Best model for HDR

[hausn]

Dear Dr. Bergstrom,

Which constitutive model is the best for High Damping Rubber (HDR)?
I'm looking for a model that requires the least material experiments but is able to represent the energy dissipation well.
The constitutive model proposed by Prof. Yoshida consists an elastoplastic body and a hyperelastic body. This model behaves well but it requires at least the uniaxial tension test, biaxial tension test and cyclic simple shear test. Moreover, it is too complex and there are 15 unknown parameters.
As for HDR, the energy absorbing property is very important.
Is there any simple model can reproduce the behavior of HDR without the cyclic test?
:?:

Thanks

Hausn

[Jorgen]

Hi Hausn,

There are a few different models that I would recommend. If the applied strains are always quite small (less than about 5%) then linear viscoelasticity might be accurate for your material. If the strains are larger then I would recommend the Bergstrom-Boyce (BB) model. This model is available as a user subroutine (http://www.polymerfem.com/modules.php?name=User_Subroutines) for numerous FE programs, and was specifically designed to capture the energy dissipation (hysteresis) and rate-effects of different rubbers, including HDR. The BB-model can be calibrated from uniaxial tension (or compression) tests only. In order to capture the energy dissipation it is necessary to perform the uniaxial tests at different rates and/or loading followed by unloading. It is not necessary to perform complete load cycles for calibration of the BB-model.

Thanks,
Jorgen

[sq]

Jorgen- Hausn brings up an interesting point. There seems to be a large (and growing) collection of constitutive models out there that require 15+ parameters to be identified, usually resulting in a huge number of experiments that need to be carried out.

These are certainly phenomenological approaches, to be sure, though "curve fit" may be a better description in some cases.

Do you think this is a neccessary consequence of trying to capture complex behaviors over a broad range of conditions, or is it a matter of not having started from the right "first principles" in deriving the models' form?

[Jorgen]

Steve, that's a good and valid question. Different people will have different answers, here is my current thinking. I don't think that you will be able to capture the large-strain, non-linear response of elastomers (or other polymer materials) that is characterized by time-dependence, distributed yielding, large strain stiffening, recovery during unloading, etc, without having and advanced and therefore "complicated" model. Most of the currently available advanced models are highly non-linear in their mathematical formulation, which make the determination of the material parameters non-trivial.

One important point here is that some of the advanced models have a strong connection with the micromechisms controlling the deformation behavior of the material. This physial connection makes it possible to calibrate the these models (e.g. the BB-model) using a rather small set of experimental tests. Other models are purely phenomenological, e.g. a hyperelastic model that is a polynomial expansion in I1 and I2. These phenomenological models often requre many more experimental tests in different loading modes in order to be calibrated.

In summary, I don't think that the number of material parameters is one of the most important features of a material model, but instead: is the model easy to calibrate, is it robust, and most importantly does it provide accurate prediction for other loading modes than it was calibrated for.

- Jorgen