define a CONTROL_IMPLICIT_AUTO card.
1. In order to create control implicit auto card by the following methods.
2. Sidebar > model > keyword manager > all > CONTROL > IMPLICIT_AUTO > parameters remain same as per default values > accept and done.

    

STEP 8C : Define a CONTROL_IMPLICIT_SOLVR card.
1. In order to create control implicit solver card by the following methods.
2. Sidebar > model > keyword manager > all > CONTROL > IMPLICIT_SOLVER > LSOLVR is 2( Parallel multi-frontal sparse solver ) and other parameters remain same as per default values > accept and done.

  

STEP 8D : Define a CONTROL_IMPLICIT_SOLUTION card.
1. In order to create control implicit solutionl card by the following methods.
2. Sidebar > model > keyword manager > all > CONTROL > IMPLICIT_SOLUTION >NSOLVR is 12 (nonlinear ) and other parameters remain same as per default values > accept & done.

  

STEP 8E : Define a CONTROL_TERMINATION card.
1. The main purpose of control termination card is to stop the job.
2. In order to assign the control termination card by the following steps.
3. Side bar > model and part > keyword manager > control > termination > specify termination time is 12 ms > accept and done.

STEP 9 : Define the outputdatabases.

STEP 9A :To define the output database as Binary D3 plot.
1. DATABASE_BINARY_D3PLOT ensures d3 plot files which its stores stress strain contour of the entire deformed model.
2. In order to create the DATABASE_BINARY_D3PLOT by the fllowing steps.
3. Side bar > model and part > keyword manager > database > select DATABASE_BINARY_D3PLOT > DT value is 0.1 ms is a time interval between output states > accept & done.

   

STEP 9B :To define the output database as ASCII.
1. ASCII can generate different outputs such as force generated in a contact like total energy and material energy etc.
2. In order to create the ASCII by the fllowing steps.
3. Side bar > model and part > keyword manager > database > select ASCII_option > check GLSTAT ,NODOUT &ELOUT >specify all DT value is 0.1 ms > accept & done.

    

STEP 9C :To define the output database as extend Binary.
1. Now we have everything for the simulation but to extract the results we need to create a database cards for the model.
2. We also need to generate the strain outputs. To do that, we can create a keyword by going to Keyword manager and selecting DATABASE > EXTENT_BINARY.
3. To create the database extend binary card by the following steps,
    Side bar > model > keyword manager > all > DATABASE > EXTEND_BINARY> and give STRFLG as ‘1’, this is due to extract the true strain values for the model and accept the card.

    

STEP10 : Model checkup
1. The model is checked for any errors before solving using model checker.
2. After all the errors are cleared, the drop test setup is saved and is ready to run in LS DYNA manager for solving the scenario.
3. Warnings we can ignore ,once model check is run , it will look like as shown in picture below.

    

STEP 13 : Run the simulation.
1.. To run the using LS-run by the following steps.
2. Title bar > file > run LS-dyna > runned the k file of tensile_test_mesh_hyperelastic_rubber > achieved normal temination. it means the model is ready for post processing.
3. During simulation run window will popup as shown in picture below,

     

STEP 14 : POST PROCESSING

1. In order to see simulation results , we have to open output file in LS-Prepost by the following steps.
2. In LS-prepost -Title bar > file > open > LS -Dyna binary plot > selected the d3 plot file > visibled to see animation file.
3. For plot the stress contour , go to sidebar > post >fringe component > selected in which results need for analysing the problem.

(a) Contour plot of vonmisses stress of tensile test of dogbone specimen(N=1)

        Max effective stress = 0.6516 Mpa

       

(b) Contour plot of effective plastic strain of tensile test of dogbone specimen(N=1)

        Max effective plastic strain = 1.8726 mm/mm

       

STEP 14 : To finout Mooney-rivin constant in simulated d3hsp file .

 The d3hsp file for hyperelastic material model is opened in notepad++ and the material constants of Mooney-Rivlin as well as final fit data of stretch and Enggineering stress is obtained .

   

  Mooney constant c1 = 0.1768E+00
  Mooney constant c2 = 0.1474E+00

 STEP 15 : Calculation of engineering stress and strain values from simulated (for N=1 ) d3hsp file

 Now we will calculate the engg. stress and engg. strain values from the calculated values by N=1 

 Engineering Strain = Exp(True strain) - 1

 Engineering stress = True stress/(1+Engineering strain)

CASE 2: HYPERELASTIC MATERIAL MODELLING N=2

STEP 2A : Creation of hyper elastic rubber material card for dogbone specimen.

1. To create the material card for dogbone specimen by the following steps.
2. I had prefereed to choose material type is MAT_077_HYPERELASTIC RUBBER.
3. This is Material Type 77. This material model provides a general hyperelastic rubber model combined optionally with linear viscoelasticity as outlined by Christensen [1980].
4. Side bar > model and part > keyword manager > MAT > all > MAT_077_HYPERELASTIC RUBBER.
5. Created new ID is 1 and give title is hyper_elastic_rubber_dogbone_specimen and specified the properties value as gm-mm-ms unit system.

