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Hysteresis and relaxation model

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Jorgen
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I dont quite follow your description 🙁

Are you solving the equations without a FE program, using something like Matlab? or Mathematica?

Solving the equations when you haeve two loading directions should be quite similar to when you have only one loading direction. You need to determine the pressure from the boundary conditions first, and the determine the stress itself.

-Jorgen

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horst
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Dear Dr.Bergstom,

Im not using a Fe program, I solve the equations in Matlab.

1.Dont we have different pressures for the two networks?

2.I cant determine the pressure p directly. Combining the expressions for T1,T3 (known quantities in each step), TA1,TA3,TB1,TB3, the boundary conditions and Fv (known quantity in each step), I result in one equation with unkwown principal stretch &#955,1, which I solve it. Now having &#955,1 (and F, Fe as well) I can calculate the pressure.

Isnt that right?

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Jorgen
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1) In the model, the sum of the stresses in the two networks need to satisfy the boundary conditions. The individual pressure components do not matter much, only the sum does.

2) I dont follow the details of your description, but in principle it sounds right.

-Jorgen

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jrw5001
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Help ansys designations

Dear Dr. Bergstrom,

I have trouble to find connection between designation of parameters from your model given on web site [url] http://polymermechanics.com/material_models/bergstrom_boyce[/url] and the one given in ansys 12 documentation. The designations are given on the uploaded picture and the example code is given as:

TB, BB, 1, , , ISO !Activate Bergstrom-Boyce ISO data table

TBDATA, 1, 1.31 !Define material constant &#956,A ,

TBDATA, 2, 9.0 !Define N0=(&#955,Alock)2

TBDATA, 3, 4.45 !Define material constant &#956,B

TBDATA, 4, 9.0 !Define N1=(&#955,Block)2

TBDATA, 5, 0.33 !Define material constant

TBDATA, 6, -1 !Define material constant c

TBDATA, 7, 5.21 !Define material constant m

!

TB, BB, 1, , , PVOL !Activate Bergstrom-Boyce PVOL data table

TBDATA, 1, 0.001 ! as 1/K, K is the bulk modulus

Can you please help me?

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jrw5001
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ANSYS V12 Bergstrom

Dear Dr. Bergstrom,

I found the answer in your PhD thesis so please ignore my previous question.

But I have another problem so I would appreciate your help. I am trying to compare the experimentally gathered hysteresis from rubber specimens with the one obtained by ANSYS V12.

My problem is in material definition, and I have full set of experimental data. I used three models (two cannot catch the hysteresis curve but I troubleshoot the convergence issue).

1. Model Yeoh, third order

After the curve fitting the only material property required by ANSYS is density

Problem converges very well

2. Model Ogden third order

After the curve fitting again the density is required from ANSYS to run the analysis. Convergence is poor but this is a problem of implementation of Ogden model in ANSYS (poor curve fitting)

3. Bergstrom Boyce model

Setup 1

I entered model parameters, but to run the analysis I need to enter density and Isotropic Elasticity (Poisson and Young modulus). I used values of 0,3 and 2 MPa from your PhD. I used other model properties from yours PhD. The only thing I dont know is the bulk modulus so I experimented with various values (I entered values of 1/K as D1 which I obtained from Yeoh model).

I have a catastrophic convergence.

Setup 2

I modified the ANSYS model and tried to expand the ANSYS model by using the D2 and D3 values like this:

TB, BB, 1, , , ISO !Activate Bergstrom-Boyce ISO data table

TBDATA, 1, 2 !Define material constant &#956,A

TBDATA, 2, 1.45 !Define N0=(&#955,Alock)2

TBDATA, 3, 8 !Define material constant &#956,B

TBDATA, 4, 1.45 !Define N1=(&#955,Block)2

TBDATA, 5, 0.01 !Define material constant

TBDATA, 6, -1 !Define material constant c

TBDATA, 7, 4 !Define material constant m

!

TB, BB, 1, , , PVOL !Activate Bergstrom-Boyce PVOL data table

TBDATA, 1, 4.55938486420696E-06 ! as 1/K, K is the bulk modulus

[COLOR=Red]TBDATA, 2, 1.49167943507736E-06 ! as 1/K, K is the bulk modulus

TBDATA, 3, -2.81403546179751E-06 ! as 1/K, K is the bulk modulus[/COLOR]

ANSYS doesnt accept highlighted text but the Isotropic Elasticity is not required anymore.

Convergence is very bad, but slightly better than at setup 1.

Where is my mistake in defining yours model. Or the implementation of the model is ANSYS is an issue?

.

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Jorgen
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I have not personally tried the ANSYS implementation yet - I dont have the final answer. The material parameters that you listed in Setup 2 seem right, except that the N0 and N1 values are smaller than what is common. I would try N0 = N1 = 9 and see if that is helping with the convergence.

-Jorgen

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horst
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Dear Dr.Bergstom

Im revisiting the problem since it persists:)

Im using first order ogden model (&#956,1-&#945,1 parameters for network A and &#956,2-&#945,2 for network B).

In a stress controlled experiment, I know T1 and T3.

For netwrok A the stresses would be like:

TA1=-pA+&#956,1*&#955,1^&#945,1

TA3=-pA+&#956,1*&#955,3^&#945,1

(&#955,1-&#955,2-&#955,3 principal stretches)

and for netwrok B the stresses would be like:

TB1=-p&#914,+&#956,2*(&#955,1,e)^&#945,2

TB3=-p&#914,+&#956,2*(&#955,3,e)^&#945,2 (where (l1,e)=l1/lv,1)

With the procedure that I follow I can determine &#955,1(and F).

In one-loading case (T3=0 and TB3=0):

TB1= TB1-TB3 = &#956,2*(&#955,1,e)^&#945,2-&#956,2*(&#955,3,e)^&#945,2

I can calculate TB1 and I can continue the procedure.

However:

In two loading directions case (this time T3 and TB3 are not 0):

I cant calculate TB1. I can only calculate TB1-TB3 and pA+pB (sum of pressures).

But in order to continue the procedure I need TB1, which with my approach cant be determined.

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