Solitary.waves on nonlinear elastic rods. I

On the Geometric Flow of Kirchhoff Elastic Rods

Recently, rod theory has been applied to the mathematical modeling of bacterial fibers and biopolymers (e.g. DNA), to study their mechanical properties and shapes (e.g. supercoiling). In static rod theory, an elastic rod in equilibrium is the critical point of an elastic energy. This induces a natural question of how to find elasticae. In this paper, we focus on how to find the critical points ...

Inextensible elastic rods with torsional friction based on Lagrange multipliers

Elastic rods are thin flexible objects typically undergoing large non-linear deformations that cannot be modeled with linear methods. They are used in a number of research fields, e. g., to represent hair or ropes in animations, or catheters or needles in medical simulations. In this paper, we propose a deformation model for inextensible elastic rods. The method of Lagrange multipliers is emplo...

Direct Position-Based Solver for Stiff Rods

In this paper, we present a novel direct solver for the efficient simulation of stiff, inextensible elastic rods within the PositionBased Dynamics (PBD) framework. It is based on the XPBD algorithm, which extends PBD to simulate elastic objects with physically meaningful material parameters. XPBD approximates an implicit Euler integration and solves the system of nonlinear equations using a non...

F Ur Mathematik in Den Naturwissenschaften Leipzig Global Injectivity and Topological Constraints for Spatial Nonlinearly Elastic Rods Global Injectivity and Topological Constraints for Spatial Nonlinearly Elastic Rods

In this paper we study the local and global injectivity of spatial deformations of shearable nonlinearly elastic rods. We adopt an analytical condition introduced by Ciarlet & Ne cas in nonlinear elasticity to ensure global injectivity in that case. In particular we verify the existence of an energy minimizing equilibrium state without self-penetration which may be also restricted by a rigid ob...

Local Complexity and Global Nonlinear Modes in Large Arrays of Elastic Rods in an Air Cross-Flow