Week - 10 Hyperelastic Material Models

HYPERELASTIC MATERIAL MODEL CREATION AND VALIDATION

Objective: In this project a MAT_77 Hyperelastic material has to be created using the given data, obtain Mooney Rivlin and Ogden material constants and using the extracted materials constants, perform a 100% strain on the Dogbone specimen and validate the results with that of given data.

Procedure: The unit system considered in this project is (g, mm, ms, N, MPa and N-mm).

Import the Dog bone specimen into the LS-PrePost Interface.

Define a curve using the given Engineering stress, strain data by using the Load XY Data tool and create another one with the Displacement vs Time

Material Creation: Create a MAT_77 HYPERELASTIC RUBBER material with density 0.001 g/mm^3 and Poisson’s ratio 0.4995. Select the Number of constants to solve for N1, N2, N3 to get the respective materials constants by performing three tests respectively. Set the gauge length, width and thickness to 1 and load the given stress-strain data.

Section creation: A shell section with ELFORM 2 (Belytschko-Tsay) has been selected with a thickness of 1.5 mm.

The material and section cards are to be further assigned to the Part card, with their respective Id’s.

Boundary conditions:

Two single point constraints, one at one of the free ends of the specimen and the other at the centre points of both the free ends. The Degrees of Freedom can be given understood from the pictures below

Prescribed boundary motion set: Only one DOF in X-direction has been created.

Control Termination of 1ms is defined and the D3PLOT AND ELOUT have also been defined with a DT of 5E-4.

Control ENERGY card has also been defined to contain any Hourglassing.

HISTORY_SHELL has been called to obtain the effective stress and effective plastic strain at shell element 311.

DATABASE_EXTENT_BINARY card has also been defined to extract the Mean IPT X-Strain at the 311 shell element.

Finally, model is run and the d3hsp file has been opened for all the numbers of constants N1, N2, N3 individually.

The Mooney Rivlin and the ogden constants can be viewed through the picture below.

From the same d3hsp the extension and the true stress values are to be excerpted and converted to Engineering strain and Engineering stress.

To find Engineering Strain, 1 is subtracted from True strain i.e.,

λ = 1+ε_e … (1)

ε_e = λ-1 = 1.05-1 = 0.05

Finally, Engineering stress is obtained by dividing the True stress with Stretch

σ _t = σ _e * (1+ε_e) … (2)

σ _t = σ _e * λ … (3) stretch replaces 1+ε_e from the equation 1

σ _e = σ _t / λ

= 0.0952/1.05 = 0.090667.

This way all the values have been converted for all the N1, N2 and N3 value of True stress and stretch to Engineering stress-strain respectively and plotted as a graph for Engineering stress vs Engineering strain.

The Stress strain values of N2,N3 values have exactly matched with the given data, while N1 values are slightly higher.

Now, having extracted Mooney rivlin and ogden constants it is required to load these constant values in the material card.

The Mooney rivlin constants are applied in the material card. likewise the Hyperelastic ogden constants of N2, N3 values are also applied respectively.

Prescribed boundary motion set: Only one DOF in X-direction has been created. To stretch the test specimen to 100% strain, i.e., If 24.1667 SF has been applied and the displacement wrt time is 6mm/ms, then the specimen gets stretched to 290mm.

These models have been run and the results are incurred.

Results:

i) The Fringe component of True stress and strain can be seen below.

Effective stress graph of N1 Constants.

The maximum Effective stress is 1.6716 MPa.

Mean X-Strain graph of N1 Constants.

The maximum Mean Ipt X-strain is 0.69378.

ii) The Fringe component of the materials constants of N2 is as follows.

Mean X-Strain graph of N2 Constants.

The maximum Mean Ipt X-strain is 0.69483.

Effective stress graph of N2 Constants.

The maximum Effective stress is 1.6648 MPa.

iii) The Fringe component of the materials constants of N3 is as follows.

Mean X-Strain graph of N3 Constants.

The maximum Mean Ipt X-strain is 0.6948.

Effective stress graph of N3 Constants.

The maximum Effective stress is 1.6644 MPa.

The values that are obtained from the LS-PrePost are True stress and True strain. These are to be converted and then plotted against the graph and validated with the actual data.

The engineering stress values range from 0.831-0.835 MPa, which is almost near to the original data.

Validating the results with the original data.

Conclusion:

• All the values did not actually match but the not deviating drastically with the given data.
• This project can further be pushed by changing the poisson's ratio of 0.49-0.4999 but not 0.5 (as there will be convergence issues ). So, by changing the poissons' ratio and then applying them to N1, N2 and N3 material constants, The output values can be matched with that of the given data.