How to Implement Nonlinear Stiffness Based on Deformation?

[cuicw]

I'm currently studying with pyelastica and am trying to implement a feature where I need to setup a nonlinear stiffness that changes with deformation.

[armantekinalp]

Do you have the stiffness model? Which stiffness are you talking about bending, axial stretch, shear etc?

[cuicw]

Yes, I have a nonlinear bending stiffness model with curvature as the independent variable. I'm currently not sure in which module to develop it.

[armantekinalp]

Seems like you are only changing bending stiffness. I want to confirm. In your relation is it still internal_torques = f(\kappa) (\kappa-\rest_kappa) where f(\kappa) is your nonlinear bending stiffness?

[cuicw]

Yes

[armantekinalp]

There are two options:

1. Easier option. You can write a forcing function and modify the bend_matrix at each time step. Note that both bend_matrix and kappa are members of the rod. Now here there is a catch with this approach, since in time-step algorithm all external_force functions computed after the internal_forces/internal_torques, updated bend_matrix will be used in the next time-step. If you expect significant changes between kappa values in between time-steps then I suggest you try the second approach.

2. Relatively harder option. You can modify the functions where internal torques are computed, but this requires changing some back end code. I suggest clone PyElastica in your local system and change the following functions. Before this line you can modify the bend matrix accordingly. Note that this is a numba function so it would not support some Numpy functions, make sure to check this link.

[cuicw]

Thank you.