TRIPLY PERIODIC MINIMAL SURFACES STRUCTURES IN ENERGY ABSORPTION: A REVIEW OF GEOMETRIC TOPOLOGIES, MANUFACTURING CONSTRAINTS, AND FUTURE SMART MATERIALS

Triply Periodic Minimal Surfaces (TPMS) have emerged as a pivotal class of cellular materials, reshaping lightweight structural design and functional integration in the context of Industry 4.0. This review provides a critical analysis of sheet-based TPMS architectures, benchmarking their performance against conventional strut-based lattices and stochastic metal foams across multiple material systems. The coupled effects of geometric topology (Gyroid, Diamond, Primitive, I-WP, and Lidinoid), additive manufacturing–induced defects, and dynamic energy absorption mechanisms under complex loading conditions are systematically examined. Particular emphasis is placed on quantifying the manufacturing-to-performance gap, demonstrating how surface roughness and lack-of-fusion porosity substantially degrade fatigue resistance and specific energy absorption through localized stress concentrations. Advanced design strategies, including functionally graded materials, numerical homogenization, and multi-phase architectures, are further discussed. The review concludes by outlining future directions toward multifunctional applications and AI-assisted inverse design, providing design-oriented guidelines for selecting flaw-tolerant TPMS architectures in safety-critical engineering systems.