A Generalized Non-local Quasicontinuum Approach for Efficient Modeling of Architected Truss-based Lattice Structures

Abstract

To mitigate the substantial computational costs associated with modeling the mechanical behavior of large-scale architected lattice structures, this work introduces a concurrent multiscale approach: the Generalized Non-local Quasicontinuum (GNQC) method. GNQC generalizes the classical nonlocal Quasicontinuum framework by eliminating the assumption of affine or high-order deformation patterns for accurate energy sampling in coarse-grained regions and by ensuring consistency with general finite element shape functions used for coarse-graining. The introduced GNQC method offers three key features: (1) a constitutive-model-consistent framework that employs the same lattice constitutive relationship in both the locally full-resolution region and the coarse-grained domain, similar to existing nonlocal QC approaches; (2) a shape-function consistent energy sampling mechanism that aligns with the interpolation order of the generally employed shape functions, differing significantly from existing Quasicontinuum works and substantially reducing computational costs; and (3) consistent interfacial compatibility, which enables seamless energy and force transfer across interfaces between regions of different resolutions without cumbersome interfacial treatments. The performance of GNQC is validated through a series of numerical test cases, including tension, clamped bending, three-point bending, and crack propagation problems, that demonstrate good accuracy. Additionally, the error analysis and convergence behavior of GNQC are investigated.