MSC MARC - UPHI Subroutine?

[CRHNA]

Hi All,

I am working on an analysis project to predict the dynamic stiffness K*(w) in N/mm and loss factor of a small EPDM rubber component that is first subjected to a large strain preload with a small strain fixed displacement amplitude sinusoidal input superimosed.
I am a MARC and MARC.MENTAT user and have found documentation discussing a fortran based user subroutine named "UPHI" used to generate "phi-functions," which are material constants characterizing rubber behavior based on Complex Shear Modulus (G) material data from physical testing.

My questions are:
1) Does anyone have experience using MARC + UPHI to predict K*(w) and loss factor and willing to discuss how they did it using Dynamic Harmonic analysis?

2) Can someone share the fortran code for the MARC UPHI subroutine?

Thank you for your help and consideration.

Regards,
Chris

[Richard Kennison]

Chris,

It a long shot give the time since you wrote the orginal thread, but did you manage to get the UPHI working ?

Regards

Richard

[CRHNA]

Richard,

It was a while ago, but yes, in the end I did get the UPHI subroutine working. Do you have a particular interest in it?

Regards,
Chris

[Richard Kennison]

Hi Chris,

I'm trying to run a vibration analysis on a machine mount. The marc manual does not seem to have any particularly relevant examples; I am assuming that I need to be using the PHI data.
I have the PHI data and have a 3 load case simulation.
1 Installation of central rigid surface
2 Initial load displacement 20N (Compression under weight of support unit)
3 I stuck on the third load case, what I want to do is apply a sine wave excitation to the mount using the 20N up to around 3 g and monitor the amplification.
Could you give me any pointers on how to get the third load case to work?

Kind Regards

Richard

[CRHNA]

Richard,
I have some difficulting picturing the exact geometry but to clarify, you first have 1 installation loadstep, followed by a large-strain preload of 20N that eases to a stress-relaxed state, and finally you want to superimpose a small-amplitude sine wave at 3g and measure the vibration isolation across the mount?

Also, another question, you said you have the PHI data, but I'm curious how did you obtain the PHI coefficients?

[Richard Kennison]

Hi Chris,

You are correct; I think it’s almost the same simulation as your original thread.
I have what I assume is the PHI data from DMA testing giving me storage and loss modulus vs. frequency, well correction I will have when it’s complete. The actual data is the material labs estimation on the properties based on past knowledge of the compounf type and hardness.

The rubber mount is a cotton reel shape with metal caps at either end and a central metal ring to which the initial load and sin wave is applied

Kind Regards

Richard

[CRHNA]

Richard,

For starters, it does sound like the problem is similar to the one I was working one in terms of load step with a few possible exceptions. First, you're looking to apply a constant acceleration (3g) in step 3, where I applied a predetermine displacement. I don't have access to MARC at this time, and I can't remember exactly whether if it is possible to apply step 3 as a set acceleration and evaluate across many frequencies in a single job. If not, you may just have to convert your acceleration (x'') to a displacement value (x) for each frequency. Second, you're looking to measure the vibration loss across the mount where I was trying to measure the dynamic stiffness (K*, N/mm) and Damping Loss Factor, which are both derived from the drive-point frequency response of the system and the phase difference between the displacement (mm) input and the measured reaction force (N) output. So, it is similar but your load and response points maybe different.

Now, about PHI coefficients. Maybe you know but just to clarify - PHI coefficients are derived as a function of the complex shear properties measured in a DMA test. The PHI coefficients are not the complex shear values themselves. The easiest way to calculate the PHI coefficients is to let MARC do it for you, but you need to use a FORTRAN User Subroutine called "UPHI" which MSC.Software can provide and which is called by MARC during the analysis. The complex shear moduli are inputs for UPHI and the output are the calculated PHI functions. One little potential roadblock that I ran into was I discovered I had to purchase a specific kind of Intel® Fortran Compiler for MARC to compile the subroutine. The freebee compiler I had wouldn't work.

Anyway, I can recommend a couple resources that may help explain how to convert the complex shear modulus data you receive from a DMA, to coding it in UPHI, etc. It may not get you all the way there but it'll get you going in a good direction I think. The first is a paper by the guy who developed the PHI theory and later implemented it in MARC some years ago. If you google this paper I think you can download at no cost. I learned a lot from this paper.

Morman, K.N. Jr., “On The Application of Finite Linear
Viscoelasticity Theory to Rubber-Like Materials Exhibiting
Separability of Time and Strain Effects Under the Conditions
of Small Strains Superposed on Large,” ANSOL Corporation
(2005).

Second, is an SAE paper I wrote on my project that was just recently published. (This isn't a shameless plug, I really made it a point to explain in good detail how to do this type of analysis.)
I also think the list of references I have may provide good sources.
Title: "Simulating the Static and Dynamic Response of an
Automotive Weatherstrip Component" SAE 2011-01-1602, 2011.

Third, is a MARC publication I received from MSC titled

MARC Analysis Research Corporation-Europe, “The
Determination of Phi-Functions in a Non-Linear Pre-Stressed
Rubber Compound Subjected to Harmonic Vibrations,
MTR-9310, 2.6-2.8 (1993).

Not sure if this is available via a google search or not. I'm not sure where you're located but the MSC.Software office in Ann Arbor, MI helped me with this project. I can also recommend them as a possible source for support.

Lastly, it's worth mentioning there maybe other ways to go about this problem from a material modeling standpoint. The strength of the PHI function approach is it's ability to capture the non-linear dynamic amplitude dependency of a filled rubber material, often refered to as the Paybe Effect. However, another common approach is build a hyperelastic+linear-viscoelastic material model using a prony series (also available in Marc) that is capable of capture the preload and frequency dependency. This approach comes up short on capturing the non-linear amplitude dependency though. Just depends if capturing the Paybe Effect is important for your application.

I hope some of this has been helpful. Please feel free to continue our discussion as well, I just thought I'd provide some additional sources for you to consider.

-Chris

[Richard Kennison]

Chris,

Thanks for all you help so far, I have downloaded your paper looks very interesting, I shall read it tonight.

I am attempting to get hold of the other two references.

I might have a few more questions if you don't mind after i have digested all the information.

Kind Regards

Richard

[Richard Kennison]

Chris,

I really enjoyed your paper, thank you for explaining your method so clearly, I have also managed to get hold of the MARC research paper on PHI constants, which gives a great overview of the UPHI routine, thank for suggesting that.

Now my only issue is that my Compaq Visual Fortran is only 32 bit and my current version of marc is 64bit, so of course it will not compile, whilst it try and work around that, I believe you said that it was possible to calculate the PHI constants and input manualy, I have the Phi Function formulas and now know how to calculate the relevant g' or g" depending of the Iflag.

How do you go about getting the strain invariants and the variables w,w1,w2,w11 etc. out of marc ?


Best Regards

Richard