Persistent homology-driven optimization of effective relative density range for triply periodic minimal surfaces

Triply periodic minimal surfaces (TPMSs) play a vital role in the design of porous structures, with applications in bone tissue engineering, chemical engineering, and the creation of lightweight models. However, fabrication of TPMSs via additive manufacturing is feasible only within a specific range of relative densities, termed the effective relative density range (EDR), outside of which TPMSs exhibit unmanufacturable features. In this study, the persistent homology is applied to theoretically calculate and extend the EDRs of TPMSs. To expand the design domain of TPMSs while maintaining their symmetry, TPMSs are transformed into a new representation based on B-spline functions and a series of operators, which is referred to as Generalized-TPMSs. Through topological analysis, the Generalized-TPMSs are further optimized to expand their EDRs while maintaining a high degree of similarity to the original TPMSs. The optimized Generalized-TPMSs are referred to as EDR-Variant TPMS (EDR-VTPMS). Experimental validation confirms the effectiveness of the approach in extending the EDRs of TPMSs. Moreover, EDR-VTPMS exhibits enhanced performance in heterogeneous and high-stiffness model design compared to their conventional counterparts. The EDR-VTPMSs with increased EDRs hold promise for replacing traditional TPMSs in applications that require porous structures with varying densities.