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.

翻译：预测大型结构网络（如基于梁的架构材料）的力学行为，需要一种多尺度计算策略，既能保留离散结构信息，又适用于大规模杆件装配。特别是此类梁格构的断裂特性需要双尺度建模策略，因为断裂韧性取决于离散梁的失效事件，而远程载荷施加需要大规模模拟域。由于经典均匀化方法在裂纹尖端缺乏尺度分离时失效，我们提出一种并发多尺度技术：基于保形网格的梁网络全非局部拟连续介质（QC）多格点公式。与原始原子QC公式类似，我们在需要处（如裂纹尖端周围）保持离散分辨率，同时在其余模拟域中高效粗粒化。关键挑战在于粗粒化域中的合适模型——经典QC采用仿射插值。该公式在弯曲主导格构中失效，因为它通过阻止梁弯曲而不拉伸过度约束格构。因此，我们提出基于粗粒化区域混合阶插值的梁QC公式——在可能处结合线性插值的效率与需要处二次插值的精度优势。这形成了强大的计算框架，通过验证与基准算例表明，该框架克服了先前QC公式的缺陷，能够预测二维与三维拉伸主导和弯曲主导梁格构的断裂韧性及应力分布的多样性。