Cosserat nets are networks of elastic rods that are linked by elastic
joints. They allow to represent a large variety of objects such as
elastic rings, coarse nets, or truss structures. In this paper, we
propose a novel approach to model and dynamically simulate such Cosserat
nets. We first derive the static equilibrium of the elastic rod model
that supports both bending and twisting deformation modes. We further
propose a dynamic model that allows
Jonas Spillmann, Matthias Teschner, "Cosserat Nets",
[divx] Movie (23MB)
Figure 1: Cosserat nets are non-manifold branched structures whose struts are modelled as CORDE rods, with elastic joints. They can be used to represent a large variety of different objects, such as rings, nets and trusses.
Figure 2: Comparison of CORDE (blue rod) to an accurate mechanical reference deformation model (red rod). In this experiment, both rods are subject to torsional deformation. As long as the centerlines stay straight, the rods are in an unstable equilibrium (left). When the centerlines are perturbed, then the rods start to bend in order to balance stretching, bending and torsional deformation, until a stable equilibrium is found (right).
An Adaptive Contact Model for the Robust Simulation of Knots
In this paper, we present an adaptive model for dynamically deforming
hyper-elastic rods. In contrast to existing approaches, adaptively
introduced control points are not governed by geometric subdivision
rules. Instead, their states are determined by employing a non-linear
energy-minimization approach. Since valid control points are computed
instantaneously, post-stabilization schemes are avoided and the
stability of the dynamic simulation is improved.
Jonas Spillmann, Matthias Teschner, "An Adaptive Contact
Model for the Robust Simulation of Knots",
[divx] Movie (23MB)
[Another DivX movie sequence (8MB) illustrating a massive stacking of rods]
CORDE - Cosserat Rod Elements for the Dynamic Simulation of One-Dimensional Elastic Objects
Simulating one-dimensional elastic objects such as threads, ropes or
hair strands is a difficult problem, especially if material torsion is
considered. In this paper, we present CORDE (french 'rope'), a novel
deformation model for the dynamic interactive simulation of elastic rods
with torsion. We derive continuous energies for a dynamically deforming
rod based on the Cosserat theory of elastic rods. We then discretize the
rod and compute energies per element by employing finite element methods.
Thus, the global dynamic behavior is independent of the discretization.
The dynamic evolution of the
J. Spillmann, M. Teschner, "CORDE: Cosserat Rod Elements for the
Dynamic Simulation of One-Dimensional Elastic Objects,"
[divx] Movie (25MB)
Figure 1: Dynamic looping phenomenon of a rod under torsional strain: A rod is spanned between two anchors, and its ends are clamped. A torque transducer on the left varies the end-to-end rotation of the rod. We observe a bifurcation sequence that results in a looping with an increasing number of self-contacts. Bottom: Comparison to a real rope under torsional strain. [DivX movie sequence (2 MB)]
Figure 2: Interactive simulation of threads. The user can freely interact with the thread. Oscillations are minimized by modeling internal friction. A robust collision handling enables the simulation of difficult collision and self-collision configurations. Threads with intrinsic twist and bend are also supported. [Torsion: DivX movie (4.5 MB)] [Intrinsic twist: DivX movie (4.3 MB)] [Knot-tying: DivX movie (8 MB)]