Introducing Nonlinear Stiffness for Bars Under Compression

[caba0404]

Intro

Hi!

I am a graduate student at UCI, I use MuJoCo for my research.

My setup

I am utilizing Python to generate XML files and execute MuJoCo simulations.

My question

Is there a way to introduce nonlinear stiffness for bars under compression without using plugins?

More specifically, I want the bars to exhibit linear behavior under compression up to a certain deformation threshold. Beyond this point, I need the stiffness to change to a different value as the compression increases further.

Minimal model and/or code that explain my question

No response

Confirmations

• I searched the latest documentation thoroughly before posting.
• I searched previous Issues and Discussions, I am certain this has not been raised before.

[yuvaltassa]

You can manually change the stiffnesses in the model

[caba0404]

Do you mean during the simulation?
I was wondering if it’s possible to do it directly in the XML file.

[yuvaltassa]

Yes, I mean during the simulation.

No, there is currently no way to specify nonlinear stiffness in XML.

A feature I've been considering is to add higher order terms, say 3rd and 5th order. So saying stiffness = "a b c" would mean, letting $d = x_0 - x$ i.e. the negative displacement relative to the spring setpoint, give you a spring force $f(x) = ad + bd^3 + cd^5$, or maybe $f(x) = ad + bd^3/6 + cd^5/120$. Would that satisfy your needs?

[caba0404]

This is not what I want to implement right now, but I think this type of spring could be useful in other scenarios. At the moment, I want to model the post-buckling behavior of a bar, which should exhibit a force-displacement relationship like the one shown in the figure.

[caba0404]

Do you think it might be possible to achieve this using a combination of cables and tendons??? Or setting a maximum force that a tendon can exert??

[yuvaltassa]

Easiest thing is what I told you. Just modify mjModel during the sim. Why is this not a good solution?