 

6. further steps same as did in case one. Run the simulation got the results as show below.

(a) Contour plot of vonmisses stress of tensile test of dogbone specimen(N=2)

        Max effective stress = 0.6519 Mpa

     

   (b) Contour plot of effective plastic strain of tensile test of dogbone specimen(N=2)

        Max effective plastic strain = 1.8878 mm/mm

     

STEP 2B : To finout hyperelastic constants in simulated d3hsp file .

 The d3hsp file for hyperelastic material model is opened in notepad++ and the material constants of Mooney-Rivlin as well as final fit data of stretch and Enggineering stress is obtained .

   

      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

STEP 2C: Calculation of engineering stress and strain values from simulated (for N=2 ) d3hsp file

 Now we will calculate the engg. stress and engg. strain values from the calculated values by N=2 

 Engineering Strain = Exp(True strain) - 1

 Engineering stress = True stress/(1+Engineering strain)

  

 Comparison of raw data with hyperelastic material model (N=1) and hyper elastic material model (N=2)

CASE 3: HYPERELASTIC MATERIAL MODELLING N=3

STEP 3A : Creation of hyper elastic rubber material card for dogbone specimen.

1. To create the material card for dogbone specimen by the following steps.
2. I had prefereed to choose material type is MAT_077_HYPERELASTIC RUBBER.
3. This is Material Type 77. This material model provides a general hyperelastic rubber model combined optionally with linear viscoelasticity as outlined by Christensen [1980].
4. Side bar > model and part > keyword manager > MAT > all > MAT_077_HYPERELASTIC RUBBER.
5. Created new ID is 1 and give title is hyper_elastic_rubber_dogbone_specimen and specified the properties value as gm-mm-ms unit system.

    

(a) Contour plot of vonmisses stress of tensile test of dogbone specimen(N=3)

        Max effective stress = 0.6513 Mpa

       

(b) Contour plot of effective plastic strain of tensile test of dogbone specimen(N=2)

        Max effective plastic strain = 1.8718 mm/mm

         

STEP 3B : To finout hyperelastic constants in simulated d3hsp file .

The d3hsp file for hyperelastic material model is opened in notepad++ and the material constants of Mooney-Rivlin as well as final fit data of stretch and Enggineering stress is obtained .

  

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

STEP 3C: Calculation of engineering stress and strain values from simulated (for N=3 ) d3hsp file

 Now we will calculate the engg. stress and engg. strain values from the calculated values by N=3

 Engineering Strain = Exp(True strain) - 1

 Engineering stress = True stress/(1+Engineering strain)

  

  

Comparison of raw data with hyperelastic material model (N=1) Vs hyper elastic material model (N=2) Vs hyper elastic material model (N=3)

     From Case1,Case2& Case3 the above comparison table and comparison plots we understand as ,

• Calculated engineering stress and strain plot of constant N=1 is slightly deviated values from Raw engineering stress and strain values.
• But in case(2) engineering stress and strain plot of constant N=2 and N=3 are  more close values to Raw engineering stress and strain values.
• So engineering stress and strain plot of constant N=2  is more curve fit to the modelling of hyperelastic material from the experimental values.

CASE 4: OGDEN RUBBER MATERIAL MODELLING N=1

STEP4A : Creation of Ogden rubber material card for dogbone specimen.

1. To create the material card for dogbone specimen by the following steps.
2. I had prefereed to choose material type is MAT_OGDEN_ RUBBER_077.
3. This is also Material Type 77. This material model provides the Ogden [1984] rubber model combined optionally with linear viscoelasticity as outlined by Christensen [1980].
4. Side bar > model and part > keyword manager > MAT > all > MAT_OGDEN_ RUBBER_077.
5. Created new ID is 1 and give title is Ogden_rubber_dogbone_specimen and specified the properties value as gm-mm-ms unit system.

     

6. further steps same as did in hyperelastic material modelling. Run the simulation got the results as show below.

(a) Contour plot of vonmisses stress of tensile test of dogbone specimen(N=1)

        Max effective stress = 0.6516 Mpa

       

(b) Contour plot of effective plastic strain of tensile test of dogbone specimen(N=1)

        Max effective plastic strain = 1.8726 mm/mm

      

STEP 4B : To finout Mooney-rivin constant in simulated d3hsp file .

 The d3hsp file for Ogden material model is opened in notepad++ and the material constants of Ogden as well as final fit data of stretch and Enggineering stress is obtained .

 

 Mooney constant c1 = 0.1768E+00
 Mooney constant c2 = 0.1474E+00

STEP 4D : Calculation of engineering stress and strain values from simulated (for N=1 ) d3hsp file

 Now we will calculate the engg. stress and engg. strain values from the calculated values by N=1 

 Engineering Strain = Exp(True strain) - 1

 Engineering stress = True stress/(1+Engineering strain)

 

 

CASE 5: OGDEN RUBBER MATERIAL MODELLING N=2

STEP 5A : Creation of Ogden rubber material card for dogbone specimen.

