A novel surrogate model for optimizing lattice for desired force-displacement response

Abstract

Optimizing lattice structures for energy absorption and load-bearing applications necessitates accurately capturing their nonlinear mechanical response under large deformation. However, traditional nonlinear finite element analysis (NL-FEA) can often fail, particularly at higher compression, which creates numerical gaps in the design space, hindering gradient-based optimization algorithms, ultimately resulting in suboptimal designs. We propose here a neural network (NN) surrogate model that is trained on data generated using Abaqus, a commercial FEA solver. A unique feature of the model is that it exploits both fully and partially successful NL-FEA simulations. This significantly improves the surrogate model’s accuracy and predictive coverage across the design space. The resulting model enables efficient, gradient-driven optimization of lattice structures to match a desired force-displacement response. By replacing expensive NL-FEA evaluations, the surrogate model substantially reduces computational cost while maintaining a coefficient of determination (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R^2$$\end{document}) of 0.98 in prediction. The effectiveness and versatility of this framework are demonstrated by successfully optimizing \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3 \times 3$$\end{document} lattice structures under 40% compression, with the lattice radii as design variables.