Continuous transitions of triply periodic minimal surfaces

Triply periodic minimal surfaces (TPMS) have been extensively studied in functionally graded structures due to their excellent geometric and mechanical properties. However, existing methods often suffer from deformation and distortion due to inadequate TPMS period calculations, consequently compromising the mechanical performance of TPMS structures. In this paper, we investigate the period and phase of TPMS and establish a relationship between the period and cell size. We introduce an optimization method that effectively reduces mean curvature deviations and geometric distortions while enabling localized control of TPMS. Consequently, we minimize distortion in functionally graded TPMS structures. To evaluate the effectiveness of our proposed method, we conduct a comparative analysis with existing TPMS modification methods, both through simulation and physical experiments. Results demonstrate that our structures exhibit reduced distortions, with mean curvature values closer to the standard TPMS. Physical tests indicate that our approach yields greater stiffness and improved energy absorption compared to existing methods for transitioning TPMS period. This offers the additive manufacturing community a novel solution for producing TPMS with controllable period transitions and higher energy absorption.