1. To create the material card for dogbone specimen by the following steps.
2. I had prefereed to choose material type is MAT_OGDEN_ RUBBER_077.
3. This is also Material Type 77. This material model provides the Ogden [1984] rubber model combined optionally with linear viscoelasticity as outlined by Christensen [1980].
4. Side bar > model and part > keyword manager > MAT > all > MAT_OGDEN_ RUBBER_077.
5. Created new ID is 1 and give title is Ogden_rubber_dogbone_specimen and specified the properties value as gm-mm-ms unit system.

    

6. further steps same as did in hyperelastic material modelling. Run the simulation got the results as show below.

(a) Contour plot of vonmisses stress of tensile test of dogbone specimen(N=2)

        Max effective stress = 0.6519 Mpa

       

(b) Contour plot of effective plastic strain of tensile test of dogbone specimen(N=2)

        Max effective plastic strain = 1.8878 mm/mm

      

STEP 5B : To finout Ogden constant in simulated d3hsp file .

 The d3hsp file for Ogden material model is opened in notepad++ and the material constants of Ogden as well as final fit data of stretch and Enggineering stress is obtained .

 

     mu(1)= 9.1564732574771E-01               alpha(1)= 1.3399091914039E+00
     mu(2)= 2.2259557307116E+00              alpha(2)=-1.8434702588025E-03.

STEP 5C : Calculation of engineering stress and strain values from simulated (for N=2 ) d3hsp file

 Now we will calculate the engg. stress and engg. strain values from the calculated values by N=2 

 Engineering Strain = Exp(True strain) - 1

 Engineering stress = True stress/(1+Engineering strain)

 

CASE 6 : OGDEN RUBBER MATERIAL MODELLING N=3

STEP 6A : Creation of Ogden rubber material card for dogbone specimen.

1. To create the material card for dogbone specimen by the following steps.
2. I had prefereed to choose material type is MAT_OGDEN_ RUBBER_077.
3. This is also Material Type 77. This material model provides the Ogden [1984] rubber model combined optionally with linear viscoelasticity as outlined by Christensen [1980].
4. Side bar > model and part > keyword manager > MAT > all > MAT_OGDEN_ RUBBER_077.
5. Created new ID is 1 and give title is Ogden_rubber_dogbone_specimen and specified the properties value as gm-mm-ms unit system.

    

6. further steps same as did in hyperelastic material modelling. Run the simulation got the results as show below.

(a) Contour plot of vonmisses stress of tensile test of dogbone specimen(N=3)

        Max effective stress = 0.6519 Mpa

       

       

(b) Contour plot of effective plastic strain of tensile test of dogbone specimen(N=3)

        Max effective plastic strain = 1.8879 mm/mm

      

       

STEP 6B : To finout Ogden constant in simulated d3hsp file .

 The d3hsp file for Ogden material model is opened in notepad++ and the material constants of Ogden as well as final fit data of stretch and Enggineering stress is obtained .

   

       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

 STEP 6C : Calculation of engineering stress and strain values from simulated (for N=3) d3hsp file

 Now we will calculate the engg. stress and engg. strain values from the calculated values by N=2 

 Engineering Strain = Exp(True strain) - 1

 Engineering stress = True stress/(1+Engineering strain)

 

Comparison of raw data with Ogden material model (N=1) ,Ogden material model (N=2) and Ogden material model (N=3)

     From Case4,Case5 & Case6 the above comparison table and comparison plots we understand as ,

• In case (4) Calculated engineering stress and strain plot of constant N=1 is little more deviated values from Raw engineering stress and strain values.
• But in case(5) and case(6) engineering stress and strain plot of constant N=2 and N=3 are  totally more deviation from Raw engineering stress and strain values.
• So case (4) Engineering stress and strain plot of constant N=1 is close fit to the modelling of ogden material from the experimental values other than  case(5) and case(6) 

RESULT :

Overall Comparison output datas of Hyperelastic rubber model and Ogden rubber model.

Comparison of raw data plot with hyperelastic rubber models.

Comparison of raw data plot with Ogden rubber models.

 By comparing raw data with hyperelastic material model and ogden material modle we can understand as,

• Comparison of raw data with hyperelastic rubber material model mooney constants for N=2 is more closer engineering stress and strain values are curve fit to the raw data.
• but Comparison of raw data with ogden rubber material model mooney constants for N=1 is slight deviation engineering stress and strain values are curve fit to the raw data.
• Finally hyperelastic rubber material model mooney constants for N=2 engineering stress and strain values are more closer to the raw engineering stress and strain values,then ogden model N=1 is less accuracy compared to hyperelastic rubber material model mooney constants N=2 .
• So Hyper elastic rubber  material model N=2  and their constants  C10= 0.2595E+00 , C01= 0.4594E-01,C11= -0.2092E-0 , C20= 0.2914E-02, C02= 0.1016E-02 and C30= 0.0000E+00 are more accuracy, so i had prefered Hyper elastic rubber  material model N=2 is perfect for hyper elastic material modelling.