XPBD slides and stiffness

Posted: October 12th, 2016 | No Comments »

The slides for my talk on XPBD are now up on the publications page, or available here.

I spoke to someone who had already implemented the method and who was surprised to find they needed to use very small compliance values in the range of 10-6 to get stiffness comparable to regular PBD.

The reason for this is that, unlike stiffness in PBD, compliance in XPBD has a direct correspondence to engineering stiffness, i.e.: Young's modulus. Most real-world materials have a Young's modulus of several GPa (109 N/m2), and because compliance is simply inverse stiffness it must be correspondingly small.

Below are stiffness values for some common materials, I have listed the compliance in the right hand column, which is of course just the reciprocal of the stiffness.

Material Stiffness (N/m^2) Compliance (m^2/N)
Concrete 25.0 x 109 0.04 x 10-9
Wood 6.0 x 109 0.16 x 10-9
Leather 1.0 x 108 1.0 x 10-8
Tendon 5.0 x 107 0.2 x 10-7
Rubber 1.0 x 106 1.0 x 10-6
Muscle 5.0 x 103 0.2 x 10-3
Fat 1.0 x 103 1.0 x 10-3

Note that for deformable materials, like soft tissue, the material stiffness depends heavily on strain. In the case of muscle it may become up to three orders of magnitude stiffer as it is stretched, even the surrounding temperature can have a large impact on these materials. The values listed here should only be used as a rough guide for a material under low strain.

This may not be a very convenient range for artists to work with, so it can make sense to expose a parameter in the [0,1] range, map it to the desired stiffness range, and then take the reciprocal to obtain compliance.

Sources:

[1] http://biomechanics.stanford.edu/me338/me338_project02.pdf
[2] http://mdp.eng.cam.ac.uk/web/library/enginfo/cueddatabooks/materials.pdf
[3] http://www-mech.eng.cam.ac.uk/profiles/fleck/papers/259.pdf
[4] http://brl.illinois.edu/Publications/1996/Chen-UFFC-191-1996.pdf

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