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Low-frequency and low-strain limits of the BB model and its applicability

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Hi all,

I am faced with the problem of simulating the strain- and frequency-dependent behavior of components made from fluorocarbon rubber. Mainly, there are two fundamental simulation tasks:

  • Determination of the oscillatory response of a prestressed geometry (alteration of viscoelastic behavior with respect to unloaded geometry due to large strains)
  • Determination of the transient creep behavior of a prestressed geometry (alteration of creep time constants and moduli due to large, changing strains) 

Because of internal constraints, the simulations will have to be carried out with Ansys Mechanical. While researching possible options in terms of material modelling, I stumbled upon the hyperviscoelastic “Bergström-Boyce” model. However, I am not sure whether it is really applicable to my problem and – if it is applicable – which material tests are required to parameterize it properly. Using the vocabulary of small-strain mechanics (engineering stress, engineering strain, Young’s modulus), I am imagining fluorocarbon rubbers to possess a Young’s modulus (e.g. for uniaxial strain) which is both frequency- and (engineering) strain-dependent, i.e. E(f, epsilon). If I would look at the two-dimensional projection E(0, epsilon) of this three-dimensional surface at zero frequency, I would obtain the quasistatic Young’s modulus as a function of engineering strain (i.e. pure hyperelasticity). If I were to consider a projection E(f, x) at an arbitrary strain x, I would obtain the (linearized) complex Young’s modulus as a function of the frequency (i.e. linearized viscoelasticity). My question is: What “fidelity” (i.e. complexity of function, e.g. whether there is an inflection point or not) would the BB material model be able to cover in these two projections? A possible answer could be – for example – that the constant-strain projection is able to represent a third-order generalized Kelvin-Voigt element. Since I – based on existing experiments – would be able to plot these functions, I would be able to judge the applicability of the BB model. Furthermore, I would like to understand which experiments would have to be conducted (in which way) to parameterize the model.



1 Reply
Posts: 3998
Joined: 5 years ago

The BB-model, in general, can can predict both strain and frequency dependent behavior of rubbers. It is a non-linear viscoelastic model. I don't know how well it will predict the behavior of your specific rubber material. I recommend that you simply try to calibrate it to relevant experimental data. It the predictions are accurate enough then you are OK, otherwise you may need to add additional parallel networks.