Week - 10 Hyperelastic Material Models

Aim:

• To 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.
• The given data is the engineering stress-strain in MPa/(mm/mm).
• The comparison should be shown from the d3hsp file and using simulation.

Theory:

A hyperelastic material is designed for modeling rubber or rubber-like materials in which the elastic deformation can be extremely large.Hyperelastic materials use something called a strain energy density function to derive the relationship between stress and strain. This allows them to model the relationship between stress and strain accurately even when the strain is between 100% to 700%, depending on the exact hyperelastic model that is used.

Various hyperelastic models are accurate over different range of strains. You must choose the model to use depending on the expected range of strains, the computational expense of the formulation and the amount of data that you have to define in the stress-strain relationship.

RecurDyn offers 4 kinds of hyperelastic material models as below.

1. Neo-Hooke
2. Mooney-Rivlin
3. Arruda-Boyce
4. Ogden

• Neo-Hooke: Fastest, Strains up to 100%, Most accurate for Uniaxial strain
• Mooney-Rivlin: Slower than Neo-Hooke, Strains up to 200%, often the most popular
• Arruda-Boyce; Slower than Mooney-Rivlin, Strains up to 300%, Special purpose hyperelastic material for certain rubbery materials such as silicon and neoprene
• Ogden: Slowest, Strains up to 700%, Very general purpose hyperelastic material model.

The strain energy density function for an incompressible Mooney–Rivlin material is

where C1 and C2 are empirically determined material constants,I1 and I2 are the 1st and 2nd invariant.

Procedure:

The given data of Eng stress and Eng strain of hyperelastic material is shown in the img.

MAT77-OGDEN_RUBBER_MATERIAL:

The ogden rubber material MAT77 is assigned to the model with n=1 and RO and PR values are given in the below.

the curve is defined with the stress strain data from the excel and assigned to the LCID.

the ogden constant for N=1 found from the d3hsp file.

Final approximate solution
mu(1)= 9.1076024661337E-01 alpha(1)= 1.3427238801352E+00

the values of stretch ratio, stress and strain values are avalable in the d3hsp file.

the ogden constant for n=2 found from the d3hsp file.

Final approximate solution
mu(1)= 9.1564732574771E-01 alpha(1)= 1.3399091914039E+00
mu(2)= 2.2259557306992E+00 alpha(2)=-1.8434702588141E-03

Test and fitted data
stretch ratio stress(input) stress(fitted)
1.0000000E+00 0.0000000E+00 0.0000000E+00
1.0250000E+00 4.4600000E-02 4.4558651E-02
1.0500000E+00 8.6700000E-02 8.6672037E-02
1.0750000E+00 1.2700000E-01 1.2654161E-01
1.1000000E+00 1.6400000E-01 1.6434781E-01
1.1250000E+00 2.0000000E-01 2.0025268E-01
1.1500000E+00 2.3400000E-01 2.3440214E-01
1.1750000E+00 2.6700000E-01 2.6692785E-01
1.2000000E+00 2.9800000E-01 2.9794891E-01
1.2250000E+00 3.2800000E-01 3.2757330E-01
1.2500000E+00 3.5600000E-01 3.5589911E-01
1.2750000E+00 3.8300000E-01 3.8301562E-01
1.3000000E+00 4.0900000E-01 4.0900426E-01
1.3250000E+00 4.3400000E-01 4.3393944E-01
1.3500000E+00 4.5800000E-01 4.5788928E-01
1.3750000E+00 4.8100000E-01 4.8091623E-01
1.4000000E+00 5.0300000E-01 5.0307765E-01
1.4250000E+00 5.2400000E-01 5.2442631E-01
1.4500000E+00 5.4500000E-01 5.4501085E-01
1.4750000E+00 5.6500000E-01 5.6487612E-01
1.5000000E+00 5.8400000E-01 5.8406360E-01
1.5250000E+00 6.0300000E-01 6.0261163E-01
1.5500000E+00 6.2000000E-01 6.2055578E-01
1.5750000E+00 6.3800000E-01 6.3792903E-01
1.6000000E+00 6.5500000E-01 6.5476203E-01
1.6250000E+00 6.7100000E-01 6.7108327E-01
1.6500000E+00 6.8700000E-01 6.8691930E-01
1.6750000E+00 7.0200000E-01 7.0229486E-01
1.7000000E+00 7.1700000E-01 7.1723305E-01
1.7250000E+00 7.3200000E-01 7.3175545E-01
1.7500000E+00 7.4600000E-01 7.4588224E-01
1.7750000E+00 7.6000000E-01 7.5963232E-01
1.8000000E+00 7.7300000E-01 7.7302340E-01
1.8250000E+00 7.8600000E-01 7.8607210E-01
1.8500000E+00 7.9900000E-01 7.9879402E-01
1.8750000E+00 8.1100000E-01 8.1120382E-01
1.9000000E+00 8.2300000E-01 8.2331531E-01
1.9250000E+00 8.3500000E-01 8.3514145E-01
1.9500000E+00 8.4700000E-01 8.4669451E-01
1.9750000E+00 8.5800000E-01 8.5798601E-01
2.0000000E+00 8.6900000E-01 8.6902684E-01

