PSI - Issue 80

Thi Ngoc Diep Tran et al. / Procedia Structural Integrity 80 (2026) 378–391 Thi Ngoc Diep Tran/ Structural Integrity Procedia 00 (2019) 000–000

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1. Introduction Characterized by their high void volume fraction, porous structures offer several advantageous properties such as low weight, efficient thermal management, and high energy absorbing capacities for the intended applications (Mines et al. (2013), Fuller et al. (2005), Fan et al. (2021)). However, conventional porous structures like two-dimensional honeycombs or three-dimensional foams present inherent limitations in controlling pore characteristics and performance. Lattice structures, constructed from a network of struts, can also introduce localized imperfections at the nodal points, leading to stress concentration and decreased overall stiffness (Nguyen et al. (2016)). Triply periodic minimal surfaces are characterized by zero mean curvature, where their geometries can be completely expressed via algebraic equations (Chen et al. (2009), Torquato and Donev (2004)). Therefore, the structure’s design can be conveniently controlled by adjusting the equation parameters. Primitive structure was the first TPMS to be studied, described by Schwarz in 1865 (Schwarz (1890)), followed by Neovius by Edvard Neovius, a Finnish mathematician, in 1883 (Neovius, E. R. (1883)). In 1970, Schoen discovered the Gyroid and IWP surface (Schoen, A. H. (1970)). The fundamental unit cell possesses a well-defined geometry periodically replicated in three dimensions and can significantly influence the structural performance (Vigliotti et al. (2014), Khaderi et al. (2014)). Periodic TPMS can be fabricated as uniform structures where all the unit cells are the same size throughout. However, the uniform structural design may exhibit limitations under complex loading conditions. By varying cellular porosity and wall thickness, graded porous structures are found widely in nature and demonstrate outstanding mechanical efficiency while maintaining their lightweight (Qureshi et al. (2022), Yang et al. (2022), Novak et al. (2022)). Despite the varying pore sizes and distributions, the internal surfaces of graded TPMS structures remain smooth and continuous (Yu et al. (2019)). This study examined the geometric characteristics of individual TPMS unit cells as a basis for understanding the behavior of large-scale periodic structures. Due to the complex topologies, most current TPMS-based structures are fabricated using additive manufacturing (AM) techniques. Selective laser melting (SLM) is one of the AM processes that uses a high-power laser to melt and fuse metal powders layer by layer to create three-dimensional structures (C. Yan et al. (2012), X. Fan et al. (2021b)). However, achieving precise control over the gradient of porosity within the graded structure can be challenging since the surface roughness is increased by bonded particles and semi-melted powders (Feng et al. (2022)). Similar to the SLM method, Selective laser sintering (SLS) utilizes laser for fabricating structures layer by layer. Instead of melting the powder, the SLS technique sinters it, allowing for use in more materials such as metals, ceramics, and plastics (Ambekar et al. (2021), Elmadih et al. (2019)). Other AM techniques such as Stereo lithography appearance (SLA) and Fused deposition modeling (FDM) are widely used for 3D-printed TPMS due to their higher manufacturing precision and effective supplementary for required special materials, respectively (Yu et al. (2019), L. Zhang et al. (2020), Alizadeh-Osgouei et al. (2021), Khan et al. (2019), Plocher and Panesar (2020)). However, all these AM techniques still encounter several fabrication imperfections due to process limitations and geometric design, especially with complex morphologies like TPMS. For example, overhang issues arise when surfaces are inclined below a certain angle, leading to poor support by the underlying layers, which causes geometric inaccuracies and reduced surface quality (Yang et al. (2019), Maconachie et al. (2020), Maconachie et al. (2019)). For a cylindrical or rectangular specimen, it is uncomplicated to determine the cross-sectional area. Several studies on axial compression of thin-walled tubes with different cross-sectional shapes have been conducted by Z. Fan et al. (2013), Yamashita et al. (2003), Karagiozova et al. (2005). It has been shown that increasing the number of the cross sectional shape’s corners to an appropriate value can lead to higher compressive strength and improve energy absorption (Z. Fan et al. (2013)). However, the shapes studied were limited to circles and polygons, and the geometry of each cross-section remained the same along the whole structure. TPMS-based porous architectures possess a symmetrical geometry that varies across their cross-sections. The shape of each TPMS unit cell’s cross-section is unique and irregular, thus, its area must be numerically computed. Zhang et al. (2020) have investigated how the specimen’s cross-sectional shape impacts the damage and failure behavior of rock-like materials under uniaxial compression. Their findings indicated that the cross-sectional geometry influenced the distribution of contact damage and determined the macroscopic form of failure. In this paper, the failure behavior of four typical TPMS unit cells (Primitive, Gyroid, Neovius, and IWP) under compression was studied using FE analysis considering each structure’s morphology. The material used in this investigation is alumina ceramic (aluminum oxide � � ), which is widely used for its high strength, hardness and