Hyperelastic Material Modeling

HYPERELASTIC MATERIAL MODELING:

INTRODUCTION:

Material modeling is a widely performed process in industries. This process involves testing new material or alloy and modeling this material through the extracted test data and validating it with the test data and thus the material can be further used in later stages of the simulation.

Material modeling is carried out in most of the industries mainly in Research and development sectors because new materials are preferred by the industries to eliminate certain parameters and impart new one that could be beneficial for a certain application due to its certain properties like improved fatigue, life cycle, thermal and wear-resistant, eliminating manufacturing costs, etc.

This newly modeled material can later be carried out in future engineering analysis using FEA tools thus preventing testing using a physical model and thus eliminating errors and increasing productivity.

OBJECTIVE:

In this blog, we will define a new HYPERELASTIC_RUBBER material whose behavior is defined in a stress-strain curve. This material is used to perform a tensile test simulation from which the necessary parameters that are required to define the curve using the Mooney Rivlin and Ogden constitutive laws are extracted which further helps in remodeling the curve based on the Mooney Rivlin and Ogden constant parameters.

The following constant parameters are, C10, C01, C20, C02, C30

PROCEDURE:

1. DEFINE CURVE:

Newly materials are modeled using the test data that is extracted during physical testing. In our case, the extracted data is in the form of engineering stress and strain. However in case if the gathered data is in force vs displacement, then it is preferred to convert it into valid engineering stress-strain data.

NOTE: Conversion of extracted engineering stress-strain data into True stress and strain data is not required since the Load curve defined in the case of a MAT_077 card requires only the engineering stress-strain data, unlike the MAT_024 card which requires its data in True stress-strain form.

2. MATERIAL CARD [MAT_077]:

As we are modeling a hyperelastic card, it is mandatory to use a material card that can access the necessary parameters pertaining to that of a hyperelastic material.

The following cards can be used to model a hyperelastic material, MAT_007, 027, 031, 038, 057, 063, 077, 083, 092, 127, 129.

However, in our case, we will use the MAT_077_HYPERELASTIC_RUBBER material card.

The SGL, SW, and ST parameters of the MAT_077 card are set to 1 since the defined load curve data is in engineering stress-strain. However in case, only the force-displacement data is available, then the cross-section of the geometry model must be defined in the 3 parameters.

3. CONSTITUTIVE LAWS [Mooney Rivlin and Ogden]:

The Mooney Rivlin and Ogden constant parameters are computed by defining the necessary parameters in the MAT_077 card.

The N parameter is used to define the number of constant parameters that are required to be computed. This involves 3 cases, each with different N values from 1,2 and 3 from which the different constant parameters are computed along with the stretch and true strain data.

The required Mooney Rivlin and Ogden constant parameters are computed and stored in the binary file d3hsp. These parameters are shown below,

N=1

Mooney constants c1 and c2 are computed

N=2

Mooney constants c10, c01, c11, c20, c02, c30 are computed

N=3

Mooney constants c10, c01, c11, c20, c02, c30 are computed

COMPARISON:

Hence the Mooney Rivlin and Ogden material constants computed are fitted to define the behavior of the material. This curve data are obtained from the same d3hsp file. However, this data is in the form of Stretch and True Stress. Hence this Stretch data can be converted into True strain using the below equations.

Stretch, `lamda = 1 + epsilon`

This converted data is still in the form of True stress and strain however to compare it without our test data, this must be further converted into engineering stress-strain. This can be achieved using the below equations.

True stress = `sigma * exp( epsilon)` where, `epsilon`> True Strain

True Strain = `ln (1+ epsilon)` , where `epsilon` -> Engg. Strain

After conversion, the newly converted data for all three cases N=1,2 and 3 are plotted along with the actual data as shown below,

CONCLUSION:

Hence from the above graph, we can compare the fitted curve along with the actual test data. We can notice that the engineering stress and strain data gathered from all three cases align almost in the same curve line with a small displacement from the actual data. This curve generated now represents a clear behavior of a MAT_077 hyperelastic material and can be further used to represent a hyperelastic material behavior.