the ogden constant for n=3 found from the d3hsp file.

Final approximate solution
mu(1)=-3.1842578654629E-02 alpha(1)= 1.9263321434400E+00
mu(2)= 2.6137553190073E-01 alpha(2)= 1.5503405403717E+00
mu(3)= 6.8199192356941E-01 alpha(3)= 1.2887820953261E+00

Test and fitted data
stretch ratio stress(input) stress(fitted)
1.0000000E+00 0.0000000E+00 0.0000000E+00
1.0250000E+00 4.4600000E-02 4.4559859E-02
1.0500000E+00 8.6700000E-02 8.6673966E-02
1.0750000E+00 1.2700000E-01 1.2654388E-01
1.1000000E+00 1.6400000E-01 1.6435014E-01
1.1250000E+00 2.0000000E-01 2.0025488E-01
1.1500000E+00 2.3400000E-01 2.3440406E-01
1.1750000E+00 2.6700000E-01 2.6692939E-01
1.2000000E+00 2.9800000E-01 2.9795004E-01
1.2250000E+00 3.2800000E-01 3.2757400E-01
1.2500000E+00 3.5600000E-01 3.5589939E-01
1.2750000E+00 3.8300000E-01 3.8301551E-01
1.3000000E+00 4.0900000E-01 4.0900381E-01
1.3250000E+00 4.3400000E-01 4.3393871E-01
1.3500000E+00 4.5800000E-01 4.5788833E-01
1.3750000E+00 4.8100000E-01 4.8091512E-01
1.4000000E+00 5.0300000E-01 5.0307646E-01
1.4250000E+00 5.2400000E-01 5.2442510E-01
1.4500000E+00 5.4500000E-01 5.4500968E-01
1.4750000E+00 5.6500000E-01 5.6487505E-01
1.5000000E+00 5.8400000E-01 5.8406267E-01
1.5250000E+00 6.0300000E-01 6.0261090E-01
1.5500000E+00 6.2000000E-01 6.2055528E-01
1.5750000E+00 6.3800000E-01 6.3792878E-01
1.6000000E+00 6.5500000E-01 6.5476205E-01
1.6250000E+00 6.7100000E-01 6.7108358E-01
1.6500000E+00 6.8700000E-01 6.8691988E-01
1.6750000E+00 7.0200000E-01 7.0229571E-01
1.7000000E+00 7.1700000E-01 7.1723415E-01
1.7250000E+00 7.3200000E-01 7.3175676E-01
1.7500000E+00 7.4600000E-01 7.4588372E-01
1.7750000E+00 7.6000000E-01 7.5963391E-01
1.8000000E+00 7.7300000E-01 7.7302504E-01
1.8250000E+00 7.8600000E-01 7.8607372E-01
1.8500000E+00 7.9900000E-01 7.9879553E-01
1.8750000E+00 8.1100000E-01 8.1120514E-01
1.9000000E+00 8.2300000E-01 8.2331631E-01
1.9250000E+00 8.3500000E-01 8.3514204E-01
1.9500000E+00 8.4700000E-01 8.4669455E-01
1.9750000E+00 8.5800000E-01 8.5798538E-01
2.0000000E+00 8.6900000E-01 8.6902540E-01

Results:

Conclusion:

the tensile specimen has been performed with the ogden rubber material and results are obtained.