Using Eigenvector Centrality to Predict the Mechanical Properties of Structured Materials

We seek to link mesoscale organization to macroscopic mechanical response using a combination of 3D printing, mechanical testing, and theory. Our ultimate objectives are to provide a simple reduced-order model for predicting mechanical parameters for tailored structures and to better inform engineering models. Here, we report our efforts toward accomplishing these objectives by examining a set of lattice structures with controlled strut deletion. Octet lattice structures overlaying body-centered cubic unit cells were 3D-printed at two different length scales, using either the two-photon polymerization (2PP) method or the vat photopolymerization method with commercially available acrylate-based resins. A set of 10 lattice structures were printed in which struts were randomly removed to give a fraction of deleted struts up to 0.35, and each sample was compression-tested to obtain the Young's modulus. We applied graph theoretical tools typically used in complex network theory to analyze this set of samples. In particular, we propose that the bulk mechanical properties are dictated by a network free energy calculated from the principle eigenvector of the adjacency matrix encoding the mesoscopic structure.