Geometrically exact dynamic splines

Abstract

In this paper, we propose a complete model handling physical simulation of deformable 1D objects. We formulate continuous expressions for stretching, bending and twisting energies. These expressions are mechanically rigorous and geometrically exact. Both elastic and plastic deformations are handled to simulate a wide range of materials. We validate the proposed model on several classical test configurations. The use of geometrical exact energies with dynamic splines provides very accurate results as well as interactive simulation time, which shows the suitability of the proposed model for constrained CAD applications. We illustrate the application potential of the proposed model by describing a virtual system for cable positioning, that can be used to test compatibility between planned fixing clip positions, and mechanical cable properties.

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

“…Third, capturing the typical stick-slip effects, or tangles and knots that often occur in fibrous materials (see Figure 1), requires a realistic, nonsmooth model for friction. Recently, a number of successful models for the dynamics of thin elastic rods (also referred to as "strands") were proposed in the computer graphics (CG) community [Bertails et al 2006;Hadap 2006;Theetten et al 2008;Bergou et al 2008;Selle et al 2008]. In this paper, we focus on the specific problem of the contact and friction response applied to thin elastic rods.…”

Geometrically exact Cosserat rods with Kelvin–Voigt type viscous damping

“…In addition, other model variants for geometrically nonlinear rods or beams exist, like the already mentioned ANCF approach used by Abdel-Nasser and Shabana (2011), or the recent approach of dynamic splines investigated by Theetten et al (2008) and Valentini and Pennestri (2011), where geometrically exact extensible Kirchhoff rods, which require only a single angle variable to account for twisting, are desribed using computer-aided geometrical design functions, very similar to the usage of cubic Hermite splines on the element level as employed by Weiss (2002b).…”

Stable inverse dynamic curves

“…Various discrete models have been proposed in graphics for 3d inextensible rods with bending and twisting elasticity. While many of them rely on maximal coordinates formulations [Spillmann and Teschner 2007;Spillmann and Teschner 2008;Theetten et al 2008;Bergou et al 2008;Selle et al 2008], others prefer to use reduced coordinates models because they offer a compact and intuitive parameterization of the rod [Bertails et al 2006;Hadap 2006;Bertails 2009]. Using a reduced chain of articulated bodies as a rod model, Hadap [2006] was the only one to propose a method for fitting a rod at rest under gravity to a given input curve.…”