Graph-theoretical description and continuity problems for stress propagation through complex strut lattices

Interconnected networks of rigid struts are critical for the design of lightweight, load-bearing structures. However, modeling stress distribution in them is difficult due to complex organizational patterns and collective effects. Leveraging visualization of local elastic deformations by birefringence imaging, we investigate how graph theory (GT) provides a framework for stress prediction. We investigate the role that geometric features play in the collective mechanical behavior of anisotropic networks, which also addresses the fundamental problem of applying discrete mathematics to physical structures. We show that modified centrality parameters combining lattice topology with structural metrics describing geometry more accurately predict local stress, as validated through finite element modeling. Further improvements are made by incorporating boundary conditions into the centrality definition, in a manner that simultaneously simplifies the computational cost demonstrating capabilities of GT for predictions of mechanical properties that can be extended to various types of complex soft matter.