Modelling of Anisotropic Electrical Conduction in Layered Structures 3D-Printed with Fused Deposition Modelling

3D-printing conductive structures have recently been receiving increased attention, especially in the field of 3D-printed sensors. However, the printing processes introduce anisotropic electrical properties due to the infill and bonding conditions. Insights into the electrical conduction that results from the anisotropic electrical properties are currently limited. Therefore, this research focuses on analytically modeling the electrical conduction. The electrical properties are described as an electrical network with bulk and contact properties in and between neighbouring printed track elements or traxels. The model studies both meandering and open-ended traxels through the application of the corresponding boundary conditions. The model equations are solved as an eigenvalue problem, yielding the voltage, current density, and power dissipation density for every position in every traxel. A simplified analytical example and Finite Element Method simulations verify the model, which depict good correspondence. The main errors found are due to the limitations of the model with regards to 2D-conduction in traxels and neglecting the resistance of meandering ends. Three dimensionless numbers are introduced for the verification and analysis: the anisotropy ratio, the aspect ratio, and the number of traxels. Conductive behavior between completely isotropic and completely anisotropic can be modeled, depending on the dimensionless properties. Furthermore, this model can be used to explain the properties of certain 3D-printed sensor structures, like constriction-resistive strain sensors.