Week - 10 Hyperelastic Material Models

Aim-

• Use the given material data to build a hyper elastic material cards using Ls-Dyna.
• Build Mooney Rivlin and Ogden material card by finding their constants using d3hsp file.
• Perform uniaxial tensile test on Dogbone specimen with 100% strain (i.e. strain = 1) and compare the stress strain data in above cases.

Theory-

• Hyper elastic materials are the material which has the capability to stretch with more than 100 % strain without any sort of failure.
• These material are hard to replicate as the strain value are high. These materials have Poisson’s ratio of almost 0.5. Although keeping 0.5 poisson’s ratio creates instability so for simulation purpose the value is assigned that is almost equal to 0.5 but not 0.5 like 0.4999, 0.4995 etc
• Various material models like Mooney Rivlin, Ogden, Yeoh etc are used to model these materials.
• These materials can be defined using strain energy vs stretch relations, where strain energy is the area under stress-strain graph.
• Here we will discuss modelling of Mooney Rivlin and Ogden material using the given stress strain data.

Procedure-

• We have to open the given LS-Dyna keyword (.k file) file in LS-PrePost, using option File>Open>LS-Dyna Keyword File as shown in below snap.

• Now from Experimental data Image we will input the given data into Excel and create the stress-strain curve in the excel.

Mooney Rivlin Material

• Now from Experimental data Image we will input the given data into Excel and input the same data in the curve data of LS-DYNA.
• Now we will go to the Define>>curve and input the value of curve data to get the curve.

• First we will start with section card, to create section card from keyword>>all>>section>>shell>>here we will input id, elform type as shown below.

• Now we will create the MAT card for it as MAT_HYPERELASTIC_RUBBER (MAT_077_H).

• Initially we will start with N=1, then N=3 and calculate the stress and stretch ratio and then calculate the engg. stress and strain and also we will get the values of constants, C10, C01 and other constants.
• Finally we have to assign the section and material to the part.

• Constrain all the nodes of one end of the dog bone specimen in all directions except translational Y direction.

• Constrain the mid nodes of both ends of the dog bone specimen in Y translation to restrict the slip during simulation.

• Assign Displacement for the specimen onset of nodes on another side with the curve defined.

• Now we have to create the control cards for finalisation of output.
• Now we will create the control_ternimation card.

• Now we will create Control Implicit General, Control Implicit Auto & Control Implicit Solver.

Note- As is a tensile type of test so we have used implicit analysis method here.

• Now we will create the database file.
• BINARY_D3PLOT -  It defines the frequency at which the animation file is to be created and is set to 0.1ms.
• Extent Bianry database card.

The output request in ASCII format, The following keyword are activated

1. ELOUT-Element Output Data
2. GLSTAT- Global Data
3. MATSUM- Material Energies and
4. RCFORC: Resultant Interface Forces

• Now we will check the model and then head for simulation.

• Since there is no error we can proceed further to save and run the keyword file.

• The d3hsp file for each material model is opened in notepad++ and the material constants of Mooney-Rivlin as well as final fit data of stretch and Engg. stress is obtained for each case.

• Now we will calculate the engg. stress and engg. strain values from the calculated values by N=1 & 3.

Engineering Strain = Exp(True strain) - 1

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

• Now we will create graphs for the each constants.

• Since above all the graphs looks similar to experimental data we had earlier, now to get exact material model we have to compare the values of stress from N1 & N3 values.
• After comparing this we will come to know that the N3 values are more closer to the values of experimental data.
• So N3 model can be selected from that material model.

Results- 

N=1

Effective Stress (V-M)-

Effective Plastic Strain-

N=3

Effective Stress (V-M)-

Effective Plastic Strain-

Conclusion-

• The above exercise gives us understanding the detailed process involved in generating a hyper elastic material card.
• Also here we have taken 0.495 Poisson’s ratio. The solution can be checked for different values of Poisson’s ratio which will give different material constant values and thus a more accurate material card can generated for practical applications.
• But from our simulation report we can conclude that at poissons ratio 0.495, ogden material model is more accurate to experimental data, so we can use this material model for future reference.

Animation-

N=1

Effective Stress (V-M)-

Effective Plastic Strain-

N=3

Effective Stress (V-M)-

Effective Plastic Strain-