Fe2 model links beam theory with lattice truss microstructures
An FE2 model for shear-deformable beams considering periodic lattice-like truss mesostructures
Computational Engineering, Finance, and Science
Summary
Some structures use lattice designs made of repeating tiny trusses to be strong but light. This paper presents a new way to analyze these structures by combining a beam-level model with a small truss-level model, connecting the big and small parts. The authors made sure the method gives consistent results regardless of how big a sample you analyze. They tested it with different shapes and found it matches detailed models well, even when accounting for bending and shearing.
What this means in practice
- •For structural engineers: Analyze slender lattice-based beams efficiently by linking beam models with microscopic truss structures for better design accuracy.
- •For additive manufacturing experts: Predict mechanical responses of 3D-printed lattice components accurately using a combined multiscale beam-truss modeling framework.
Authors
Julian Ochs, Jens Wackerfuß
Abstract
The increasing use of lattice-like architectures in load-bearing members, facilitated by advances in additive manufacturing, calls for efficient multiscale approaches to their structural analysis. For slender lattice-like structures, beam models provide a computationally efficient macroscopic representation while retaining the ability to account for the underlying lattice architecture through an homogenization approach. Although finite element squared (FE2) approaches combining beam models at the macroscopic scale with continuum models at the microscopic scale have been established, an FE2 framework combining a beam-based macroscopic model with a truss-based microscopic model of a lattice structure has not yet been reported. To address this gap, an FE2 framework is developed for three-dimensional shear-deformable beams with periodically repeated lattice-like microstructures and periodic displacement boundary conditions. The proposed FE2 framework introduces constraint equations that (a) prevent rigid-body translations and rotations of the representative volume element (RVE) without imposing additional kinematic restrictions and (b) ensure that the homogenized stress resultants and material matrix are independent of the selected RVE length. To mitigate artificial boundary effects arising at the boundaries of the lattice-like RVE, local correction factors are introduced. The framework is assessed through numerical studies of two- and three-dimensional lattice-like structures with different geometries, considering both geometric and material linearity and nonlinearity. The results demonstrate the independence of the homogenized stress resultants and material matrix from the selected RVE length and show good agreement with the corresponding reference models in all investigated cases.