Ideas for a material model that includes damping/hysteresis

[stfnp]

This issue is for collecting requirements and some first ideas about damping as a material property. The goal is that the damping characteristics of the limb, just like its elastic characteristics, should be predicted from material properties instead of being prescribed by the user in the form of a damping ratio.

The problem is just that modelling damping/friction/hysteresis accurately is tricky and it can be very hard to get the required material data. A good overview is provided in ANSYS: Fundamentals of Damping.

The current state

VirtualBow currently uses a form of Rayleigh damping, which is one of the most simple ways to add damping to a finite element model at the system-level. It has the following characteristics:

• Damping is linear/viscous: The damping forces are proportional to the speed of deformation (strain rate)
• The distribution of the damping coefficients is stiffness propotional (higher stiffness -> more material -> more damping)
• The total amount of damping is chosen such that the first natural oscillation of the limb decays with a certain user-provided damping ratio

The requirements when this type of damping was introduced were quite low: A simulation without any damping just doesn't "look right", especially after the arrow has left the bow and the vibrations of the limb and string should slowly decrease. So the damping should take a small, configurable amount of energy away from the system while also looking somewhat realistic.

It has to be added that only the upcoming version 0.10 of VirtualBow with the new solver starts to resolve the damping forces correctly. So serious conclusions about the merit of this damping model can only be drawn from newer simulations. But it can already be said that linear viscous damping is not how typical solid materials behave. The energy loss in this model is proportional to the frequency of the deformation and therefore gets high very fast for high frequencies. In reality the energy loss is more evenly distributed over the frequency range (see also below). In practical terms this means that fast movements of a bow (high frequencies) are overdamped while slow movements (lower frequencies) are underdamped.

One bit of feedback I got is that VirtualBow (still with the old solver) underestimates the arrow speed of flight bows when using very light arrows, which could be due to the shortcomings of this type of damping. This is also how new damping models could be evaluated: Tweak the damping of a model so that the arrow speed matches the measured speed at one particular arrow weight. Then try a range of different arrow weights and see if the results still match or if they systematically diverge.

Requirements

Relevant frequency range

TODO: Before looking at the behaviour of real materials, like wood, we should know which frequency range is relevant. Simulate a few example bows (including very light arrows), evaluate the strain over time at different points of the limb and determine the frequency spectrum. That should give us a good idea.

Behaviour of real materials

Wood

Application of dynamic mechanical analysis for
the study of viscoelastic properties and
identification of softwood and hardwood species

Characterisation and categorisation of the diversity in viscoelastic vibrational
properties between 98 wood types

Viscoelastic properties of wood materials characterized
by nanoindentation experiments

Fiberglass

TODO

Carbon fiber

TODO

Sinew

TODO

Material models

TODO