A Generalized Summation Rule‐Based Nonlocal Quasicontinuum Approach (GSR‐QC) for Efficient Modeling of Architected Lattice Structures

To address the substantial computational cost in modeling the mechanical behavior of large‐scale architected lattice structures, this work introduces a concurrent multiscale framework: the generalized summation rule‐based nonlocal quasicontinuum (GSR‐QC) method. The core innovation is a generalized summation rule that enables accurate coarse‐graining consistent with general finite element shape functions. While a few existing approaches have explored summation rules for higher‐order interpolation, such efforts remain limited and are typically tailored to specific element types or applications. In contrast, the proposed framework provides a unified and systematic approach that ensures compatibility with general shape functions, significantly enhancing the flexibility and applicability of nonlocal quasicontinuum methods. The GSR‐QC method features: (1) constitutive‐model consistency, employing the same discrete lattice model in both fully resolved and coarse‐grained regions; (2) shape‐function‐consistent energy sampling, aligned rigorously with the interpolation order of general finite elements; and (3) interfacial compatibility, enabling seamless energy and force transfer across regions of differing resolutions without additional interface treatment. The performance of GSR‐QC is validated using bilinear quadrilateral and quadratic triangular elements across benchmark problems—including uniaxial tension, clamped bending, three‐point bending, and crack propagation in truss‐based lattice structures—demonstrating good accuracy. Additionally, the error analysis and convergence behavior of GSR‐QC are investigated.