NURBS-Based Homogenization of TPMS for Modal Characterization using Abaqus

Abstract In recent years, lightweight and material-efficient cellular structures, such as triply periodic minimal surfaces (TPMS), have garnered increasing attention for advanced engineering applications. This study introduces a novel homogenization approach for TPMS structures, including Gyroid, Primitive, IWP, Diamond, and Neovius, employing Non-Uniform Rational B-Splines (NURBS) for precise geometric representation. Unlike traditional finite element method (FEM) models requiring fine meshes to represent TPMS curvature, NURBS ensures accurate geometric fidelity independent of mesh refinement, eliminating volume fraction inconsistencies. Homogenization is conducted without periodic boundary conditions, utilizing standard boundary conditions across representative volume elements (RVEs) from 1 × 1 × 1 to 4 × 4 × 4 unit cells. Effective material properties are derived and validated in Abaqus by comparing the mechanical response of homogenized TPMS structures to equivalent solid structures, verifying consistent stiffness predictions. The results are compared with previous TPMS homogenization studies, helping to clarify the change in material properties when changing the geometric description method. The NURBS-based approach facilitates efficient computations and enables isogeometric analysis (IGA), offering a versatile framework for analyzing TPMS-based cellular structures in additive manufacturing applications.