Finite element modeling of the free boundary effect on gyroid additively manufactured samples

Elizabeth Mathey, Amanda Heimbrook, R. D. Carpenter, Cambre N. Kelly and Ken Gall

Computer Methods in Biomechanics and Biomedical Engineering, 2025, vol. 28, issue 9, 1477-1488

Abstract: There is a significant need for models that can capture the mechanical behavior of complex porous lattice architectures produced by 3D printing. The free boundary effect is an experimentally observed behavior of lattice architectures including the gyroid triply periodic minimal surface where the number of unit cell repeats has been shown to influence the mechanical performance of the lattice. The purpose of this study is to use finite element modeling to investigate how architecture porosity, unit cell size, and sample size dictate mechanical behavior. Samples with varying porosity and increasing number of unit cells (relative to sample size) were modeled under an axial compressive load to determine the effective modulus. The finite element model captured the free boundary effect and captured experimental trends in the structure’s modulus. The findings of this study show that samples with higher porosity are more susceptible to the impact of the free boundary effect and in some samples, the modulus can be 20% smaller in samples with smaller numbers of unit cell repeats within a given sample boundary. The outcomes from this study provide a deeper understanding of the gyroid structure and the implications of design choices including porosity, unit cell size, and overall sample size.

Date: 2025
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DOI: 10.1080/10255842.2024.2326929

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