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A Hybrid Iterative Solver for Robustly Capturing Coulomb Friction in Hair Dynamics
Gilles Daviet, Florence Bertails-Descoubes, Laurence Boissieux
Hybrid iterative solver robustly handling Coulomb friction in hair dynamics using a Signorini-Coulomb contact model.
Abstract
Dry friction between hair fibers plays a major role in the collective hair dynamic behavior as it accounts for typical nonsmooth features such as stick-slip instabilities. However, due the challenges posed by the modeling of nonsmooth friction, previous mechanical models for hair either neglect friction or use an approximate smooth friction model, thus losing important visual features. In this paper we present a new generic robust solver for capturing Coulomb friction in large assemblies of tightly packed fibers such as hair. Our method is based on an iterative algorithm where each single contact problem is efficiently and robustly solved by introducing a hybrid strategy that combines a new zero-finding formulation of (exact) Coulomb friction together with an analytical solver as a fail-safe. Our global solver turns out to be very robust and highly scalable as it can handle up to a few thousand densely packed fibers subject to tens of thousands frictional contacts at a reasonable computational cost. It can be conveniently combined to any fiber model with various rest shapes, from smooth to curly. Our results, visually validated against real hair motions, depict typical hair collective effects and greatly enhance the realism of standard hair simulators.
How to read this
- Category
- Method: a friction solver for hair dynamics
- Contributions
- A robust hybrid iterative solver capturing exact Coulomb (Signorini-Coulomb) friction in large assemblies of tightly packed fibers
- Per-contact solving via a new zero-finding formulation of exact Coulomb friction with an analytical solver as a fail-safe
- Scaling to a few thousand densely packed fibers and tens of thousands of frictional contacts at reasonable cost, combinable with various fiber models and rest shapes
- Context
- Targets nonsmooth dry friction (stick-slip) in hair, applicable on top of fiber models such as Discrete Elastic Rods, replacing earlier neglected or smoothed-friction treatments.Builds on: Discrete Elastic Rods
- Correctness
- Results are visually validated against real hair motions and emphasize robustness and scalability; the validation is qualitative/visual rather than quantitative, and cost grows with the very large contact counts the method targets.
- Clarity
- Technically dense; a first pass conveys why nonsmooth Coulomb friction matters, but the contact formulation and hybrid solver need a careful second and likely third pass.
- How to read it
- Read first for the motivation (stick-slip from exact friction) and the hybrid zero-finding plus analytical fail-safe strategy; reserve a deeper pass for the per-contact Signorini-Coulomb math if you implement it.
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