Week - 10 Hyperelastic Material Models

AIM:

The given material data is used to calculate Mooney-Rivlin and Ogden material constants and compared both with the stress and strain curves of dog bone specimen tensile test with 100% strain.

CASE 1: MOONEY-RIVLIN

PROCEDURE:

STEP 1: OPEN THE MODEL.

STEP 2: GIVE MATERIAL CURVE DATA BY USING DEFINE OPTION.

STEP 3: DEFINE SECTION

STEP 4: DEFINE MATERIAL

The material card is assigned using the 077_HYPERELASTIC_RUBBER card which will give the Mooney-rivlin constant , using the LCID curve 1 set SGL, SW, ST to be 1 with the order of the polynomial N is set to 1.

STEP 5: DEFINE PART

The part is set with SECTION ID and MATERIAL ID.

STEP 6: DEFINE BOUNDARY CONDITION

1. FIXED LEFT EDGE

2. Y-DIRECTION IS CONSTRAINED

3. DEFINE MOTION

The displacement boundary condition is set using the prescribed boundary condition which is set for scale factor as 200 mm as given condition for 100% strain.

STEP 7: DEFINE CONTROL IMPLICIT CARDS.

The Implicit analysis is selected for this type of simulation where it is stable, tensile test analysis which will be faster compared with explicit analysis.

STEP 8: DEFINE CONTROL TERMINATION.

STEP 9: DEFINE DATABASE

The data base option has to activate the ASCII option , d3plot, Extent binary is set to 1.

THEN THE FILE SAVED, AND THE SIMULATION IS RUN ,THE RESULTS OS THE CONSTANTS ARE NOTED DOWN USING THE d3hsp file in Note pad.

Mooney constants.

The Mooney constant C1 and C2 are obtained are then input into material card into the A and B option in the MOONEY-RIVLIN RUBBER CARD.

The file is saved and run.. The true stress and strain are obtained

The true strain is converted into Engineering strain by using this formula,

True strain= ln(Engineering strain + 1)

Engineering strain= Exp(true strain)-1

True stress is converted into Engineering stress by using this formula,

True stress = Engineering stress(1+ Engineering strain)

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

CASE 2: OGDEN_MATERIAL

The same procedure followed for the ogden material card by replacing the card even with same boundary conditions. The material card is assigned using the 077_OGDEN_RUBBER card.

Which will give the constants alpha and mu, using the LCID 1 curve and set SGL, SW, ST to be 1 with the order of polynomial N is set to 1.

OGDEN material card with N=3

OGDEN material card with N=5

The files are saved individually and run to obtain the values of constants. The value of alpha and mu are then input in N=0.

OGDEN MATERIAL card with N=0 for alpha1 and mu1

OGDEN MATERIAL card with N=0 for alpha1-3 and mu1-3

OGDEN MATERIAL card with N=0 for alpha1-5 and mu1-5

Then the files are saved individually and run to obtain the stress vs strain curve.

RESULTS:

Stress contour of the Mooney-rivlin model is compared with Ogden model in X- direction stress.

stress contour of Mooney-Rivlin model

stress contour of Ogden model