Week-6 Calculate the Stretch Ratio by comparing the ELFORM (-2,-1,1,2) with Ogden_Material Model.

Introduction:

The Ogden material model is a hyper elastic material model used to describe the non-linear stress–strain behavior of complex materials such as rubbers, polymers, and biological tissue. The model was developed by Raymond Ogden in 1972. The Ogden model, like other hyper elastic material models, assumes that the material behavior can be described by means of a strain energy density function, from which the stress–strain relationships can be derived. For modeling rubbery materials at higher strains, the more sophisticated Ogden material model has been developed.

Stress, Strain and Stretch Ratio

Stretch ratio is defined as the ratio between the final length to the initial length of a component.

Stretch ratio = (1 + Engineering Strain). 

we know that the values of stress and strain we get in LS -Dyna are in the form of True Stress and True Strain. So we have to convert it into Engineering Stress and Engineering Strain to get the Stretch Ratio.

These conversions can be done by the equations as given below:

where;

Stretch ratio is given by

First we will create a block of 10*10*10 as shown in below figure

We will import the given material Ogden_Material.k model and assign it to the block

then we create a section solid for the created box

A part is created assigning section and material as shown below

boundary condition is created by constraining at one end surface of the box model as shown in image below.

a curve is created for the load purpose

boundary prescribed motion with 50mm is created as shown below

Control implicit auto, Control implicit general and control termination keywords are defined as shown below.

Then define database keywords as shown below

After running this model I was getting an error related to equilibrium, so to avoid it we make some extra constrains in the model as shown in below images

Save the model and submitted for run.

Extracted plots for stress in the direction load as shown below

In case of ELFORM 1

In case of ELFORM -1

In case of ELFORM 2

In case of ELFORM -2

Form the results we extracted true stresses and true strain values, from these we calculated engineering stress, engineering strain and stretch ratio.

Below are the respective values and plots

Conclusion:

Plots obtained from the simulation results, we can observe the Stress and Strain results are same for different solid element formulations.

We can observe same stretch ratio for all different element formulations.

But we can see the distribution of stress over the length of the cube is in different manner while stretching. This is due to different behavior of element formulations.

Since this is the uniaxial tensile test, we are getting similar results for different element formulations.

Also the deformation we have given to the cube was not so large for this type of hyper elastic material, so the difference cannot be observed.

For different boundary conditions and different loading conditions, we can get the different results with change in element formulation type in more efficient manner and clearly visible.

Since the element formulation (1) is constant stress solid element, which default, cosserat point element is invoked, which is good to propose the strain energy function.

Element formulation (2) is selective reduced integrated solid element, which give constant pressure throughout the element to avoid pressure locking, but type (1) is more accurate the type (2) for implicit problems.

Element formulations type (-1) and (-2) are fully integrated elements intended for elements with poor aspect ratios. Among which type (-1) is more efficient and type (-2) is more accurate formulation.

Since Element formulation (-1) has some side effects related to some particular deformation modes , we can conclude that Element formulation (-2) is more accurate and mostly preferred for the solid elements in Implicit problems.