How physically accurate is MuJoCo's Saint Venant-Kirchoff elasticity model?

[kurtenkera]

Intro

Hi!

I am a PhD researcher from Australia, and I am currently using MuJoCo for my research on soft robotics. However, I am considering using another soft robotic simulator as I'm worried that MuJoCo's SVK elasticity model only appears to be physically accurate for a limited range of cases (this is not a knock on MuJoCo by the way, which is clearly amongst the state-of-the-art for rigid robotics simulators). I have provided an example below which demonstrates my concern.

My setup

I am currently on the latest release of MuJoCo, and access MuJoCo via the Python bindings.

My question

I have created a model soft gripper in MuJoCo (softgripper.xml) that grasps objects and deforms reasonably well. However, when I performed topology optimisation on the gripper, making the soft fingers more lightweight, the material properties of the resulting lightweight gripper (lightweight_softgripper.xml) appear completely different, even though I kept all elasticity parameters the same. I've attached videos below of my softgripper.xml and lightweight_softgripper.xml below, as well as a zip folder containing my two models and .msh files of my soft fingers.

gripper.mp4

lightweight_gripper.mp4

The issue is that my lightweight gripper has lost all the stiffness it originally had, despite the fact that I didn't change the elasticity parameters in MuJoCo? As a result, it fails to grasp the test object. Even when I played around with the elasticity parameters for my lightweight model, I couldn't get my model to demonstrate desirable deformation behaviour. Is this just a sign that MuJoCo's elasticity model isn't sufficient for modelling my lightweight gripper, or perhaps have I made a silly mistake/oversight?

From playing with many of MuJoCo's flex models, I feel like the parameters young and poisson offered by MuJoCo aren't really being used to precisely model certain materials (e.g. silicone rubber has a young's modulus of ~1MPa and a poisson's ratio of 0.45). The documentation says the elasticity model is limited to materials with large displacements and small strains, but I was just curious if others know if there are certain strict bounds on what materials can be modelled accurately and which cannot with MuJoCo's SVK model? Any input is greatly appreciated!

Cheers!

Minimal model and/or code that explain my question

softgripper_models.zip

Confirmations

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

[quagla]

Hi, the model is a standard piecewise linear FE, written in a nicer form instead of basis functions (something I did ages ago for fun in my PhD), but equivalent to it.

However, looking at your videos, I am a little concerned about the contacts you are getting in the second one. Since it's very easy to get inverted elements with coarse meshes and large deformations, we have added an option to generate "internal" contacts when a vertex tries to cross the opposite face of a tetrahedron. This is a safety measure but doesn't arise from a proper discretization of the equations, which I fear could be causing your issues. It can be disabled with internal="false" as explained here https://mujoco.readthedocs.io/en/latest/XMLreference.html#flex-contact. Can you try it and see if you are getting a different result? I think it was perhaps a mistake on our side to leave it on as default.

[kurtenkera]

Setting internal = false still gives me strange deformation. In the video below, I simply set internal = false, keeping all else fixed. You can see a kind of 'locking' where the tetrahedral mesh locks into larger triangular shapes. I've observed this kind of locking while keeping internal = false and even increasing young and poisson. Is this locking due to inverted elements i.e. from using a mesh that is too coarse? I might try aiming for a higher resolution mesh if so?

internal_false.mp4

[kurtenkera]

Hi @quagla, may I also clarify the effect that flex damping has on stiffness/elasticity? The documentation says that damping "scales the stiffness defined by Young’s modulus", but what is this scaling relationship e.g. linear/quadratic? I've played around with this parameter empirically and haven't found a clear relationship between damping and stiffness

[quagla]

Hi, I downloaded the files and played with the example. It does look like this element compresses and inverts

I guess we should check for that and throw an error when it happens. Unfortunately, linear elements are very mesh-dependent in the context of elasticity. Normally one solution would be to use quadratic elements but we don't have those in mujoco because they are expensive. The other solution is to use a finer mesh.

As for the damping, the damping coefficient is the damping value you set in the XML multiplied by the Lamé parameters obtained from the Young and Poisson values.

[kurtenkera]

Thankyou! Do you know why my lightweight_softgripper.xml loses so much stiffness relative to the softgripper.xml, despite the fact that the two models share exactly the same elasticity parameter settings? I thought there would be no difference, given the parameters are equal?

[quagla]

How did you do the topology optimization? I'm not sure I have the answer but the lightweight gripper has got so much less material than the other one, it's expected to be somehow softer - the question is if it's softer than expected (hence my question on how you did the optimization).

[yuvaltassa]

I'm wondering if one could do an inverted-tet-guided topology optimization, basically start with a coarse mesh, run the sim, and if I see a tet inverting then I subdivide it? Would probably lead to some weirdness though. You really want proper topology optimization for this, don't you. The problem here is that the deformation is quite substantial, topology based on linearization at the base pose is probably not what you want... I don't know 🤷

Also I just came here to say that your model is super cool. The MuJoCo model but also the thing itself. Really clever design!

[quagla]

Yes one way to do adaptive mesh refinement is to split tets that have high stress.