Numerical investigation on the static and modal characterization of functionally graded Triply Periodic Minimal Surface (FG-TPMS) structures: From homogenization to explicit modelling

This study presents a finite element framework to analyse the static bending, stress-strain fields, and dynamic eigenfrequencies of functionally graded Triply Periodic Minimal Surface (FG-TPMS) beam structures. Effective material properties of a Gyroid unit cell are extracted via micromechanical homogenization and assigned to a macro-scale solid continuum beam following a power-law distribution. To capture localized microstructural responses, an explicit Gyroid TPMS beam modelled in NX-CAD and a hybrid sandwich configuration with dense Alumina face sheets are evaluated. Numerical investigations assess varying power-law indices (p) and beam thicknesses (h) under cantilever and clamped boundary conditions subjected to transverse loading. The eigenfrequency analysis reveals an orthogonal mode pairing phenomenon in square cross-sections, in which adjacent bending modes exhibit nearly identical natural frequencies. The sandwich TPMS beam exhibits superior structural performance, achieving the lowest overall deformation, enhanced global rigidity, and significantly reduced internal stress and strain concentrations compared to the explicit core alone. These results provide useful design guidelines for developing cellular structures with high stiffness and light weight for various modern engineering applications. In particular, the suggested hybrid FG-TPMS sandwich configuration has enormous potential for application in aerospace structural elements, biomedical implants, and automotive crash absorption parts.