  Predicting the mechanics of large structural networks, such as beam-based
architected materials, requires a multiscale computational strategy that
preserves information about the discrete structure while being applicable to
large assemblies of struts. Especially the fracture properties of such beam
lattices necessitate a two-scale modeling strategy, since the fracture
toughness depends on discrete beam failure events, while the application of
remote loads requires large simulation domains. As classical homogenization
techniques fail in the absence of a separation of scales at the crack tip, we
present a concurrent multiscale technique: a fully-nonlocal quasicontinuum (QC)
multi-lattice formulation for beam networks, based on a conforming mesh. Like
the original atomistic QC formulation, we maintain discrete resolution where
needed (such as around a crack tip) while efficiently coarse-graining in the
remaining simulation domain. A key challenge is a suitable model in the
coarse-grained domain, where classical QC uses affine interpolations. This
formulation fails in bending-dominated lattices, as it overconstrains the
lattice by preventing bending without stretching of beams. Therefore, we here
present a beam QC formulation based on mixed-order interpolation in the
coarse-grained region -- combining the efficiency of linear interpolation where
possible with the accuracy advantages of quadratic interpolation where needed.
This results in a powerful computational framework, which, as we demonstrate
through our validation and benchmark examples, overcomes the deficiencies of
previous QC formulations and enables, e.g., the prediction of the fracture
toughness and the diverse nature of stress distributions of stretching- and
bending-dominated beam lattices in two and three dimensions.
