Adding the s_mu and k_mu to the tangent force Collision

[antoinebou12]

Description

Including the addition of multiple friction materials and blending types for friction coefficients. The changes span across documentation, collision mesh structures, and tangential collision calculations.

Documentation Updates:

• Added a comprehensive tutorial on setting up and working with multiple friction types, including creating collision meshes, defining tangential collisions, specifying blend types, and computing friction forces. (docs/source/tutorial/frictions.rst)

Code Enhancements:

• Collision Mesh Enhancements:

  • Added support for material IDs in the CollisionMesh class, allowing different friction properties for various materials. (src/ipc/collision_mesh.cpp, src/ipc/collision_mesh.hpp) [1] [2] [3] [4] [5] [6]

• Tangential Collisions Enhancements:

  • Introduced a BlendType enum and MaterialPairFriction struct to handle various methods of blending friction coefficients and defining friction interactions between materials. (src/ipc/collisions/tangential/tangential_collisions.hpp, src/ipc/collisions/tangential/tangential_collisions.cpp) [1] [2] [3] [4] [5] [6] [7] [8]

• Friction Potential Calculations:

  • Updated the TangentialPotential::gradient method to use dynamic friction coefficients (k_mu and s_mu) if available, enhancing the accuracy of friction force calculations. (src/ipc/potentials/tangential_potential.cpp)

These changes collectively enhance the IPC Toolkit's ability to model and compute friction forces accurately, accommodating multiple materials.

Fixes # (issue)
polyfem/polyfem#199

Type of change

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• Enhancement (non-breaking change which improves existing functionality)
• New feature (non-breaking change which adds functionality)
• This change requires a documentation update

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Checklist

• I have followed the project style guide
• My code follows the clang-format style guidelines of this project
• I have performed a self-review of my code
• I have commented my code, particularly in hard-to-understand areas
• I have made corresponding changes to the documentation
• My changes generate no new warnings
• I have added tests that prove my fix is effective or that my feature works
• New and existing unit tests pass locally with my changes
• Any dependent changes have been merged and published in downstream modules

[zfergus]

Thanks again for the PR @antoinebou12!

A few years ago, I thought about how we could have different static and dynamic coefficients of friction. I hit a wall with it for two reasons

1. unlike the contact potential, we know what the friction force is and we have to work backward to derive a dissipative potential whose negative gradient gives us the expected force
2. much like the smooth friction mollifier, the transition between $\mu_s$ and $\mu_k$ needs to be smooth

However, I reviewed my notes from then, and I think I figured out a way to fix both problems. Here is a PDF of my Jupyter notebook.

The main idea is to multiply the smooth friction force mollifier $f_1(x)$ by a smooth coefficient of friction function $\mu(x)$. Then to get the correct mollifier for the potential we can integrate this function

$$f_0^\mu(x) = \int \mu(x) f_1(x)~\mathrm{d}x.$$

The nice thing, which I didn't realize back then, is the chain rule of this function will produce the same outcome as the original chain-rule. That is for a potential

$$ D_k(\mathbf{v}) = \lambda_k^n f_0^\mu (|\mathbf{u}|), $$

the force is

$$ F_k(\mathbf{v}) = -\nabla D_k(\mathbf{v}) = \lambda_k^n ~ \mu(|\mathbf{u}|) ~ f_1 (|\mathbf{u}|) / |\mathbf{u}| \mathbf{T}_k \mathbf{u}, $$

where $\mathbf{u}=\mathbf{T}_k^{\top} \mathbf{v}$ is the tangential relative velocity.

Hopefully, implementing this should be pretty easy. If not, let me know and I am happy to help in my spare time.