Parametric reduced order models for graded lattice structures

Graded lattice structures, characterized by smoothly varying mechanical properties, hold significant promise for optimizing material distribution in advanced engineering applications. However, accurately modeling these structures poses substantial computational challenges due to the continuous geometric variations within their unit cells. To address these challenges, this paper introduces a novel Element Reduced Order Model (EROM) that integrates the Matrix Discrete Empirical Interpolation Method (MDEIM) and Discrete Empirical Interpolation Method (DEIM) with polynomial regression to manage geometric parametrization in lattice structures. Unlike traditional reduced order models (ROMs) that require extensive precomputed libraries for each geometric configuration, our approach enables continuous geometric variations through a flexible algebraic formulation, significantly reducing computational costs while preserving high accuracy. The method constructs projection matrices for individual unit cells that can be assembled into global systems, leveraging the repetitive nature of lattice structures. Numerical studies demonstrate that our EROM achieves displacement errors below 1% and von Mises stress prediction errors below 4%, coupled with computational speedups exceeding two orders of magnitude compared to full-order simulations. The proposed method’s modularity and scalability make it particularly suitable for design optimization and real-time simulation of functionally graded lattice structures, with applications spanning aerospace to nuclear engineering. • A parametric element reduced-order model (EROM) enables continuous geometry variation in lattice unit cells. • MDEIM/DEIM with polynomial regression removes the need for large libraries of precomputed ROMs. • Higher-order finite-element shape-function bases allow standard FE assembly of graded lattices. • Benchmarks show > 100× speedups over full-order simulations with < 1% displacement and < 4% von Mises stress error. • Modularity and scalability support design optimization and analysis of lattices too large for direct simulation.