Modeling and simulation of electrification delivery in functionalized textiles in electromagnetic fields

This work investigates the deformation of electrified textiles in the presence of an externally supplied magnetic field (BextBext). The electrification is delivered by running current (JJ) through the fibers from an external power source. Of primary interest is to ascertain the resulting electromagnetic forces imposed on the fabric, and the subsequent deformation, due to the terms J×BextJ×Bext and PEPE, where PP is the charge density, EE is the electric field and the current given by J=σ(E+v×Bext)J=σ(E+v×Bext), where σσ is the fabric conductivity, and vv is the fabric velocity. As the fabric deforms, the current changes direction and magnitude, due to the fact that it flows through the fabric. The charge density is dictated by Gauss’ law, ∇·D=P∇·D=P, where D=ϵE,ϵD=ϵE,ϵ is the electrical permittivity and DD is the electric field flux. In order to simulate such a system, one must solve a set of coupled equations governing the charge distribution, current flow and system dynamics. The deformation of the fabric, as well as the charge distribution and current flow, are dictated by solving the coupled system of differential equations for the motion of lumped masses, which are coupled through the fiber-segments under the action of electromagnetically-induced forces acting on a reduced order network model. In the work, reduced order models are developed for (a) Gauss’ law (∇·D=P∇·D=P), (b) the conservation of current/charge, ∇·J+∂P∂t=0, and (c) the system dynamics, ∇·T+f=ρdvdt, where TT is the Cauchy stress and ff represents the induced body forces, which are proportional to PE+J×BextPE+J×Bext. A temporally-adaptive, recursive, staggering scheme is developed to solve this strongly coupled system of equations. We also consider the effects of progressive fiber damage/rupture during the deformation process, which leads to changes (reduction) in the electrical conductivity and permittivity throughout the network. Numerical examples are given, as well as extensions to thermal effects, which are induced by the current-induced Joule-heating.