Convergence problems with *HYSTERESIS

Dear Dr. Bergstrm

My name is Per Bryntheson and I work at Saab Automobile AB in Trollhttan, Sweden.

I just found the card *HYSTERESIS in the ABAQUS manual and that is exactly what I need. I also found the reference to yours and Boyce report Constitutive Modeling of the Large Strain Time-Dependent Behavior of Elastomers. I have now downloaded all the reports I have found that you have written. I also found your website polymerfem.com. I must say that it felt like winning the lottery when I found all this. The reason to my excitement is that I am working with hood and door slams (fast closings of the car closures) and I therefore need the force displacement curve for the rubber sealings at fast compressions. I do however have some questions that you perhaps would be kind enough to help me with.

I use to calculate the force displacement curve for the sealings in Abaqus/explicit using a plain strain FE-model with displacement driven compression (compressing the seal profile with a rigid body with a friction coefficient of 0.3 between them). I have now tried to implement *HYSTERESIS in my calculation but got into some difficulties. First of all I had to switch to Abaqus/standard since *HYSTERESIS only worked in standard. My big problem is now that the calculation doesnt converge. I have tried to do the calculation in Abaqus/standard without *HYSTERESIS and that works fine, but when I include that card the problem gets really hard to solve for Abaqus.

I am using a mix of CPE3 and CPE4 elements and the rubber material (EPDM 30 shore A) looks like this (my model is in [mm] and I use [N] and [MPa]):

*MATERIAL, NAME=RUBBER_30_SHORE_A

*DENSITY

0.35E-09,0.0

*HYPERELASTIC,MOONEY-RIVLIN

0.122,0.031,6.55e-2

*HYSTERESIS

1.6,0.556,4.0,-1.0

I got the *HYSTERESIS values from the ABAQUS Analysis Users Manual ver 6.5 where they with a reference to you gave the typical values: S=1.6, A=5/((SQRT of 3)^m) = 5/(1.732^4)=0.556, m=4.0 and C=-1.0.

Do you have any ideas on hove I should get convergence? Have I misunderstood the units? should I perhaps try to change any of the *HYSTERESIS values? Should I perhaps make an ever finer element mesh, the elements are already rather small. Do you think that I should try only using triangular mesh (CPE3 elements).

I am grateful to any help from you.

Best regards

Per Bryntheson

By the way, are you perhaps in any way related to Sweden. It does sound like it on your name Jrgen Bergstrm.

Hej Per,

Visst r jag svensk, men jag bor sedan ett antal r i USA.

I will write the rest in English, since you are asking some very good questions that other people might also be interested in.

[quote]I just found the card *HYSTERESIS in the ABAQUS manual and that is exactly what I need. I also found the reference to yours and Boyce report Constitutive Modeling of the Large Strain Time-Dependent Behavior of Elastomers.[/quote]

You are right: ABAQUS has implemented the Bergstrom-Boyce model into their software, and it is available through the *Hysteresis option.

As you have noticed, there are some rather serious limitation with the [i]*Hysteresis[/i] option. For example, it is only available for ABAQUS/Standard and not ABAQUS/Explicit. In addition to this, I have noticed that the ABAQUS implementation is not very stable and that is also slow.

To overcome these problems I have developed and refined for many years now my own implementation of the Bergstrom-Boyce model. My implementation has the following advantages:

➡ Its available both for ABAQUS/Standard and Explicit (through external material model subroutines, so called UMAT and VUMAT)

➡ It is both more stable and more computationally effective

➡ In includes 3 different models for simulating the Mullins effect that is often seen in elastomers

➡ It includes the ability to simulate different temperatures with one set of material parameters, i.e. it is a thermomechanical model

➡ It includes the ability to predict failure through the chain-stretch failure condition

[quote] ... I am working with hood and door slams (fast closings of the car closures) and I therefore need the force displacement curve for the rubber sealings at fast compressions.

I use to calculate the force displacement curve for the sealings in Abaqus/explicit using a plain strain FE-model with displacement driven compression (compressing the seal profile with a rigid body with a friction coefficient of 0.3 between them). [/quote]

This sounds like a very interesting project. Based on my experience I suspect that the Bergstrom-Bocye model (BB) should be able to handle this quite nicely.

[quote] I am using a mix of CPE3 and CPE4 elements and the rubber material (EPDM 30 shore A) looks like this (my model is in [mm] and I use [N] and [MPa]):

*MATERIAL, NAME=RUBBER_30_SHORE_A

*DENSITY

0.35E-09,0.0

*HYPERELASTIC,MOONEY-RIVLIN

0.122,0.031,6.55e-2

*HYSTERESIS

1.6,0.556,4.0,-1.0

I got the *HYSTERESIS values from the ABAQUS Analysis Users Manual ver 6.5 where they with a reference to you gave the typical values: S=1.6, A=5/((SQRT of 3)^m) = 5/(1.732^4)=0.556, m=4.0 and C=-1.0.

[/quote]

This all sound right to me. The problems that you are running into could be do to many things. How far do your simulation get before you get numerical problems? Do you see significant element distortions? I would not be surpriced if all your problems went away with a more refined implementation of the Bergstrom-Boyce model (i.e. my UMAT/VUMAT subroutines).

Lycka till,

Jrgen