Finite Element Simulation of Dense Wire Packings

TL;DR

This paper introduces a finite element simulation method for modeling the packing and coiling of elastic wires in complex 3D cavities, comparing implicit and explicit integration schemes and exploring packing preferences in ellipsoidal geometries.

Contribution

It develops a novel finite element approach using third order beam elements with advanced integration methods to simulate dense wire packings in non-spherical cavities.

Findings

Implicit and explicit integration methods have different suitability for dense wire packing.

Packings in ellipsoidal cavities are energetically more favorable than in spherical ones.

The simulation captures large rotations and deformations of elastic wires in confined spaces.

Abstract

A finite element program is presented to simulate the process of packing and coiling elastic wires in two- and three-dimensional confining cavities. The wire is represented by third order beam elements and embedded into a corotational formulation to capture the geometric nonlinearity resulting from large rotations and deformations. The hyperbolic equations of motion are integrated in time using two different integration methods from the Newmark family: an implicit iterative Newton-Raphson line search solver, and an explicit predictor-corrector scheme, both with adaptive time stepping. These two approaches reveal fundamentally different suitability for the problem of strongly self-interacting bodies found in densely packed cavities. Generalizing the spherical confinement symmetry investigated in recent studies, the packing of a wire in hard ellipsoidal cavities is simulated in the frictionless elastic limit. Evidence is given that packings in oblate spheroids and scalene ellipsoids are energetically preferred to spheres.