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• Enhanced flexural properties of four point bend (4 PB) beam specimens through relative density gradation and hybridization based on TPMS topologies. • Strategies for gradation and hybridization deduced through stress state in 4 PB beam. • Hybridization and relative density gradation schemes is accomplished based on level-set functions of stretching-dominated TPMS sheet-based lattices. • Numerical results are validated through 4 PB testing on additive manufactured beams. • Enhanced flexural stiffness achieved by combining relative density gradation and hybridization with several different TPMS topologies. Due to the recent boom in digital design for additive manufacturing and 3D printing, there has been a significantly growing interest in latticed structures for light design and improved mechanical properties. However, the focus in the literature has mostly been on compressive mechanical properties of uniformly latticed structures with little emphasis on flexural properties of latticed-beams that are functionally graded and hybridized with different lattice topologies. Therefore, this paper aims to explore the effect of lattice relative density gradation and hybridization on the specific flexural properties of prominent sheet-based triply periodic minimal surfaces (TPMS) cellular four-point loaded beams. First, the effective elastic properties of the cubic porous topologies are evaluated computationally to converge to certain sheet-based TPMS cellular structures capable of providing high flexural properties. Schwartz primitive (P) revealed high stiffness to shear loading, meanwhile, the F-Rhombic Dodecahedron (FRD) showed better resistance to uniaxial loading, and the Diamond (D) showed well-combined uniaxial and shear moduli. The selected four-point bend (4 PB) latticed-beams are functionally graded following a bilinear pattern and hybridized through the span of their length inspired by the shearing force and bending moment diagrams arising in the 4 PB beam, in view of the effective elastic properties of the TPMS topologies. The additively manufactured AlSi10Mg uniform, functionally-graded, and hybridized latticed-beams are tested in four-point bending and the results are compared with the finite element results. Both the experimental and numerical outcomes show good agreement within the elastic-plastic regime. From experimental results, it is found that functional grading and hybridization can considerably enhance the specific flexural modulus of sheet-based TPMS latticed-beams. Also, relative density gradation within the four-point bend specimens proved very essential in deflecting crack growth thereby retarding the final failure, meanwhile hybridization is conveyed to mitigate shear-band failure. Combination of functional gradation and hybridization on the latticed-beams resulted in a significant increase in the specific flexural stiffness. Therefore, this study provides guidelines on how to enhance the flexural properties of lightweight beams through lattice functional grading and hybridization. [Display omitted] [ABSTRACT FROM AUTHOR]