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

Abstract

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.