Week - 10 Hyperelastic Material Models

AIM : calculate the Mooney Rivlin and Ogden material constants and compare the both using stress-strain data from a Dogbone specimen tensile test with 100 percent strain.

OBJECTIVE :

• Extract the engg stress- strain data in MPa/(mm/mm) from the given raw data image and do the cleaning of data.
• Calculate Mooney Rivlin and Ogden material constants and compare between them.
• Validate the constants by using them in the following material card.

THEORY :

• Mooney Rivlin Material : Mooney Rivlin material desfined as
  
  `W = sum C_(ij)(I_1-3)^i(I_2-3)^j`
  
  where Cij are empirically determined material constatnts.
  I1 and I2 are the first and second invariants.
  W is hydrostatic work term which will be included in strain energy functional. By varying the index values of i and j we can change the constitutive equations and use it approximately for our component.
• Ogden Material : this material model is derived from the equation
  
  `W(lambda_1, lambda_2, lambda_3)= sum_(p=1)^n mu_p/ alpha_p(lambda_1^(alphap)+lambda_2^(alphap) +lambda_3^(alphap)-3)`
  
  mu and alpha are ogden constants

PROCEDURE :

• Extract the data from the given raw data image file.
  
• extracted data plotted of Engg Stress- Strain
• the data we taken is to the point 5.00E-01 engg strain and 5.84E-01.
  
• Import the Dogbone Specimen into LS-PrePost.
• Define curve of the following Engg stress- strain data by using define curve card.
  
  
  
  
• SECTION_SHELL card is used to define as shell section elements for the dogbone specimen with element formulation 16 and thickness as 2mm
  
  
  
• Boundary Conditon applied using BOUNDARY_SPC_SET and PRESCRIBED_BOUNDARY_MOTION.
• As we doing Tensile test, to fix one end of the specimen we constrain all the DOF except Y- direction for contraction while testing.
  
• now, middle nodes in both corner get arrested in Y-direction so that it can maintain its axis for specimen.
  
• For the right side edge nodes we apply PRESCRIBED_BOUNDARY_MOTION for displacement in X- direction.
• here the displacement is defined with respect to time using DEFINE_CURVE card.
  
  
  
  
• CONTROL_IMPLICIT_GENERAL card is used to activate the Implicit Analysis for Tensile Test.
  
• CONTROL_IMPLICIT_AUTO card is used to adjust the timestep automatically while running test.
  
• CONTROL_TERMINATION card is used to determine the end time of the simulation as 1ms.
  
• DATABASE_BINARY_D3PLOT card is used to store the output data of the tensile test with the given interval timestep of 0.01ms.
• DATABASE_EXTENT_BINARY is used to define STRFLG as 1 to store computed data of the elastic strain.
• MATERIAL CARD :
  MAT_HYPERELASTIC_RUBBER card used to define the material properties of hyperelastic material for the dogbone specimen elements.
• N=1 is set to find the Mooney Rivlin material constants and load the curve data of engg stress strain in LCID.
  
  
  
• Similarly we take N= 2 and 3 to get the Mooney Rivlin material constants.
  
  
  
  
  
• save the file with using .k extension and run the test.
• After the successfull run of the test the output files are stored in the following assigned location.
• the d3hsp file of the following models opened seperately in Notepad++.
• the value of Mooney constants for N=1 are as
  

  Mooney constant c1 = 0.2082E+00

  Mooney constant c2 = 0.1038E+00

• the value of Mooney constants for N=2 are as
  

  Hyperelastic Constant C10= 0.2123E+00

  Hyperelastic Constant C01= 0.9508E-01

  Hyperelastic Constant C11= -0.5392E+00

  Hyperelastic Constant C20= 0.1830E+00

  Hyperelastic Constant C02= 0.3996E+00

  Hyperelastic Constant C30= 0.0000E+00

• the value of Mooney constants for N=3 are as
  

  Hyperelastic Constant C10= 0.1613E+00

  Hyperelastic Constant C01= 0.1478E+00

  Hyperelastic Constant C11= -0.3843E+01

  Hyperelastic Constant C20= 0.1631E+01

  Hyperelastic Constant C02= 0.2346E+01

  Hyperelastic Constant C30= -0.7246E-01

• To validate the material model, the value of N in material card is set to ZERO and the value of Mooney Rivlin Constants are assigned.
  
  
  
• save the file and run the file for tensile test with same conditions.
• Similarly we run Tensile test by using OGDEN_RUBBER material card.
• To find OGDEN Material Constants, the value of N is set to be 1,2 and 3 seperately.
  
  
  
  
  
• the output file d3hsp file for ogden rubber material opened in notepad++.
• the values of Ogden constants while N=1
  

  mu(1)= 9.1145211941364E-01

  alpha(1)= 1.3417986826832E+00

• the values of Ogden constants while N=2
  

  mu(1)= 1.0154180079001E+00

  mu(2)= 1.7140859254594E+00

  alpha(1)= 1.2802059946916E+00

  alpha(2)=-4.5428513121422E-02

• the values of Ogden constants while N=3
  

  mu(1)= 5.2009287842598E-02

  mu(2)= 1.7835344245279E+00

  mu(3)= 2.6730832691892E-01

  alpha(1)= 2.8616428966198E+00

  alpha(2)= 7.5526430881141E-01

  alpha(3)=-1.0282035613356E+00

• For Material model validation, the value of N is set to be zero and the Ogden constants are assigned.
  
  
  

RESULTS AND CONCLUSION :

VON-MISES STRESS

• HYPERELASTIC RUBBER (MOONEY RIVLIN) N=1
  https://youtu.be/6mIXr1YclBk
  
  
• OGDEN RUBBER N=1
  https://youtu.be/nr3z5ZMJmWs

PLOTTING OF EXPERIMENTAL DATA OF CONSTANTS WITH RAW DATA

(1) Mooney-Rivlin material

(2) Ogden Material

CONCLUSION :

• From above data you can see the comparision between Mooney Rivlin and Ogden material constants output Engg stress- strain for N=1.we learned to verify and validate material model of hyper elastic material card.
• the stress-strain data extracted from the d3hsp file is converted into Engg stress- strain and compare with given raw data.
• the results from both the simulation of tensile test showed a slight deviation in decimal values.
• Result shows both the hyperelastic material cards are valid for the use to describe the hyperelastic behaviour.