spring-dashpot setup

[kd]

Dr. Bergstrom,

Could you point me to some literature or guide me on - how a spring-dashpot model is setup for modeling a thermoplastic? I have looked thro literature and found some setups. How are they developed, and what aspects should I look into if I need to develop one. Are the components modeled to capture specific physical phenomena in thermoplastics and how do I determine those?

Thanks.

Krish

[Jorgen]

Hi Krish,

The first thing that you need to decide is if you want linear or non-linear springs and dashpots. If you are simply interested in linear elements then you might be able to formulate your model as a linear viscoelastic model. If you want to use non-linear elements then you will have to implement your model as a user material subroutine.

The selection of spring and dashpot types is also determined by what thermoplastic you are interested inn and what conditions that you are trying to model. For example, what temperatures and strain levels are you interested in?

- Jorgen

[kd]

Dr. Bergstrom,

I am looking into modeling a crystallizing thermoplastic in the range between room and glass transition temperatures. Also the stretch levels will typically be 3-6 times (when temp is around Tg). I understand there are many models (buckley,boyce etc.) to capture loading to finite strains approximately. I am curious as to know how the polymer physics is captured through the complicated network of springs and dasphots. With that understanding, specifically my purpose is to see if a model can capture unloading correctly (with not very large elastic recovery), if not work on developing one. I have experience working on umat (basic models).

Krish

[Jorgen]

You are asking a very good question. Correctly capturing the physics of the deformation behavior, i.e. the micromechanisms controlling the response, is quite challenging. If you the different papers that have been published you will see how the different authors attibute their models to the physical behavior of the macromolecular microstructure. I think that it is perhaps fair to say that most constitutive models are still only physics-inspired, and not completely physics-based.

Best of luck,
Jorgen

[sq]

May I add that there are some recent papers that attempt to completely address the transition behavior (i.e., capturing rubbery through leathery to glassy) for a broad range of strains, rates, and temperatures. Try Arruda, Wang, and Przybylo (who worked on plasticised PVC), and more recently I have been made aware of Mulliken and Boyce. Both of the above named models use lots of material parameters that require a gooddeal of experimental data to identify, but do an admirable job of capturing material behavior over a broad range of conditions.

Actually, as the field matures, it will be intersting to see if some of these ideas might ever be consolidated into a first-principles model that starts with the macromolecules and and works it way up. It would be difficult to forsee as much, however.