Publications

We examine several conducting spheres moving through a magnetic field gradient. An analytical approximation is derived and an experiment is conducted to verify the analytical solution. The experiment is simulated as well to produce a numerical result. Both the low and high magnetic Reynolds number regimes are studied. Deformation of the sphere is noted in the high Reynolds number case. It is suggested that this deformation effect could be useful for designing or enhancing present protection systems against space debris.

The modeling of solids is most naturally placed within a Lagrangian framework because it requires constitutive models which depend on knowledge of the original material orientations and subsequent deformations. Detailed kinematic information is needed to ensure material frame indifference which is captured through the deformation gradient F. Such information can be tracked easily in a Lagrangian code. Unfortunately, not all problems can be easily modeled using Lagrangian concepts due to severe distortions in the underlying motion. Either a Lagrangian/Eulerian or a pure Eulerian modeling framework must be introduced. We discuss and contrast several Lagrangian/Eulerian approaches for keeping track of the details of material kinematics.