Week - 10 Hyperelastic Material Models

Aim: The given material data is used to calculate Mooney-Rivlin and Ogden material constants and comparison between both by using stress strain curves.

Procedure:

The given material data is used to calculate Mooney-Rivlin and Ogden material constants and compared Both with the stress Vs
strain curves of dog bone specimen tensile test with 100% strain. Since the given material curves are in engineering stress and strain form, the results of true stress and strain obtained from the simulation are converted to engineering stress and engineering strain and compared with the Ogden and Mooney-Rivlin stress Vs strain results. The hyper elastic Rubber will be having large strain therefore we can use it in terms of stress to strech ratio rather than strain unlike in ductile material where we use young's modulus to define the material, use the strain energy density to define hyperelastic material.

I)Hyperelastic Material card

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".

II)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.

III)Section ID and Material ID and part ID

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

IV)Apply Boundary condition

SPC Set1-All DOF fixed for one end of specimen

SPC Set2-Apply translation in X direction at other end of specimen

Prescribed Motion Set-Add velocity curve to define the pulling force for other end of specimen.

V)Run the model

The model is run for the simulation with boundary condition and to determine only the constants for the curve fitting.

VI)Mooney Rivlin Continuity constants

Open the d3hsp file with notepad and search for constants c1 and c2.

C1=0.1765E+00

C2=0.1480E+00

Now repeat the above procedure for MAT_HYPERELASTIC RUBBER put value of N=2,3 respectively.

Case(II)

Now follow the same procedure as above and set material card as Ogden Rubber.

I)For N=1,

Tne derived stresses and strains are as follows,

Results:

1)Sterss Vs Strain curve i.e.energy curve for MAT_HYPERELASTIC RUBBER and Ogden Rubber after solving the model is,

From above graph the comparison study of engineering stress and strain is done.

2)By applying different material cards we can do the comparison study for behaviour of the material for tensile loading.