A singularity free approach for Kirchhoff rods having uniformly distributed electrostatic charge

We present a singularity free formulation and its efficient numerical implementation for the spatial deformation of Kirchhoff rods having uniformly distributed electrostatic charge. Due to the presence of continuously distributed charge, the governing equations of the Kirchhoff rod become a system of integro-differential equations which is singular at every arc-length. We show that this singularity is of removable type which, ones removed, makes the system well defined everywhere. No cutoff length or mollifier is used to remove this singularity. An efficient finite difference scheme is presented for the numerical solution of this singularity free system of equations. We show that the presented numerical scheme turns out to be computationally efficient compared to an alternate approach in which the uniformly distributed charge is modeled by placing equivalent lumped charge at discrete locations along the rod. The scheme is demonstrated through an example problem of supercoiling in a charged elastic ring when twist is inserted in it.

The article will soon appear in Computer Methods in Applied Mechanics and Engineering and the same can also be accessed at the following link: https://www.researchgate.net/publication/341232833_A_singularity_free_approach_for_Kirchhoff_rods_having_uniformly_distributed_electrostatic_charge