A nonsmooth Newton solver for capturing exact Coulomb friction in fiber assemblies

Abstract

We focus on the challenging problem of simulating thin elastic rods in contact, in the presence of friction. Most previous approaches in computer graphics rely on a linear complementarity formulation for handling contact in a stable way, and approximate Coulombs's friction law for making the problem tractable. In contrast, following the seminal work by Alart and Curnier in contact mechanics, we simultaneously model contact and exact Coulomb friction as a zero finding problem of a nonsmooth function. A semi-implicit time-stepping scheme is then employed to discretize the dynamics of rods constrained by frictional contact: this leads to a set of linear equations subject to an equality constraint involving a non-differentiable function. To solve this one-step problem we introduce a simple and practical nonsmooth Newton algorithm, which proves to be reasonably efficient and robust for systems that are not over-constrained. We show that our method is able to finely capture the subtle effects that occur when thin elastic rods with various geometries enter into contact, such as stick-slip instabilities in free configurations, entangling curls, resting contacts in braid-like structures, or the formation of tight knots under large constraints. Our method can be viewed as a first step towards the accurate modeling of dynamic fibrous materials.

Contact-friction modeling within elastic beam assemblies: an application to knot tightening

“…[18,19]), trying to understand local phenomena occurring in polymer chains, and particularly in DNA, or in the domain of computer graphics to improve the rendering of hairs or ropes (e.g. [2][3][4]20]). Accompanying the research in these two areas, significant developments have been achieved in the field of continuum mechanics to model self-contact and instabilities of elastic rods.…”

A GPU-accelerated finite element solver for simulation of soft-body deformation

“…kaufman [13] introduced a non-smooth contact model based the simulation of rigid bodies. Bertails [14] introduced a method to compute self-contacts with the presence of the friction. Daviet [15] introduced a robust iterative solver to compute the friction effect.…”

A hybrid iterative solver for robustly capturing coulomb friction in hair dynamics

“…Inspired by the works performed for years in the simulation of granular materials by the computational mechanics community [Alart and Curnier 1991;Moreau 1994;Jourdan et al 1998], Bertails et al [2011] recently applied a nonsmooth Newton solver based on the Alart-Curnier formulation for resolving contact with exact Coulomb friction in fiber assemblies. Their analysis of convergence shows that the solver works well for systems with a limited number of contacts, but often fails to converge in the case of over-constrained systems such as densely packed fibers.…”

“…Finally, results are presented and validated in Section 7 before concluding. In this section we mainly follow the concepts and notation introduced in [Bertails-Descoubes et al 2011] to formulate our Coulomb friction problem. We assume that one contact always occurs between exactly two bodies, and that the surface of contacting objects is sufficiently smooth so that we can define the contact normal e, from which we build a local basis (see Figure 3).…”