Week - 10 Hyperelastic Material Models

 Aim: Ford the given material data we need to calculate Mooney Rivlin and Ogden material constant and compare the both using stress-strain from a dogbone specimen tensile test with 100 percent strain.

Procedure:
step_1:

We need to create the sectioned shell for the given dogmen specimen.




Displacement vs time boundary condition is defined as shown below.



Define _curve engineering stress and strain is as shown below.



This engineering stress and strain is needed to provide in the material card(LCID)

where the value of the Row for the rubber is = 0.001
and the poisons ratio =0.4995

Step_2:

MAT_077_Hyperelastic rubber material  is defined in the material card we need to define the density of material and poisons ratio ,SGL,SW, and ST set to one and LCID is engineering stress and strain graph which is given in the challenge is provided as shown below. SGL,ST,SW is appeared when we change order 1.



Step_3:

when shell section and material are defined and we need to assign to part.
Step_4:

We need to define the boundary condition which is SPC one side and prescribed motion on other side.as shown below. And when we apply motion to other end in x-direction it will compress in Y-direction so that i have constrained free in the Y direction.



Motion apply to other end of the dogbone specimen and scale factor i specified in -145 because it has to move in opposite direction .engineering strain =del/l and engineering strain is 1 and l=145 and del=145.In LCID curve which is Displacement vs time is provided.




Step_5:

in the database ascii and binary d3plot is provided at the critical time step Dt=0.01 and to strain energy Extent_binary card and STRFLAG=1 is provided to activate the card.

step_6:

finally we end to provide the termination time to simulation and to solve it as implicit analysis we need to provide the implicit cads such as implicit general,implicit solver,control implicit auto.

Implicit general:

Imflag=1
DT0=0.01



Implicit solver:



Implicit auto:

Iauto= 1 which adjust the timestep.



Mooney Rivlin constants based on the order changes (where N=1,2,3 constants are shown below.)

Where N=1:





C1= 0.1768E+00
C2=0.1474E+00

Where N=2 constants as shown below.





C10= 0.2595E+00
C01= 0.4594E-01
C11 = -0.2092E-01
C20= 0.2914E-02
C02 = 0.1016E-02
C30= 0.0000E+00


Where N=3 and constants are shown below:







C10 = 0.2611E+00
C01 =0.4420E-01
C11 =-0.6074E-02
C20 =-0.2667E-02
C02 =-0.9968E-02
C30=0.1565E-03

Now we calculated the money rivlin constants from the simulation by changing the order from 1 to 3,in below I have used the two constants C1,C2 and in the card which is C10,C01 and save the keyword file and run the simulation. And results as shown below.







And now place the 5 constants as shown below.
































Now change the material card to MAT_OGDEN_RUBBER then input the density and poisons ratio and N=3,6,8 values are taken and simulated for each N value and and at every order we will get the contacts shown below.

Where N=3.


Where N=6.



N=8



This constant we need to apply to material card and where N=0 for above-specified values.






To convert the values from the true stress ,true strain to engineering stress,engineering strain below formulas used.

True strain=ln(1+engineering strain)
Engineering strain=e^true strain-1
Effective plastic strain=total true strain-true stress/E
True stress=(engineering stress)*(1+engineering strain)
Engineering stress=True stress/(1+engineering strain).


Observations:

1.From the Hyperelastic and the Ogden material results showing similar behavior. For the given engineering stress-strain curve which we feed as input and when we take the N=1 and simulate we will get contacts based on the order, we selected along with the stretch and true stress values well get which is curve fit values. These values we have to convert to engineering stress and strain values. we have to take the graph for N=1 and N=2,N=3 and will be exactly similar.

2. Here I have used the recommended value of poisons ratio is more than 0.495 not exactly 0.5 so that I used the 0.4985 since poisons ratio is ratio of lateral strain to longitudinal strain so that if we change the value of poisons ratio then results vary.

3. Ogden material has the higher degree of polynomial the higher the degree better adjustment of the curve.