Logo image
Back
Two-scale topology optimization of multiscale structures and materials via deep neural networks for local and global buckling
Journal article   Open access   Peer reviewed

Two-scale topology optimization of multiscale structures and materials via deep neural networks for local and global buckling

Sobhan Honarvar, Nolan Black and Ahmad R. Najafi
Computer methods in applied mechanics and engineering, v 458, 119038
Aug 2026
DOI: https://doi.org/10.1016/j.cma.2026.119038
Featured in Collection :   Drexel's Newest Publications
url
https://doi.org/10.1016/j.cma.2026.119038View
Published, Version of Record (VoR) Open Access via Drexel Libraries Read and Publish Program 2026 Open CC BY-NC V4.0

Abstract

Topology optimization Two-scale Buckling strength Stability Lattice microstructure Optimization Topology
Multiscale topology optimization can produce lightweight structures with tailored microarchitectures, yet simultaneously enforcing global (macroscale) buckling and local (microscale) buckling remains computationally prohibitive, especially for richly parameterized unit cells. This paper presents a differentiable, DNN-assisted two-scale buckling topology optimization framework that couples macroscale layout optimization with microscale stability protection in a single gradient-based loop. A deep neural network surrogate is trained on finite-element homogenization data to predict the homogenized constitutive tensor of parameterized unit cells and, crucially, its sensitivities via backpropagation. This removes the need for interpolation tables and avoids finite-difference gradients that do not scale to high-dimensional microstructure design spaces. The surrogate is embedded in a two-scale formulation that maximizes the macroscale buckling load factor while enforcing a worst-case homogenized microscale buckling load factor to safeguard against local instabilities under arbitrary stress states. Numerical studies demonstrate (i) robust trade-offs between macro–micro stability through the two-scale volume split and weighting, (ii) practical optimization and comparison of microstructures with increased design dimensionality that would be impractical with per-iteration FE homogenization, and (iii) new microstructure-level observations: smooth inclusion-based (ellipse) unit cells can achieve global buckling performance comparable to lattice-based cells while exhibiting a smaller degradation when microscale buckling protection is activated, indicating reduced vulnerability to micro-buckling.

Metrics

2 Record Views

Details

Logo image