Modeling Scaled 3D-Printed Electronic Mesostructures with Graph Theory

Additive manufacturing of electronic materials could lead to 3D-enhanced energy storage and sensing, but new approaches are needed to predict the electronic properties of these mesoscale structures. In this work, we present a scalable, graph theory-based method for efficiently computing the electronic conductance of complex 3D printed parts without requiring FEA simulations. We experimentally validate this method for SLA-printed 3D lattices from the 10 μm to 1mm scale coated in conductive nanoscale films of metals and conductive ceramics (Al:ZnO, SnO₂, etc.). This computational approach can be extended to various 3D-printed geometries, simply requiring information about the vertices of the design provided by a simple CAD model. These predictions can be integrated into an effective volumetric resistance simultaneously accounting for 3D mesostructure and the bulk material conductivity. This tool allows us to explore the <i>scaling</i> <i>laws</i> linking electrical conductance and mechanical behavior of 3D lattice structures to understand the possibilities for 3D-printing multifunctional electromechanical systems.<br/><br/>Finally, we experimentally demonstrate how these methods can be used to design robust 3D electronic mesostructures exhibiting macroscopic strain tolerance 10X beyond the limits of their nanoscale ceramic constituents. Collectively, these results reveal new opportunities to utilize computationally lightweight methods for simulating and designing 3D-printed electronics. We expect these results can guide the development of advanced manufacturing for 3D devices that simultaneously satisfy structural constraints while allowing for precision electronic design.