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

机译：电磁场中功能化纺织品带电输送的建模与仿真

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This work investigates the deformation of electrified textiles in the presence of an externally supplied magnetic field (B~(ext)). The electrification is delivered by running current (J) 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 × B~(ext) and PE, where P is the charge density, E is the electric field and the current given by J = σ(E + v × B~(ext)), where σ is the fabric conductivity, and v 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, V • D = V, where D = ∈E,∈ is the electrical permittivity and D 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), (b) the conservation of current/charge, ▽ •J + ((e)p)/((e)t) = 0, and © the system dynamics, ▽ • T +f = P(dv)/(dt) where T is the Cauchy stress and/ represents the induced body forces, which are proportional to PE +J × B~(ext). 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.
机译：这项工作研究了在外部提供磁场（B〜（ext））的情况下带电纺织品的变形。通过从外部电源流过光纤的电流（J）传递电气化。最重要的是要确定施加到织物上的电磁力以及随后的变形，这取决于项J×B〜（ext）和PE，其中P是电荷密度，E是电场，给定电流由J =σ（E + v×B〜（ext）），其中σ是织物电导率，而v是织物速度。当织物变形时，由于电流流过织物，电流会改变方向和大小。电荷密度由高斯定律（V•D = V）决定，其中D =∈E，∈是介电常数，D是电场通量。为了模拟这样的系统，必须解决一组控制电荷分布，电流和系统动力学的耦合方程。织物的变形，以及电荷分布和电流流动，是通过求解集总质量运动的微分方程的耦合系统来决定的，集总质量的运动在电磁感应力的作用下通过纤维段耦合。在降阶网络模型上。在工作中，针对（a）高斯定律（▽•D = P），（b）电流/电荷守恒，▽•J +（（e）p）/（（e）t ）= 0，并且©系统动力学，▽•T + f = P（dv）/（dt），其中T是柯西应力，/表示感应体力，与PE + J×B〜（ext ）。开发了时间自适应，递归，交错方案以解决此强耦合方程组。我们还考虑了变形过程中纤维逐渐损坏/断裂的影响，这会导致整个网络的电导率和介电常数发生变化（降低）。给出了数值示例，以及由电流引起的焦耳加热引起的热效应的扩展。

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