Angle goal and shear modulus

I am trying to simulate membranes with varying shear stiffness, similar to this work by Ballhause:

However I am at first starting with a simple quad mesh instead of the “triangle-weave-model”.

Here is a first qualitative result for vaarying shear stiffnesses with Kangaroo:

Now I am trying to apply correct stiffness values, for example some taken from the RFEM material library for PTFE coated glass fiber membrane:

E_x and E_y are straightforward to implent: Calculate the corresponding area with A=a*t for each spring and apply the spring “constant” with E*A/l_0.

The shear modulus is more tricky, however: The plan is to use the angle goal to achieve a similar behavior as Ballhause.

According to the Kangaroo manual, E*I has to be provided for the strength parameter of the Angle goal.
How can I find the correct strength parameter, given the shear modulus G, lengths of the springs and thickness of the membrane?

The article in full Dutch language but it seems you need to simulate both vertical and horizontal fibers first instead of simple mesh in quad or triangle. Need 2 step simulations.
Good luck.

you mean warp and weft direections? That can be easily achieved by sorting the mesh edges according to their warp and weft directions (Kangaroo has a native component for that).

Another solution would be to use diagonals instead of the angle goals, but with both solutions I am still not sure how to either get the correct bending stiffness, or the correct spring stiffness for the diagonals. Also, I think the equivalent stiffnesses would be a function not only of G but of the shear angle as well…

Here is my thnking so far:

Interestingly enough, the LinkedIn algorithm has “sent” me this conversation from a few years ago:

Here @DanielPiker says:

“It’s true that Kangaroo doesn’t currently have an area based triangle element for resisting shear that can be used for simulating membranes once the shape has been found (the soap-film element is for form-finding), but it’s something I’ve been meaning to add.”

If appoaches a) and b) do not make sense, I give developing a custom goal a try…

Ok here is an approach that should work for small shear angles (tan(x)=x), answers are marked with red.

Will need to do some testing…