Force–Energy Coordination Response and Size Effect of Gyroid‐Type TPMS Lattices Based on Noniterative Reference Stress Field Mapping

Graded triply periodic minimal surface (TPMS) lattices improve load‐bearing and energy absorption capacity through relative‐density tailoring. However, noniterative mapping of a reference stress field to a continuous relative‐density field remains insufficiently investigated. A noniterative reference stress field mapping method is proposed. A three‐dimensional von Mises equivalent stress field from a single static finite element (FE) analysis of a uniform TPMS lattice (U‐TPMS) is mapped pointwise using a stress–density power‐law scaling relation derived from the stationarity condition for compliance minimization under a mass constraint. After density bounding and global normalization, the field is converted into a Gyroid surface offset parameter field without FE reanalysis or repeated geometric reconstruction. U‐TPMS, linearly graded TPMS (LG‐TPMS), sinusoidally graded TPMS (SG‐TPMS), and stress‐driven graded TPMS (SDG‐TPMS) are compared under the same Gyroid topology and material usage through static FE analysis, quasistatic compression simulations, and experiments. A force–energy coordination framework integrates relative stiffness, relative yield strength margin, and relative energy absorption. SDG‐TPMS reduces maximum displacement by 36.1%, 27.1%, and 12.6% relative to U‐TPMS, LG‐TPMS, and SG‐TPMS, respectively; lowers peak equivalent stress by 48.3% relative to U‐TPMS; and achieves a coordination efficiency index of 1.638, 63.8% higher than U‐TPMS. The load‐bearing advantage persists across three geometric scales.